The Database of Integer Sequences, Part 1
Part of the On-Line Encyclopedia of Integer Sequences
This is a section of the main database for the On-Line Encyclopedia of Integer Sequences.
For more information see the following pages:
( www.research.att.com/~njas/sequences/ then )
Seis.html: Welcome
index.html: Lookup
indexfr.html: Francais
demo1.html: Demos
Sindx.html: Index
WebCam.html: WebCam
Submit.html: Contribute new sequence or comment
eishelp1.html: Internal format
eishelp2.html: Beautified format
transforms.html: Transforms
Spuzzle.html: Puzzles
Shot.html: Hot
classic.html: Classics
ol.html: Superseeker
JIS/index.html: Journal of Integer Sequences
pages.html: More pages
Maintained by: N. J. A. Sloane (njas@research.att.com),
home page: www.research.att.com/~njas/
(start)
%I A016381
%S A016381 1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,
%T A016381 0,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,
%U A016381 0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1
%V A016381 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,
%W A016381 0,0,1,-1,0,0,1,-1,0,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,0,1,-1,0,
%X A016381 0,1,-1,0,1,-1,0,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,0,1,-1,0,1
%N A016381 319th cyclotomic polynomial.
%Y A016381 Sequence in context: A016413 A016403 A016387 this_sequence A016356 A016405 A016351
%Y A016381 Adjacent sequences: A016378 A016379 A016380 this_sequence A016382 A016383 A016384
%K A016381 sign,fini
%O A016381 0,1
%A A016381 njas
%I A016356
%S A016356 1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0,
%T A016356 0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,
%U A016356 0,1,1,1,1,0,1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,1,1,0,1,1,1
%V A016356 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,1,-1,0,1,-1,0,0,0,
%W A016356 0,0,0,1,-1,0,1,-1,0,0,0,1,-1,0,1,-1,0,1,-1,0,0,0,1,-1,0,1,-1,
%X A016356 0,1,-1,1,-1,0,1,-1,0,1,-1,0,1,-1,1,-1,0,1,-1,0,1,-1,1,0,-1,1,-1
%N A016356 209th cyclotomic polynomial.
%Y A016356 Sequence in context: A016403 A016387 A016381 this_sequence A016405 A016351 A016394
%Y A016356 Adjacent sequences: A016353 A016354 A016355 this_sequence A016357 A016358 A016359
%K A016356 sign,fini
%O A016356 0,1
%A A016356 njas
%I A016405
%S A016405 1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0,
%T A016405 0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,
%U A016405 0,1,1,1,1,0,1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,1,1,0,1,1,1
%V A016405 1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,-1,-1,0,1,1,0,0,0,
%W A016405 0,0,0,1,1,0,-1,-1,0,0,0,1,1,0,-1,-1,0,1,1,0,0,0,-1,-1,0,1,1,
%X A016405 0,-1,-1,-1,-1,0,1,1,0,-1,-1,0,1,1,1,1,0,-1,-1,0,1,1,1,0,-1,-1,-1
%N A016405 418th cyclotomic polynomial.
%Y A016405 Sequence in context: A016387 A016381 A016356 this_sequence A016351 A016394 A016335
%Y A016405 Adjacent sequences: A016402 A016403 A016404 this_sequence A016406 A016407 A016408
%K A016405 sign,fini
%O A016405 0,1
%A A016405 njas
%I A016351
%S A016351 1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,0,
%T A016351 0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,
%U A016351 0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1
%V A016351 1,-1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,1,-1,0,0,0,1,-1,0,0,0,
%W A016351 0,1,-1,0,0,0,1,0,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,0,1,0,-1,0,
%X A016351 0,1,0,-1,0,0,0,1,0,-1,0,0,1,0,0,-1,0,0,1,0,-1,0,0,1,0,0,-1
%N A016351 187th cyclotomic polynomial.
%Y A016351 Sequence in context: A016381 A016356 A016405 this_sequence A016394 A016335 A016373
%Y A016351 Adjacent sequences: A016348 A016349 A016350 this_sequence A016352 A016353 A016354
%K A016351 sign,fini
%O A016351 0,1
%A A016351 njas
%I A016394
%S A016394 1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,0,
%T A016394 0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0,
%U A016394 0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1
%V A016394 1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,-1,-1,0,0,0,1,1,0,0,0,
%W A016394 0,1,1,0,0,0,-1,0,1,0,0,0,-1,-1,0,0,0,1,0,-1,0,0,0,1,0,-1,0,
%X A016394 0,-1,0,1,0,0,0,-1,0,1,0,0,1,0,0,1,0,0,1,0,-1,0,0,-1,0,0,-1
%N A016394 374th cyclotomic polynomial.
%Y A016394 Sequence in context: A016356 A016405 A016351 this_sequence A016335 A016373 A010057
%Y A016394 Adjacent sequences: A016391 A016392 A016393 this_sequence A016395 A016396 A016397
%K A016394 sign,fini
%O A016394 0,1
%A A016394 njas
%I A016335
%S A016335 1,1,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,
%T A016335 1,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,
%U A016335 0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1
%V A016335 1,-1,0,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,1,-1,1,-1,1,
%W A016335 -1,0,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,1,-1,1,-1,1,-1,1,-1,1,-1,
%X A016335 0,1,-1,1,-1,1,-1,1,-1,1,-1,1,0,-1,1,-1,1,-1,1,-1,1,-1,1,0,0,0,-1
%N A016335 143rd cyclotomic polynomial.
%Y A016335 Sequence in context: A016405 A016351 A016394 this_sequence A016373 A010057 A060396
%Y A016335 Adjacent sequences: A016332 A016333 A016334 this_sequence A016336 A016337 A016338
%K A016335 sign,fini
%O A016335 0,1
%A A016335 njas
%I A016373
%S A016373 1,1,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,
%T A016373 1,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,
%U A016373 0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1
%V A016373 1,1,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,1,1,1,1,1,
%W A016373 1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,1,1,1,1,1,1,1,1,1,1,
%X A016373 0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,-1
%N A016373 286th cyclotomic polynomial.
%Y A016373 Sequence in context: A016351 A016394 A016335 this_sequence A010057 A060396 A016355
%Y A016373 Adjacent sequences: A016370 A016371 A016372 this_sequence A016374 A016375 A016376
%K A016373 sign,fini
%O A016373 0,1
%A A016373 njas
%I A010057
%S A010057 1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A010057 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A010057 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A010057 1 if n is a cube else 0.
%C A010057 Multiplicative with a(p^e) = 1 if 3 divides e, 0 otherwise. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 09, 2005.
%F A010057 Dirichlet generating function: zeta(3s). - Franklin T. Adams-Watters, Sep 11 2005.
%Y A010057 Cf. A000578.
%Y A010057 Sequence in context: A016394 A016335 A016373 this_sequence A060396 A016355 A016402
%Y A010057 Adjacent sequences: A010054 A010055 A010056 this_sequence A010058 A010059 A010060
%K A010057 nonn,mult
%O A010057 0,1
%A A010057 njas
%I A060396
%S A060396 1,1,0,0,0,0,0,1,0,0,0,0,0,1,0
%N A060396 Values of k associated with A060392.
%H A060396 C. Rivera, www.primepuzzles.net, Conjecture 17
%Y A060396 Sequence in context: A016335 A016373 A010057 this_sequence A016355 A016402 A016377
%Y A060396 Adjacent sequences: A060393 A060394 A060395 this_sequence A060397 A060398 A060399
%K A060396 nonn,easy,more
%O A060396 0,1
%A A060396 njas, Apr 04 2001
%I A016355
%S A016355 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016355 0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,
%U A016355 0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1
%V A016355 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016355 0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,
%X A016355 0,0,1,0,0,-1,0,0,0,1,0,0,-1,0,0,0,1,0,0,-1,0,0,0,1,0,0,-1
%N A016355 203rd cyclotomic polynomial.
%Y A016355 Sequence in context: A016373 A010057 A060396 this_sequence A016402 A016377 A016425
%Y A016355 Adjacent sequences: A016352 A016353 A016354 this_sequence A016356 A016357 A016358
%K A016355 sign,fini
%O A016355 0,1
%A A016355 njas
%I A016402
%S A016402 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016402 0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,
%U A016402 0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1
%V A016402 1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,
%W A016402 0,1,0,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,0,-1,0,1,0,0,
%X A016402 0,0,1,0,0,1,0,0,0,-1,0,0,-1,0,0,0,1,0,0,1,0,0,0,-1,0,0,-1
%N A016402 406th cyclotomic polynomial.
%Y A016402 Sequence in context: A010057 A060396 A016355 this_sequence A016377 A016425 A014016
%Y A016402 Adjacent sequences: A016399 A016400 A016401 this_sequence A016403 A016404 A016405
%K A016402 sign,fini
%O A016402 0,1
%A A016402 njas
%I A016377
%S A016377 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016377 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,
%U A016377 0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0
%V A016377 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016377 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,
%X A016377 0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0
%N A016377 301st cyclotomic polynomial.
%Y A016377 Sequence in context: A060396 A016355 A016402 this_sequence A016425 A014016 A014023
%Y A016377 Adjacent sequences: A016374 A016375 A016376 this_sequence A016378 A016379 A016380
%K A016377 sign,fini
%O A016377 0,1
%A A016377 njas
%I A016425
%S A016425 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016425 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A016425 0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0
%V A016425 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016425 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,
%X A016425 0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0
%N A016425 497th cyclotomic polynomial.
%Y A016425 Sequence in context: A016355 A016402 A016377 this_sequence A014016 A014023 A016428
%Y A016425 Adjacent sequences: A016422 A016423 A016424 this_sequence A016426 A016427 A016428
%K A016425 sign,fini
%O A016425 0,1
%A A016425 njas
%I A014016
%S A014016 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A014016 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A014016 0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0
%V A014016 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A014016 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,
%X A014016 0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0
%N A014016 Inverse of 7th cyclotomic polynomial.
%p A014016 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014016 Sequence in context: A016402 A016377 A016425 this_sequence A014023 A016428 A016417
%Y A014016 Adjacent sequences: A014013 A014014 A014015 this_sequence A014017 A014018 A014019
%K A014016 sign
%O A014016 0,1
%A A014016 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014023
%S A014023 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A014023 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A014023 0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0
%V A014023 1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,
%W A014023 0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,
%X A014023 0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,0,0
%N A014023 Inverse of 14th cyclotomic polynomial.
%p A014023 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014023 Sequence in context: A016377 A016425 A014016 this_sequence A016428 A016417 A016407
%Y A014023 Adjacent sequences: A014020 A014021 A014022 this_sequence A014024 A014025 A014026
%K A014023 sign
%O A014023 0,1
%A A014023 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016428
%S A016428 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016428 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A016428 0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1
%V A016428 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016428 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,
%X A016428 0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,1,-1,0,0,1,-1,0,1
%N A016428 511-th cyclotomic polynomial.
%Y A016428 Sequence in context: A016425 A014016 A014023 this_sequence A016417 A016407 A016404
%Y A016428 Adjacent sequences: A016425 A016426 A016427 this_sequence A016429 A016430 A016431
%K A016428 sign,fini
%O A016428 0,1
%A A016428 njas
%I A016417
%S A016417 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016417 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A016417 0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0
%V A016417 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016417 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,
%X A016417 0,0,1,-1,0,0,0,0,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0
%N A016417 469th cyclotomic polynomial.
%Y A016417 Sequence in context: A014016 A014023 A016428 this_sequence A016407 A016404 A016393
%Y A016417 Adjacent sequences: A016414 A016415 A016416 this_sequence A016418 A016419 A016420
%K A016417 sign,fini
%O A016417 0,1
%A A016417 njas
%I A016407
%S A016407 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016407 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A016407 0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0
%V A016407 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016407 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,
%X A016407 0,0,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0
%N A016407 427th cyclotomic polynomial.
%Y A016407 Sequence in context: A014023 A016428 A016417 this_sequence A016404 A016393 A016384
%Y A016407 Adjacent sequences: A016404 A016405 A016406 this_sequence A016408 A016409 A016410
%K A016407 sign,fini
%O A016407 0,1
%A A016407 njas
%I A016404
%S A016404 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016404 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,
%U A016404 0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1
%V A016404 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016404 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,
%X A016404 0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1
%N A016404 413th cyclotomic polynomial.
%Y A016404 Sequence in context: A016428 A016417 A016407 this_sequence A016393 A016384 A016374
%Y A016404 Adjacent sequences: A016401 A016402 A016403 this_sequence A016405 A016406 A016407
%K A016404 sign,fini
%O A016404 0,1
%A A016404 njas
%I A016393
%S A016393 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016393 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,1,
%U A016393 1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0
%V A016393 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016393 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,1,
%X A016393 -1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0
%N A016393 371st cyclotomic polynomial.
%Y A016393 Sequence in context: A016417 A016407 A016404 this_sequence A016384 A016374 A016367
%Y A016393 Adjacent sequences: A016390 A016391 A016392 this_sequence A016394 A016395 A016396
%K A016393 sign,fini
%O A016393 0,1
%A A016393 njas
%I A016384
%S A016384 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016384 0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,
%U A016384 1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0
%V A016384 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016384 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,0,0,
%X A016384 1,-1,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0
%N A016384 329th cyclotomic polynomial.
%Y A016384 Sequence in context: A016407 A016404 A016393 this_sequence A016374 A016367 A016358
%Y A016384 Adjacent sequences: A016381 A016382 A016383 this_sequence A016385 A016386 A016387
%K A016384 sign,fini
%O A016384 0,1
%A A016384 njas
%I A016374
%S A016374 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016374 0,1,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,
%U A016374 0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0
%V A016374 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016374 0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,
%X A016374 0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0,0,0,1,0,-1,0,0
%N A016374 287th cyclotomic polynomial.
%Y A016374 Sequence in context: A016404 A016393 A016384 this_sequence A016367 A016358 A016409
%Y A016374 Adjacent sequences: A016371 A016372 A016373 this_sequence A016375 A016376 A016377
%K A016374 sign,fini
%O A016374 0,1
%A A016374 njas
%I A016367
%S A016367 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016367 0,1,1,0,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,
%U A016367 0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,1,1,0,1,1,1,1
%V A016367 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016367 0,1,-1,0,0,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,
%X A016367 0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,1,-1,0,1,-1,1,-1
%N A016367 259th cyclotomic polynomial.
%Y A016367 Sequence in context: A016393 A016384 A016374 this_sequence A016358 A016409 A016341
%Y A016367 Adjacent sequences: A016364 A016365 A016366 this_sequence A016368 A016369 A016370
%K A016367 sign,fini
%O A016367 0,1
%A A016367 njas
%I A016358
%S A016358 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016358 0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,
%U A016358 0,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1
%V A016358 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,
%W A016358 0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,
%X A016358 0,0,1,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,0,1
%N A016358 217th cyclotomic polynomial.
%Y A016358 Sequence in context: A016384 A016374 A016367 this_sequence A016409 A016341 A016382
%Y A016358 Adjacent sequences: A016355 A016356 A016357 this_sequence A016359 A016360 A016361
%K A016358 sign,fini
%O A016358 0,1
%A A016358 njas
%I A016409
%S A016409 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,
%T A016409 0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,
%U A016409 0,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1
%V A016409 1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,0,0,0,0,
%W A016409 0,1,1,0,-1,-1,0,0,-1,-1,0,1,1,0,0,1,1,0,-1,-1,0,0,-1,-1,0,1,1,
%X A016409 0,0,1,1,0,-1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1
%N A016409 434th cyclotomic polynomial.
%Y A016409 Sequence in context: A016374 A016367 A016358 this_sequence A016341 A016382 A016332
%Y A016409 Adjacent sequences: A016406 A016407 A016408 this_sequence A016410 A016411 A016412
%K A016409 sign,fini
%O A016409 0,1
%A A016409 njas
%I A016341
%S A016341 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,1,0,0,
%T A016341 0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,
%U A016341 1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1
%V A016341 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,1,-1,0,0,
%W A016341 0,1,-1,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,1,-1,0,1,-1,1,-1,1,
%X A016341 -1,0,1,-1,1,-1,1,-1,0,1,-1,1,-1,1,-1,1,0,-1,1,-1,1,-1,1,0,-1,1,-1
%N A016341 161-th cyclotomic polynomial.
%Y A016341 Sequence in context: A016367 A016358 A016409 this_sequence A016382 A016332 A016369
%Y A016341 Adjacent sequences: A016338 A016339 A016340 this_sequence A016342 A016343 A016344
%K A016341 sign,fini
%O A016341 0,1
%A A016341 njas
%I A016382
%S A016382 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,1,0,0,
%T A016382 0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,1,1,0,1,1,1,1,1,
%U A016382 1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1
%V A016382 1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,0,0,-1,-1,-1,-1,0,0,
%W A016382 0,1,1,1,1,0,0,0,-1,-1,-1,-1,0,0,0,1,1,1,1,1,1,0,-1,-1,-1,-1,-1,
%X A016382 -1,0,1,1,1,1,1,1,0,-1,-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,1,0,-1,-1,-1
%N A016382 322th cyclotomic polynomial.
%Y A016382 Sequence in context: A016358 A016409 A016341 this_sequence A016332 A016369 A016363
%Y A016382 Adjacent sequences: A016379 A016380 A016381 this_sequence A016383 A016384 A016385
%K A016382 sign,fini
%O A016382 0,1
%A A016382 njas
%I A016332
%S A016332 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,
%T A016332 1,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,
%U A016332 1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1
%V A016332 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,0,0,1,
%W A016332 -1,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,-1,0,1,-1,1,-1,1,-1,0,1,-1,
%X A016332 1,-1,1,0,-1,1,-1,1,-1,1,0,-1,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1
%N A016332 133th cyclotomic polynomial.
%Y A016332 Sequence in context: A016409 A016341 A016382 this_sequence A016369 A016363 A011654
%Y A016332 Adjacent sequences: A016329 A016330 A016331 this_sequence A016333 A016334 A016335
%K A016332 sign,fini
%O A016332 0,1
%A A016332 njas
%I A016369
%S A016369 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,
%T A016369 1,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,
%U A016369 1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1
%V A016369 1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,0,0,-1,-1,-1,-1,0,0,0,1,
%W A016369 1,1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,1,0,-1,-1,-1,-1,-1,-1,0,1,1,
%X A016369 1,1,1,0,-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,1,1
%N A016369 266th cyclotomic polynomial.
%Y A016369 Sequence in context: A016341 A016382 A016332 this_sequence A016363 A011654 A016348
%Y A016369 Adjacent sequences: A016366 A016367 A016368 this_sequence A016370 A016371 A016372
%K A016369 sign,fini
%O A016369 0,1
%A A016369 njas
%I A016363
%S A016363 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,
%T A016363 0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,
%U A016363 0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0
%V A016363 1,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,1,0,-1,-1,0,0,-1,-1,0,1,1,0,
%W A016363 0,1,1,0,-1,-1,0,1,0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,0,-1,-1,0,1,
%X A016363 0,-1,0,1,1,0,-1,0,1,0,-1,-1,0,1,1,0,0,1,1,0,-1,-1,0,0,-1,-1,0
%N A016363 238th cyclotomic polynomial.
%Y A016363 Sequence in context: A016382 A016332 A016369 this_sequence A011654 A016348 A015556
%Y A016363 Adjacent sequences: A016360 A016361 A016362 this_sequence A016364 A016365 A016366
%K A016363 sign,fini
%O A016363 0,1
%A A016363 njas
%I A011654
%S A011654 1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,
%T A011654 0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,
%U A011654 0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1
%V A011654 1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,-1,0,1,
%W A011654 0,-1,0,1,-1,0,1,0,-1,0,1,-1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,-1,1,0,
%X A011654 0,-1,1,0,-1,1,0,0,-1,1,0,-1,1,0,0,0,0,0,-1,1,0,0,0,0,0,-1,1
%N A011654 119th cyclotomic polynomial.
%Y A011654 Sequence in context: A016332 A016369 A016363 this_sequence A016348 A015556 A015780
%Y A011654 Adjacent sequences: A011651 A011652 A011653 this_sequence A011655 A011656 A011657
%K A011654 sign,fini,full
%O A011654 0,1
%A A011654 njas
%E A011654 Corrected by Matthias Koch (Matthias.Koch(AT)uni-bayreuth.de), May 20 2007
%I A016348
%S A016348 1,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,1,
%T A016348 0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0,
%U A016348 0,0,0,1,0,1,0,0,0,0,1,1,0,0,0,0,0,1,1
%V A016348 1,1,0,0,0,0,0,-1,-1,0,0,0,0,-1,0,1,0,0,0,0,1,0,-1,0,0,0,1,
%W A016348 0,0,1,0,0,0,-1,0,0,-1,0,0,-1,0,0,0,1,0,0,1,0,0,0,-1,0,1,0,
%X A016348 0,0,0,1,0,-1,0,0,0,0,-1,-1,0,0,0,0,0,1,1
%N A016348 182th cyclotomic polynomial.
%Y A016348 Sequence in context: A016369 A016363 A011654 this_sequence A015556 A015780 A011642
%Y A016348 Adjacent sequences: A016345 A016346 A016347 this_sequence A016349 A016350 A016351
%K A016348 sign,fini
%O A016348 0,1
%A A016348 njas
%I A015556
%S A015556 1,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,1,0,1,1,1,
%T A015556 0,0,1,1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0,1,0,1,
%U A015556 1,0,0,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0
%V A015556 1,-1,0,0,0,0,0,1,-1,0,0,0,0,1,0,-1,0,1,-1,0,1,0,-1,0,1,-1,1,
%W A015556 0,0,-1,1,0,-1,1,1,-1,-1,1,0,0,0,1,-1,0,0,0,0,1,0,-1,0,1,0,-1,
%X A015556 1,0,0,-1,1,0,0,0,0,0,0,1,-1,0,1,0,-1,0,1,0,-1,1,0,0,0,0,0
%N A015556 Inverse of 1547th cyclotomic polynomial.
%p A015556 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015556 Sequence in context: A016363 A011654 A016348 this_sequence A015780 A011642 A016338
%Y A015556 Adjacent sequences: A015553 A015554 A015555 this_sequence A015557 A015558 A015559
%K A015556 sign
%O A015556 0,1
%A A015556 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015780
%S A015780 1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,0,0,1,1,1,
%T A015780 0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,
%U A015780 1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,1,0,0
%V A015780 1,-1,0,0,0,0,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,0,0,-1,1,-1,
%W A015780 0,1,0,0,-1,1,0,0,0,0,0,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,
%X A015780 -1,1,0,0,0,-1,1,-1,1,0,0,0,0,1,-1,1,-1,0,0,0,1,-1,1,-1,1,0,0
%N A015780 Inverse of 1771-th cyclotomic polynomial.
%p A015780 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015780 Sequence in context: A011654 A016348 A015556 this_sequence A011642 A016338 A113052
%Y A015780 Adjacent sequences: A015777 A015778 A015779 this_sequence A015781 A015782 A015783
%K A015780 sign
%O A015780 0,1
%A A015780 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A011642
%S A011642 1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,0,1,0,1,1,
%T A011642 0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,
%U A011642 0,0,0,0,0,1,1
%V A011642 1,-1,0,0,0,0,0,1,-1,0,0,1,-1,0,1,-1,0,0,1,-1,0,1,0,-1,0,1,-1,
%W A011642 0,1,0,-1,0,1,0,-1,1,0,-1,0,1,0,-1,1,0,0,-1,1,0,-1,1,0,0,-1,1,
%X A011642 0,0,0,0,0,-1,1
%N A011642 77th cyclotomic polynomial.
%Y A011642 Sequence in context: A016348 A015556 A015780 this_sequence A016338 A113052 A117964
%Y A011642 Adjacent sequences: A011639 A011640 A011641 this_sequence A011643 A011644 A011645
%K A011642 sign,fini,full
%O A011642 0,1
%A A011642 njas
%I A016338
%S A016338 1,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,0,1,0,1,1,
%T A016338 0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,
%U A016338 0,0,0,0,0,1,1
%V A016338 1,1,0,0,0,0,0,-1,-1,0,0,-1,-1,0,1,1,0,0,1,1,0,-1,0,1,0,-1,-1,
%W A016338 0,1,0,-1,0,1,0,-1,-1,0,1,0,-1,0,1,1,0,0,1,1,0,-1,-1,0,0,-1,-1,
%X A016338 0,0,0,0,0,1,1
%N A016338 154th cyclotomic polynomial.
%Y A016338 Sequence in context: A015556 A015780 A011642 this_sequence A113052 A117964 A094875
%Y A016338 Adjacent sequences: A016335 A016336 A016337 this_sequence A016339 A016340 A016341
%K A016338 sign,fini
%O A016338 0,1
%A A016338 njas
%I A113052
%S A113052 1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%T A113052 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A113052 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A113052 Binomial(5n,n)/(4n+1) mod 5.
%C A113052 Conjecture: for p prime, mod(C(p*n,n)/((p-1)*n+1),p) is the indicator function of the sequence (p^n-1)/(p-1).
%Y A113052 Sequence in context: A015780 A011642 A016338 this_sequence A117964 A094875 A012245
%Y A113052 Adjacent sequences: A113049 A113050 A113051 this_sequence A113053 A113054 A113055
%K A113052 easy,nonn
%O A113052 0,1
%A A113052 Paul Barry (pbarry(AT)wit.ie), Oct 12 2005
%I A117964
%S A117964 1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,
%T A117964 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,
%U A117964 0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A117964 A117963 mod 2.
%C A117964 a(3n+2)=0, a(3n)=a(3n+1). a(3n) may be equal to A088917(n).
%F A117964 a(n)=sum{k=0..floor(n/2), L(C(n-k,k)/3)} mod 2 where L(j/p) is the Legendre symbol of j and p.
%Y A117964 Sequence in context: A011642 A016338 A113052 this_sequence A094875 A012245 A089801
%Y A117964 Adjacent sequences: A117961 A117962 A117963 this_sequence A117965 A117966 A117967
%K A117964 easy,nonn
%O A117964 0,1
%A A117964 Paul Barry (pbarry(AT)wit.ie), Apr 05 2006
%I A094875
%S A094875 1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A094875 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A094875 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A094875 a(n)=1 if floor(Pi*10^n) is prime, otherwise a(n)=0.
%e A094875 a(0)=1 because 3 is prime,
%e A094875 a(2)=0 because 314 is divided by 2
%e A094875 a(5)=1 because 314159 is prime
%e A094875 a(13)=0 because 31415926535897 is divided by 163
%o A094875 (PARI) \p 120 a=vector(100);v=1;for(i=1,100,a[i]=isprime(floor(Pi*v));v=v*10)
%Y A094875 Cf. A089281, A000796, A010051.
%Y A094875 Sequence in context: A016338 A113052 A117964 this_sequence A012245 A089801 A089802
%Y A094875 Adjacent sequences: A094872 A094873 A094874 this_sequence A094876 A094877 A094878
%K A094875 nonn
%O A094875 0,1
%A A094875 Frederic E.D. Michaud (famillesmichaud(AT)hotmail.com), Jun 16 2004
%E A094875 More terms from Johan Claes (Johan.Claes(AT)luc.ac.be), Jun 16 2004
%I A012245
%S A012245 1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%T A012245 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A012245 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A012245 Characteristic function of factorial numbers; also decimal expansion of Liouville's number or Liouville's constant).
%C A012245 Read as decimal fraction 1100010... in any base > 1 (arbitrary decimal point) Lioville's numbers are transcendental; read as a continued fraction it is also transcendental [G. H. Hardy and E. M. Wright, Th. 192].
%D A012245 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 162.
%D A012245 T. W. Koerner, Fourier Analysis, Camb. Univ. Press 1988, p. 177.
%D A012245 J. Liouville, C. R. Acad. Sci. Paris 18, 883-885 and 993-995, 1844.
%D A012245 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 58.
%H A012245 G. Xiao, Contfrac
%H A012245 Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
%H A012245 Index entries for continued fractions for constants
%F A012245 G.f.: sum(i=1, oo, x^product(j=1, i, j)) - Jon Perry (perry(AT)globalnet.co.uk), Mar 31 2004
%e A012245 a(25) = a(26) =..= a(119) = 0 because 4! = 24 and 5! = 120
%Y A012245 Cf. A000142.
%Y A012245 Sequence in context: A113052 A117964 A094875 this_sequence A089801 A089802 A015274
%Y A012245 Adjacent sequences: A012242 A012243 A012244 this_sequence A012246 A012247 A012248
%K A012245 nonn,nice
%O A012245 1,1
%A A012245 njas
%I A089801
%S A089801 1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,
%T A089801 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,
%U A089801 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N A089801 Expansion of Jacobi theta function (theta_3(q^(1/3))-theta_3(q^3))/2/q^(1/3).
%D A089801 I. J. Zucker, "Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums." J. Phys. A: Math. Gen. 23, 117-132, 1990.
%H A089801 Eric Weisstein's World of Mathematics, Jacobi Theta Functions
%F A089801 Euler transform of period 12 sequence [1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, -1, ...]. - Michael Somos, Apr 12 2005
%F A089801 a(n)=b(3n+1) where b(n) is multiplicative and b(3^e)=0^e, b(p^e)=(1+(-1)^e)/2 if p<>3. - Michael Somos Jun 06 2005
%F A089801 Expansion of q^(-1/3)*eta(q^2)^2*eta(q^3)*eta(q^12)/(eta(q)*eta(q^4)*eta(q^6)) in powers of q. - Michael Somos Apr 12 2005
%F A089801 Expansion of chi(q)* psi(-q^3) in powers of q where chi(), psi() are Ramanujan theta functions. - Michael Somos, Apr 19 2007
%F A089801 G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 2^(1/2) (t/i)^(1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A089807.
%e A089801 1 + q + q^5 + q^8 + q^16 + q^21 + q^33 + q^40 + q^56 + q^65 + q^85 + ...
%o A089801 (PARI) a(n)=issquare(3*n+1) /* Michael Somos Apr 12 2005 */
%Y A089801 A089802(n)=(-1)^n*a(n).
%Y A089801 Sequence in context: A117964 A094875 A012245 this_sequence A089802 A015274 A011651
%Y A089801 Adjacent sequences: A089798 A089799 A089800 this_sequence A089802 A089803 A089804
%K A089801 nonn
%O A089801 0,1
%A A089801 Eric Weisstein (eric(AT)weisstein.com), Nov 12, 2003
%I A089802
%S A089802 1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,
%T A089802 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,
%U A089802 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%V A089802 1,-1,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,
%W A089802 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,
%X A089802 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N A089802 Expansion of Jacobi theta function (theta_4(q^3)-theta_4(q^(1/3)))/2/q^(1/3).
%D A089802 I. J. Zucker, "Further Relations Amongst Infinite Series and Products. II. The Evaluation of Three-Dimensional Lattice Sums." J. Phys. A: Math. Gen. 23, 117-132, 1990.
%H A089802 Eric Weisstein's World of Mathematics, Jacobi Theta Functions
%F A089802 Expansion of q^(-1/3)*(eta(q)*eta(q^6)^2)/(eta(q^2)*eta(q^3)) in powers of q. - Michael Somos Apr 12 2005
%F A089802 Euler transform of period 6 sequence [ -1, 0, 0, 0, -1, -1, ...]. - Michael Somos, Apr 12 2005
%F A089802 |a(n)| is the characteristic function of A001082. - Michael Somos Oct 31 2005
%F A089802 G.f.: Sum_{k} (-1)^k x^((3k^2-2*k)/2) = Product_{k>0} (1-x^(6k))(1-x^(6k-1))(1-x^(6k-5)) . - Michael Somos Oct 31 2005
%F A089802 A002448(3n+1)=-2*a(n). - Michael Somos Jul 07 2006
%F A089802 Expansion of f(-x, -x^5) in powers of x, where f(a, b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
%o A089802 (PARI) a(n)=(-1)^n*issquare(3*n+1) /* Michael Somos Apr 12 2005 */
%Y A089802 a(n)=(-1)^n*A089801(n).
%Y A089802 Sequence in context: A094875 A012245 A089801 this_sequence A015274 A011651 A016264
%Y A089802 Adjacent sequences: A089799 A089800 A089801 this_sequence A089803 A089804 A089805
%K A089802 sign
%O A089802 0,1
%A A089802 Eric Weisstein (eric(AT)weisstein.com), Nov 12, 2003
%E A089802 Corrected by njas, Nov 05 2005
%I A015274
%S A015274 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,
%T A015274 0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,1,
%U A015274 0,0,1,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1
%V A015274 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,0,0,-1,1,0,
%W A015274 0,0,-1,1,0,0,1,-1,0,0,0,1,-1,0,0,0,1,0,0,0,-1,1,0,0,0,-1,1,
%X A015274 0,0,1,-1,0,0,0,1,-1,0,0,0,1,0,0,0,-1,1,0,0,0,-1,1,0,0,1,-1
%N A015274 Inverse of 1265th cyclotomic polynomial.
%p A015274 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015274 Sequence in context: A012245 A089801 A089802 this_sequence A011651 A016264 A016044
%Y A015274 Adjacent sequences: A015271 A015272 A015273 this_sequence A015275 A015276 A015277
%K A015274 sign
%O A015274 0,1
%A A015274 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A011651
%S A011651 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,
%T A011651 0,1,0,1,0,0,0,1,1,0,0,0,1,1
%V A011651 1,1,0,0,0,-1,-1,0,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,0,1,0,-1,0,
%W A011651 0,-1,0,1,0,0,0,-1,-1,0,0,0,1,1
%N A011651 110th cyclotomic polynomial.
%Y A011651 Sequence in context: A089801 A089802 A015274 this_sequence A016264 A016044 A015714
%Y A011651 Adjacent sequences: A011648 A011649 A011650 this_sequence A011652 A011653 A011654
%K A011651 sign,fini,full
%O A011651 0,1
%A A011651 njas
%I A016264
%S A016264 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,
%T A016264 0,1,0,1,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,
%U A016264 0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0,1
%V A016264 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,
%W A016264 0,-1,0,1,0,0,0,-1,1,0,0,0,-1,1,1,-1,0,0,0,1,-1,0,0,0,1,0,-1,
%X A016264 0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,0,-1,1,0,0,0,-1
%N A016264 Inverse of 2255th cyclotomic polynomial.
%p A016264 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016264 Sequence in context: A089802 A015274 A011651 this_sequence A016044 A015714 A015604
%Y A016264 Adjacent sequences: A016261 A016262 A016263 this_sequence A016265 A016266 A016267
%K A016264 sign
%O A016264 0,1
%A A016264 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016044
%S A016044 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,
%T A016044 0,1,0,1,0,0,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,
%U A016044 1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,1,1,1,1,0,1,1
%V A016044 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,
%W A016044 0,-1,0,1,0,0,0,-1,1,0,1,-1,-1,1,0,1,-1,0,0,0,1,0,-1,0,0,1,0,
%X A016044 -1,0,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,0,-1,1,0,1,-1,-1,1,0,1,-1
%N A016044 Inverse of 2035th cyclotomic polynomial.
%p A016044 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016044 Sequence in context: A015274 A011651 A016264 this_sequence A015714 A015604 A015054
%Y A016044 Adjacent sequences: A016041 A016042 A016043 this_sequence A016045 A016046 A016047
%K A016044 sign
%O A016044 0,1
%A A016044 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015714
%S A015714 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,
%T A015714 0,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0,
%U A015714 1,0,1,0,0,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0
%V A015714 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,
%W A015714 0,-1,0,1,1,-1,0,-1,1,1,-1,0,-1,1,1,0,-1,0,0,1,0,-1,0,0,1,0,0,
%X A015714 -1,0,1,0,0,-1,0,1,1,-1,0,-1,1,1,-1,0,-1,1,1,0,-1,0,0,1,0,-1,0
%N A015714 Inverse of 1705th cyclotomic polynomial.
%p A015714 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015714 Sequence in context: A011651 A016264 A016044 this_sequence A015604 A015054 A016099
%Y A015714 Adjacent sequences: A015711 A015712 A015713 this_sequence A015715 A015716 A015717
%K A015714 sign
%O A015714 0,1
%A A015714 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015604
%S A015604 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,
%T A015604 0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,
%U A015604 1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,0,1,0,0
%V A015604 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,
%W A015604 0,-1,1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,1,0,-1,0,0,1,0,0,-1,0,
%X A015604 1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,1,0,-1,0,0,1,0,0
%N A015604 Inverse of 1595th cyclotomic polynomial.
%p A015604 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015604 Sequence in context: A016264 A016044 A015714 this_sequence A015054 A016099 A014724
%Y A015604 Adjacent sequences: A015601 A015602 A015603 this_sequence A015605 A015606 A015607
%K A015604 sign
%O A015604 0,1
%A A015604 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015054
%S A015054 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0,0,0,1,1,0,0,
%T A015054 0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,
%U A015054 1,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1
%V A015054 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,0,0,1,0,-1,0,1,0,0,0,-1,1,0,0,
%W A015054 0,-1,1,1,-1,0,0,0,1,-1,0,1,-1,1,0,-1,1,0,0,0,-1,1,1,-1,0,0,0,
%X A015054 1,-1,0,1,-1,1,0,-1,1,0,0,0,-1,1,1,-1,0,0,0,1,-1,0,1,-1,1,0,-1
%N A015054 Inverse of 1045th cyclotomic polynomial.
%p A015054 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015054 Sequence in context: A016044 A015714 A015604 this_sequence A016099 A014724 A015439
%Y A015054 Adjacent sequences: A015051 A015052 A015053 this_sequence A015055 A015056 A015057
%K A015054 sign
%O A015054 0,1
%A A015054 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016099
%S A016099 1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0,0,0,1,1,0,0,
%T A016099 0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,
%U A016099 1,1,0,1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1
%V A016099 1,1,0,0,0,-1,-1,0,0,0,1,0,-1,0,0,-1,0,1,0,-1,0,0,0,1,1,0,0,
%W A016099 0,-1,-1,1,1,0,0,0,-1,-1,0,1,1,1,0,-1,-1,0,0,0,1,1,-1,-1,0,0,0,
%X A016099 1,1,0,-1,-1,-1,0,1,1,0,0,0,-1,-1,1,1,0,0,0,-1,-1,0,1,1,1,0,-1
%N A016099 Inverse of 2090th cyclotomic polynomial.
%p A016099 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016099 Sequence in context: A015714 A015604 A015054 this_sequence A014724 A015439 A016339
%Y A016099 Adjacent sequences: A016096 A016097 A016098 this_sequence A016100 A016101 A016102
%K A016099 sign
%O A016099 0,1
%A A016099 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014724
%S A014724 1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,
%T A014724 1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,
%U A014724 0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,1,1,1,0,1,1,1,1
%V A014724 1,-1,0,0,0,1,-1,0,0,0,1,0,-1,1,-1,1,0,-1,1,-1,1,0,0,0,0,0,1,
%W A014724 -1,0,0,0,1,-1,1,-1,1,0,0,0,0,0,0,0,0,1,-1,1,-1,1,0,0,0,0,0,
%X A014724 0,0,0,1,-1,1,-1,1,0,0,0,-1,1,0,0,0,0,0,1,-1,1,-1,0,1,-1,1,-1
%N A014724 Inverse of 715th cyclotomic polynomial.
%p A014724 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014724 Sequence in context: A015604 A015054 A016099 this_sequence A015439 A016339 A016379
%Y A014724 Adjacent sequences: A014721 A014722 A014723 this_sequence A014725 A014726 A014727
%K A014724 sign
%O A014724 0,1
%A A014724 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015439
%S A015439 1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,
%T A015439 1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,
%U A015439 0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,1,1,1,0,1,1,1,1
%V A015439 1,1,0,0,0,-1,-1,0,0,0,1,0,-1,-1,-1,-1,0,1,1,1,1,0,0,0,0,0,1,
%W A015439 1,0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,
%X A015439 0,0,0,-1,-1,-1,-1,-1,0,0,0,1,1,0,0,0,0,0,1,1,1,1,0,-1,-1,-1,-1
%N A015439 Inverse of 1430th cyclotomic polynomial.
%p A015439 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015439 Sequence in context: A015054 A016099 A014724 this_sequence A016339 A016379 A010891
%Y A015439 Adjacent sequences: A015436 A015437 A015438 this_sequence A015440 A015441 A015442
%K A015439 sign
%O A015439 0,1
%A A015439 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016339
%S A016339 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A016339 0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,
%U A016339 0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1
%V A016339 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,
%W A016339 0,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,
%X A016339 0,1,0,-1,0,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1
%N A016339 155th cyclotomic polynomial.
%Y A016339 Sequence in context: A016099 A014724 A015439 this_sequence A016379 A010891 A014019
%Y A016339 Adjacent sequences: A016336 A016337 A016338 this_sequence A016340 A016341 A016342
%K A016339 sign,fini
%O A016339 0,1
%A A016339 njas
%I A016379
%S A016379 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A016379 0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,
%U A016379 0,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1
%V A016379 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,
%W A016379 0,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1,0,
%X A016379 0,-1,0,1,0,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1
%N A016379 310th cyclotomic polynomial.
%Y A016379 Sequence in context: A014724 A015439 A016339 this_sequence A010891 A014019 A016349
%Y A016379 Adjacent sequences: A016376 A016377 A016378 this_sequence A016380 A016381 A016382
%K A016379 sign,fini
%O A016379 0,1
%A A016379 njas
%I A010891
%S A010891 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A010891 0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,
%U A010891 0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1
%V A010891 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,
%W A010891 0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,
%X A010891 0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1
%N A010891 Inverse of 5th cyclotomic polynomial.
%p A010891 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A010891 Sequence in context: A015439 A016339 A016379 this_sequence A014019 A016349 A016392
%Y A010891 Adjacent sequences: A010888 A010889 A010890 this_sequence A010892 A010893 A010894
%K A010891 sign
%O A010891 0,1
%A A010891 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014019
%S A014019 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A014019 0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,
%U A014019 0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1
%V A014019 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,
%W A014019 0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,
%X A014019 0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1
%N A014019 Inverse of 10th cyclotomic polynomial.
%C A014019 The g.f. is the image of the g.f. of Fib(n+1) by the transform A(x)->(1/(1+x^2)^2)A(x/(1+x^2)). The denominator is associated to the knots 4_1 and 5_1 by their Alexander and Jones polynomials respectively. - Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
%H A014019 The Rolfsen Knot Table
%F A014019 G.f. : 1/(1-x+x^2-x^3+x^4) - Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
%p A014019 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014019 Cf. A099443.
%Y A014019 Sequence in context: A016339 A016379 A010891 this_sequence A016349 A016392 A016336
%Y A014019 Adjacent sequences: A014016 A014017 A014018 this_sequence A014020 A014021 A014022
%K A014019 sign
%O A014019 0,1
%A A014019 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016349
%S A016349 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A016349 0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,
%U A016349 0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0
%V A016349 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,
%W A016349 0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,
%X A016349 0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0
%N A016349 185th cyclotomic polynomial.
%Y A016349 Sequence in context: A016379 A010891 A014019 this_sequence A016392 A016336 A016375
%Y A016349 Adjacent sequences: A016346 A016347 A016348 this_sequence A016350 A016351 A016352
%K A016349 sign,fini
%O A016349 0,1
%A A016349 njas
%I A016392
%S A016392 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A016392 0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,
%U A016392 0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0
%V A016392 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,
%W A016392 0,0,0,1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,0,-1,-1,-1,-1,0,1,1,1,1,
%X A016392 0,-1,-1,-1,-1,0,1,1,1,1,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0
%N A016392 370th cyclotomic polynomial.
%Y A016392 Sequence in context: A010891 A014019 A016349 this_sequence A016336 A016375 A011653
%Y A016392 Adjacent sequences: A016389 A016390 A016391 this_sequence A016393 A016394 A016395
%K A016392 sign,fini
%O A016392 0,1
%A A016392 njas
%I A016336
%S A016336 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A016336 0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,
%U A016336 1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0
%V A016336 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,
%W A016336 0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,
%X A016336 1,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0
%N A016336 145th cyclotomic polynomial.
%Y A016336 Sequence in context: A014019 A016349 A016392 this_sequence A016375 A011653 A016361
%Y A016336 Adjacent sequences: A016333 A016334 A016335 this_sequence A016337 A016338 A016339
%K A016336 sign,fini
%O A016336 0,1
%A A016336 njas
%I A016375
%S A016375 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,
%T A016375 0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,
%U A016375 1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0
%V A016375 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,
%W A016375 0,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0,
%X A016375 1,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0
%N A016375 290th cyclotomic polynomial.
%Y A016375 Sequence in context: A016349 A016392 A016336 this_sequence A011653 A016361 A011647
%Y A016375 Adjacent sequences: A016372 A016373 A016374 this_sequence A016376 A016377 A016378
%K A016375 sign,fini
%O A016375 0,1
%A A016375 njas
%I A011653
%S A011653 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,1,1,
%T A011653 0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,
%U A011653 1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0
%V A011653 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,1,-1,1,-1,
%W A011653 0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,0,-1,1,-1,1,0,-1,1,
%X A011653 -1,1,0,-1,1,-1,1,0,-1,1,-1,1,0,-1,1,0,0,0,-1,1,0,0,0,-1,1,0,0
%N A011653 115th cyclotomic polynomial.
%Y A011653 Sequence in context: A016392 A016336 A016375 this_sequence A016361 A011647 A016352
%Y A011653 Adjacent sequences: A011650 A011651 A011652 this_sequence A011654 A011655 A011656
%K A011653 sign,fini
%O A011653 0,1
%A A011653 njas
%I A016361
%S A016361 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,1,1,
%T A016361 0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,
%U A016361 1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0
%V A016361 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,-1,-1,-1,-1,
%W A016361 0,1,1,1,1,0,-1,-1,-1,-1,0,1,1,1,1,0,-1,-1,-1,0,1,1,1,1,0,-1,-1,
%X A016361 -1,-1,0,1,1,1,1,0,-1,-1,-1,-1,0,1,1,0,0,0,-1,-1,0,0,0,1,1,0,0
%N A016361 230th cyclotomic polynomial.
%Y A016361 Sequence in context: A016336 A016375 A011653 this_sequence A011647 A016352 A011644
%Y A016361 Adjacent sequences: A016358 A016359 A016360 this_sequence A016362 A016363 A016364
%K A016361 sign,fini
%O A016361 0,1
%A A016361 njas
%I A011647
%S A011647 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,0,1,
%T A011647 0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,
%U A011647 0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1
%V A011647 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,1,0,-1,0,0,1,0,-1,
%W A011647 0,0,1,0,-1,0,0,1,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1,0,0,-1,0,1,
%X A011647 0,0,-1,1,0,0,0,-1,1,0,0,0,-1,1,0,0,0,-1,1
%N A011647 95th cyclotomic polynomial.
%Y A011647 Sequence in context: A016375 A011653 A016361 this_sequence A016352 A011644 A016344
%Y A011647 Adjacent sequences: A011644 A011645 A011646 this_sequence A011648 A011649 A011650
%K A011647 sign,fini,full
%O A011647 0,1
%A A011647 njas
%I A016352
%S A016352 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0,1,0,1,
%T A016352 0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,
%U A016352 0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1
%V A016352 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,-1,0,1,0,0,1,0,-1,
%W A016352 0,0,-1,0,1,0,0,1,0,-1,0,1,0,0,1,0,-1,0,0,-1,0,1,0,0,1,0,-1,
%X A016352 0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,0,0,0,1,1
%N A016352 190th cyclotomic polynomial.
%Y A016352 Sequence in context: A011653 A016361 A011647 this_sequence A011644 A016344 A015244
%Y A016352 Adjacent sequences: A016349 A016350 A016351 this_sequence A016353 A016354 A016355
%K A016352 sign,fini
%O A016352 0,1
%A A016352 njas
%I A011644
%S A011644 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,
%T A011644 1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,
%U A011644 1,0,0,0,1,1,0,0,0,1,1
%V A011644 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,
%W A011644 1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,
%X A011644 1,0,0,0,-1,1,0,0,0,-1,1
%N A011644 85th cyclotomic polynomial.
%Y A011644 Sequence in context: A016361 A011647 A016352 this_sequence A016344 A015244 A015894
%Y A011644 Adjacent sequences: A011641 A011642 A011643 this_sequence A011645 A011646 A011647
%K A011644 sign,fini,full
%O A011644 0,1
%A A011644 njas
%I A016344
%S A016344 1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,0,1,1,
%T A016344 1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,
%U A016344 1,0,0,0,1,1,0,0,0,1,1
%V A016344 1,1,0,0,0,-1,-1,0,0,0,1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,0,-1,-1,
%W A016344 -1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,1,1,1,1,0,-1,-1,-1,-1,0,0,0,1,
%X A016344 1,0,0,0,-1,-1,0,0,0,1,1
%N A016344 170th cyclotomic polynomial.
%Y A016344 Sequence in context: A011647 A016352 A011644 this_sequence A015244 A015894 A011639
%Y A016344 Adjacent sequences: A016341 A016342 A016343 this_sequence A016345 A016346 A016347
%K A016344 sign,fini
%O A016344 0,1
%A A016344 njas
%I A015244
%S A015244 1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,
%T A015244 1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,
%U A015244 0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0
%V A015244 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,1,-1,1,-1,0,1,0,0,-1,0,1,0,0,0,
%W A015244 -1,1,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,0,0,0,0,
%X A015244 0,0,0,1,0,-1,0,0,1,0,0,-1,0,1,0,0,0,0,0,0,0,0,1,0,-1,0,0
%N A015244 Inverse of 1235th cyclotomic polynomial.
%p A015244 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015244 Sequence in context: A016352 A011644 A016344 this_sequence A015894 A011639 A016330
%Y A015244 Adjacent sequences: A015241 A015242 A015243 this_sequence A015245 A015246 A015247
%K A015244 sign
%O A015244 0,1
%A A015244 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015894
%S A015894 1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,
%T A015894 1,1,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,
%U A015894 1,0,1,1,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,1,0
%V A015894 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,0,
%W A015894 -1,1,0,0,0,-1,1,0,0,0,-1,1,1,-1,0,0,0,1,-1,0,0,0,1,-1,0,1,-1,
%X A015894 1,0,-1,1,0,0,0,-1,1,0,0,0,-1,1,1,-1,0,0,0,1,-1,0,0,0,1,-1,0
%N A015894 Inverse of 1885th cyclotomic polynomial.
%p A015894 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015894 Sequence in context: A011644 A016344 A015244 this_sequence A011639 A016330 A085002
%Y A015894 Adjacent sequences: A015891 A015892 A015893 this_sequence A015895 A015896 A015897
%K A015894 sign
%O A015894 0,1
%A A015894 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A011639
%S A011639 1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,
%T A011639 1,1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1
%V A011639 1,-1,0,0,0,1,-1,0,0,0,1,-1,0,1,-1,1,-1,0,1,-1,1,-1,0,1,-1,1,0,
%W A011639 -1,1,-1,1,0,-1,1,-1,1,0,-1,1,0,0,0,-1,1,0,0,0,-1,1
%N A011639 65th cyclotomic polynomial.
%Y A011639 Sequence in context: A016344 A015244 A015894 this_sequence A016330 A085002 A014394
%Y A011639 Adjacent sequences: A011636 A011637 A011638 this_sequence A011640 A011641 A011642
%K A011639 sign,fini,full
%O A011639 0,1
%A A011639 njas
%I A016330
%S A016330 1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,0,
%T A016330 1,1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1
%V A016330 1,1,0,0,0,-1,-1,0,0,0,1,1,0,-1,-1,-1,-1,0,1,1,1,1,0,-1,-1,-1,0,
%W A016330 1,1,1,1,0,-1,-1,-1,-1,0,1,1,0,0,0,-1,-1,0,0,0,1,1
%N A016330 130th cyclotomic polynomial.
%Y A016330 Sequence in context: A015244 A015894 A011639 this_sequence A085002 A014394 A014779
%Y A016330 Adjacent sequences: A016327 A016328 A016329 this_sequence A016331 A016332 A016333
%K A016330 sign,fini,full
%O A016330 0,1
%A A016330 njas
%I A085002
%S A085002 1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,
%T A085002 0,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,0,1,1,
%U A085002 0,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,1
%N A085002 A fractal sequence.
%H A085002 B. Cloitre, Graph of A085005(n) for n=1 up to 3874
%F A085002 a(n)=floor(phi*n)-2*floor(phi*n/2) where phi=(1+sqrt(5))/2 is the Golden ratio
%F A085002 a(n)=A105774(n) mod 2; a(n)=A000201(n) mod 2. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2005
%Y A085002 Cf. A083035, A083036, A083037, A083038, A085003, A085004, A085005.
%Y A085002 Sequence in context: A015894 A011639 A016330 this_sequence A014394 A014779 A014464
%Y A085002 Adjacent sequences: A084999 A085000 A085001 this_sequence A085003 A085004 A085005
%K A085002 nonn
%O A085002 1,1
%A A085002 Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 17 2003, link corrected Nov 02 2006
%I A014394
%S A014394 1,1,0,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,1,0,1,0,1,0,
%T A014394 0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,
%U A014394 1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0
%V A014394 1,-1,0,0,0,1,-1,1,-1,0,1,0,0,-1,1,0,0,0,0,0,0,1,0,-1,0,1,0,
%W A014394 0,0,0,0,0,1,0,-1,0,1,0,0,0,0,0,0,1,0,-1,0,1,0,0,0,0,0,0,
%X A014394 1,-1,0,0,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,0,0,0,0,0,0,-1,1,0,0
%N A014394 Inverse of 385th cyclotomic polynomial.
%p A014394 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014394 Sequence in context: A011639 A016330 A085002 this_sequence A014779 A014464 A014919
%Y A014394 Adjacent sequences: A014391 A014392 A014393 this_sequence A014395 A014396 A014397
%K A014394 sign
%O A014394 0,1
%A A014394 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014779
%S A014779 1,1,0,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,1,0,1,0,1,0,
%T A014779 0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,
%U A014779 1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0
%V A014779 1,1,0,0,0,-1,-1,-1,-1,0,1,0,0,1,1,0,0,0,0,0,0,-1,0,1,0,-1,0,
%W A014779 0,0,0,0,0,1,0,-1,0,1,0,0,0,0,0,0,-1,0,1,0,-1,0,0,0,0,0,0,
%X A014779 1,1,0,0,1,0,-1,-1,-1,-1,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0
%N A014779 Inverse of 770th cyclotomic polynomial.
%p A014779 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014779 Sequence in context: A016330 A085002 A014394 this_sequence A014464 A014919 A014814
%Y A014779 Adjacent sequences: A014776 A014777 A014778 this_sequence A014780 A014781 A014782
%K A014779 sign
%O A014779 0,1
%A A014779 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014464
%S A014464 1,1,0,0,0,1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,
%T A014464 0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0,
%U A014464 0,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0
%V A014464 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,0,0,0,-1,1,0,0,1,-1,0,0,0,1,0,
%W A014464 0,0,-1,1,0,0,1,-1,0,0,0,1,0,0,0,-1,1,0,0,1,-1,0,0,0,1,0,0,
%X A014464 0,-1,1,0,0,1,-1,0,0,0,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,0,0
%N A014464 Inverse of 455th cyclotomic polynomial.
%p A014464 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014464 Sequence in context: A085002 A014394 A014779 this_sequence A014919 A014814 A015619
%Y A014464 Adjacent sequences: A014461 A014462 A014463 this_sequence A014465 A014466 A014467
%K A014464 sign
%O A014464 0,1
%A A014464 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014919
%S A014919 1,1,0,0,0,1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,
%T A014919 0,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,0,
%U A014919 0,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0
%V A014919 1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,0,0,0,-1,-1,0,0,1,1,0,0,0,-1,0,
%W A014919 0,0,1,1,0,0,-1,-1,0,0,0,1,0,0,0,-1,-1,0,0,1,1,0,0,0,-1,0,0,
%X A014919 0,1,1,0,0,-1,-1,0,0,0,1,1,1,0,-1,-1,-1,-1,0,0,0,1,1,0,0,0,0
%N A014919 Inverse of 910th cyclotomic polynomial.
%p A014919 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014919 Sequence in context: A014394 A014779 A014464 this_sequence A014814 A015619 A011634
%Y A014919 Adjacent sequences: A014916 A014917 A014918 this_sequence A014920 A014921 A014922
%K A014919 sign
%O A014919 0,1
%A A014919 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A014814
%S A014814 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,
%T A014814 0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,
%U A014814 1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,1,1
%V A014814 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,0,0,0,0,
%W A014814 0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,0,0,0,0,0,1,-1,1,
%X A014814 -1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,0,0,0,0,0,1,-1,1,-1,0,1,-1
%N A014814 Inverse of 805th cyclotomic polynomial.
%p A014814 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A014814 Sequence in context: A014779 A014464 A014919 this_sequence A015619 A011634 A011641
%Y A014814 Adjacent sequences: A014811 A014812 A014813 this_sequence A014815 A014816 A014817
%K A014814 sign
%O A014814 0,1
%A A014814 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015619
%S A015619 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,
%T A015619 0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,
%U A015619 1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,1,1
%V A015619 1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,0,0,0,0,
%W A015619 0,1,1,1,1,0,-1,-1,-1,-1,-1,0,1,1,1,1,0,0,0,0,0,0,0,0,-1,-1,-1,
%X A015619 -1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,1,1,1,1,0,-1,-1
%N A015619 Inverse of 1610th cyclotomic polynomial.
%p A015619 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015619 Sequence in context: A014464 A014919 A014814 this_sequence A011634 A011641 A016144
%Y A015619 Adjacent sequences: A015616 A015617 A015618 this_sequence A015620 A015621 A015622
%K A015619 sign
%O A015619 0,1
%A A015619 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A011634
%S A011634 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1
%V A011634 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1
%N A011634 35th cyclotomic polynomial.
%Y A011634 Sequence in context: A014919 A014814 A015619 this_sequence A011641 A016144 A016074
%Y A011634 Adjacent sequences: A011631 A011632 A011633 this_sequence A011635 A011636 A011637
%K A011634 sign,fini,full
%O A011634 0,1
%A A011634 njas
%I A011641
%S A011641 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1
%V A011641 1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,1,1
%N A011641 70th cyclotomic polynomial.
%Y A011641 Sequence in context: A014814 A015619 A011634 this_sequence A016144 A016074 A015864
%Y A011641 Adjacent sequences: A011638 A011639 A011640 this_sequence A011642 A011643 A011644
%K A011641 sign,fini,full
%O A011641 0,1
%A A011641 njas
%I A016144
%S A016144 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A016144 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A016144 0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1
%V A016144 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A016144 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%X A016144 0,0,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1
%N A016144 Inverse of 2135th cyclotomic polynomial.
%p A016144 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016144 Sequence in context: A015619 A011634 A011641 this_sequence A016074 A015864 A015654
%Y A016144 Adjacent sequences: A016141 A016142 A016143 this_sequence A016145 A016146 A016147
%K A016144 sign
%O A016144 0,1
%A A016144 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016074
%S A016074 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A016074 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A016074 0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0
%V A016074 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A016074 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%X A016074 0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0
%N A016074 Inverse of 2065th cyclotomic polynomial.
%p A016074 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016074 Sequence in context: A011634 A011641 A016144 this_sequence A015864 A015654 A015514
%Y A016074 Adjacent sequences: A016071 A016072 A016073 this_sequence A016075 A016076 A016077
%K A016074 sign
%O A016074 0,1
%A A016074 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015864
%S A015864 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015864 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
%U A015864 1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0
%V A015864 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015864 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
%X A015864 -1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,0
%N A015864 Inverse of 1855th cyclotomic polynomial.
%p A015864 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015864 Sequence in context: A011641 A016144 A016074 this_sequence A015654 A015514 A015444
%Y A015864 Adjacent sequences: A015861 A015862 A015863 this_sequence A015865 A015866 A015867
%K A015864 sign
%O A015864 0,1
%A A015864 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015654
%S A015654 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015654 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,
%U A015654 1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0
%V A015654 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015654 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,1,-1,
%X A015654 1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,0,0,0,0,0,0,0
%N A015654 Inverse of 1645th cyclotomic polynomial.
%p A015654 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015654 Sequence in context: A016144 A016074 A015864 this_sequence A015514 A015444 A015304
%Y A015654 Adjacent sequences: A015651 A015652 A015653 this_sequence A015655 A015656 A015657
%K A015654 sign
%O A015654 0,1
%A A015654 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015514
%S A015514 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015514 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,
%U A015514 1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0
%V A015514 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015514 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,
%X A015514 -1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A015514 Inverse of 1505th cyclotomic polynomial.
%p A015514 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015514 Sequence in context: A016074 A015864 A015654 this_sequence A015444 A015304 A015094
%Y A015514 Adjacent sequences: A015511 A015512 A015513 this_sequence A015515 A015516 A015517
%K A015514 sign
%O A015514 0,1
%A A015514 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015444
%S A015444 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015444 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,
%U A015444 1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%V A015444 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015444 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,
%X A015444 -1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A015444 Inverse of 1435th cyclotomic polynomial.
%p A015444 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015444 Sequence in context: A015864 A015654 A015514 this_sequence A015304 A015094 A016179
%Y A015444 Adjacent sequences: A015441 A015442 A015443 this_sequence A015445 A015446 A015447
%K A015444 sign
%O A015444 0,1
%A A015444 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015304
%S A015304 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015304 0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,
%U A015304 1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1
%V A015304 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015304 0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,
%X A015304 1,-1,1,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,1,-1
%N A015304 Inverse of 1295th cyclotomic polynomial.
%p A015304 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015304 Sequence in context: A015654 A015514 A015444 this_sequence A015094 A016179 A015024
%Y A015304 Adjacent sequences: A015301 A015302 A015303 this_sequence A015305 A015306 A015307
%K A015304 sign
%O A015304 0,1
%A A015304 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015094
%S A015094 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015094 0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,
%U A015094 1,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1
%V A015094 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015094 0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,
%X A015094 -1,1,0,0,0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1
%N A015094 Inverse of 1085th cyclotomic polynomial.
%p A015094 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015094 Sequence in context: A015514 A015444 A015304 this_sequence A016179 A015024 A016039
%Y A015094 Adjacent sequences: A015091 A015092 A015093 this_sequence A015095 A015096 A015097
%K A015094 sign
%O A015094 0,1
%A A015094 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016179
%S A016179 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A016179 0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,
%U A016179 1,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1
%V A016179 1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,1,1,0,0,
%W A016179 0,0,0,0,-1,-1,0,0,0,1,1,1,1,0,-1,-1,-1,-1,-1,0,1,1,1,1,0,0,0,
%X A016179 -1,-1,0,0,0,0,0,0,1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1
%N A016179 Inverse of 2170th cyclotomic polynomial.
%p A016179 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016179 Sequence in context: A015444 A015304 A015094 this_sequence A015024 A016039 A138149
%Y A016179 Adjacent sequences: A016176 A016177 A016178 this_sequence A016180 A016181 A016182
%K A016179 sign
%O A016179 0,1
%A A016179 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A015024
%S A015024 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A015024 0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,
%U A015024 0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0
%V A015024 1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,0,0,
%W A015024 0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0,-1,1,
%X A015024 0,0,0,0,1,-1,0,0,0,1,-1,1,-1,0,1,-1,1,-1,1,0,-1,1,-1,1,0,0,0
%N A015024 Inverse of 1015th cyclotomic polynomial.
%p A015024 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A015024 Sequence in context: A015304 A015094 A016179 this_sequence A016039 A138149 A113047
%Y A015024 Adjacent sequences: A015021 A015022 A015023 this_sequence A015025 A015026 A015027
%K A015024 sign
%O A015024 0,1
%A A015024 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A016039
%S A016039 1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,
%T A016039 0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,1,1,
%U A016039 0,0,0,0,1,1,0,0,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0
%V A016039 1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0,1,1,0,0,
%W A016039 0,0,-1,-1,0,0,0,1,1,1,1,0,-1,-1,-1,-1,-1,0,1,1,1,1,0,0,0,-1,-1,
%X A016039 0,0,0,0,1,1,0,0,0,-1,-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1,-1,0,0,0
%N A016039 Inverse of 2030th cyclotomic polynomial.
%p A016039 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%Y A016039 Sequence in context: A015094 A016179 A015024 this_sequence A138149 A113047 A127692
%Y A016039 Adjacent sequences: A016036 A016037 A016038 this_sequence A016040 A016041 A016042
%K A016039 sign
%O A016039 0,1
%A A016039 Simon Plouffe (plouffe(AT)math.uqam.ca)
%I A138149
%S A138149 1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,
%T A138149 0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U A138149 0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A138149 n-th run has length n-th prime, with digits 0 and 1 only, starting with 1.
%e A138149 n ..... Run ....................... Length
%e A138149 1 ..... 1,1 ....................... 2
%e A138149 2 ..... 0,0,0 ..................... 3
%e A138149 3 ..... 1,1,1,1,1 ................. 5
%e A138149 4 ..... 0,0,0,0,0,0,0 ............. 7
%e A138149 5 ..... 1,1,1,1,1,1,1,1,1,1,1 ..... 11
%Y A138149 Cf. A000040, A057211.
%Y A138149 Sequence in context: A016179 A015024 A016039 this_sequence A113047 A127692 A023533
%Y A138149 Adjacent sequences: A138146 A138147 A138148 this_sequence A138150 A138151 A138152
%K A138149 easy,nonn
%O A138149 1,1
%A A138149 Omar E. Pol (info(AT)polprimos.com), Mar 29 2008
%I A113047
%S A113047 1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A113047 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A113047 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A113047 Binomial(3n,n)/(2n+1) mod 3.
%C A113047 Conjecture: a(n) differs from 0 only when n=(3^j-1)/2,j=0,1,...
%Y A113047 Cf. A003462, A039969.
%Y A113047 Sequence in context: A015024 A016039 A138149 this_sequence A127692 A023533 A010052
%Y A113047 Adjacent sequences: A113044 A113045 A113046 this_sequence A113048 A113049 A113050
%K A113047 easy,nonn
%O A113047 0,1
%A A113047 Paul Barry (pbarry(AT)wit.ie), Oct 11 2005
%I A127692
%S A127692 1,1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
%T A127692 0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%U A127692 0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A127692 Expansion of psi(x^4)+x*psi(x^12) in powers of x where psi() is a Ramanujan theta function.
%D A127692 R. Blecksmith; J. Brillhart; I. Gerst, Some infinite product identities, Math. Comp. 51 (1988), no. 183, 301-314. MR0942157 (89f:05017)
%F A127692 Euler transform of period 24 sequence [ 1, -1, 0, 1, -1, 1, -1, 0, 0, 0, 1, -1, 1, 0, 0, 0, -1, 1, -1, 1, 0, -1, 1, -1, ...].
%F A127692 a(n)=b(2n+1) where b(n) is multiplicative and b(2^e)=0^e, b(3^e)=1, else b(p^e)=(1+(-1)^e)/2.
%F A127692 a(3n+1)=a(n), a(3n+2)=a(4n+2)=a(4n+3)=a(6n+3)=0.
%F A127692 G.f.: Sum_{k>0} x^(2k(k-1)) +x^(6k(k-1)+1) = Product_{k>0} (1-x^(24k)) (1-x^(24k-5)) (1-x^(24k-7)) (1-x^(24k-17)) (1-x^(24k-19)) (1+x^(12k-1)) (1+x^(12k-4)) (1+x^(12k-6)) (1+x^(12k-8)) (1+x^(12k-11)).
%o A127692 (PARI) {a(n)=issquare(2*n+1)+issquare(6*n+3)}
%Y A127692 Cf. A005369(n)=a(2n). A010054(n)=a(4n). A089806(n)=a(6n). A080995(n)=a(12n).
%Y A127692 Sequence in context: A016039 A138149 A113047 this_sequence A023533 A010052 A039985
%Y A127692 Adjacent sequences: A127689 A127690 A127691 this_sequence A127693 A127694 A127695
%K A127692 nonn
%O A127692 0,1
%A A127692 Michael Somos, Jan 19 2007
%I A023533
%S A023533 1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%T A023533 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%U A023533 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A023533 a(n) = 1 if n of form m(m+1)(m+2)/6, otherwise 0.
%Y A023533 Sequence in context: A138149 A113047 A127692 this_sequence A010052 A039985 A127239
%Y A023533 Adjacent sequences: A023530 A023531 A023532 this_sequence A023534 A023535 A023536
%K A023533 nonn
%O A023533 0,1
%A A023533 Clark Kimberling (ck6(AT)evansville.edu)
%I A010052
%S A010052 1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A010052 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A010052 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
%N A010052 Characteristic function of squares: 1 if n is a square else 0.
%C A010052 For n >= 1 another formula for a(n) is: a(n) = d(n) mod 2 where d(n) is the number of divisors of n, A000005. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001
%C A010052 G.f. A(x) satisfies 0=f(A(x),A(x^2),A(x^4)) where f(u,v,w)=(u-w)^2-(v-w)(v+w-1) - Michael Somos, Jul 19 2004
%D A010052 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 4.
%D A010052 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 48, Problem 20.
%H A010052 Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H A010052 Eric Weisstein's World of Mathematics, Jacobi Theta Functions
%F A010052 a(n) = [sqrt(n)] - [sqrt(n-1)] (n>0).
%F A010052 Dirichlet generating function: zeta(2s). - Franklin T. Adams-Watters, Sep 11 2005.
%F A010052 G.f. (theta_3(0,x) + 1)/2, where theta_3 is a Jacobi theta function. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 19 2006
%p A010052 readlib(issqr): f := i->if issqr(i) then 1 else 0; fi; [ seq(f(i),i=0..100) ];
%o A010052 (PARI) a(n)=issquare(n)
%Y A010052 Cf. A008836.
%Y A010052 Sequence in context: A113047 A127692 A023533 this_sequence A039985 A127239 A129186
%Y A010052 Adjacent sequences: A010049 A010050 A010051 this_sequence A010053 A010054 A010055
%K A010052 nonn,nice,easy,mult
%O A010052 0,1
%A A010052 njas
%E A010052 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 19 2006
%I A039985
%S A039985 1,1,0,0,1,0,0,0,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,
%T A039985 1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,
%U A039985 0,0,1,0,0,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,1,1,1,1,1,1
%N A039985 An example of a d-perfect sequence.
%H A039985 D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions
%H A039985 D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions
%F A039985 a(n) = A108630(n) mod 2 - Christian G. Bower (bowerc(AT)usa.net), Jun 12 2005 - Christian G. Bower (bowerc(AT)usa.net), Jun 12 2005
%Y A039985 Sequence in context: A127692 A023533 A010052 this_sequence A127239 A129186 A095901
%Y A039985 Adjacent sequences: A039982 A039983 A039984 this_sequence A039986 A039987 A039988
%K A039985 nonn
%O A039985 1,1
%A A039985 njas
%E A039985 More terms from Christian G. Bower (bowerc(AT)usa.net), Jun 12 2005
%I A127239
%S A127239 1,1,0,0,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,1,
%T A127239 1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,
%U A127239 0,0,1,0,1,1,1,1,1,0,0,1,1,0
%N A127239 Central coefficients of Thue-Morse binomial triangle A127236.
%C A127239 Hankel transform may be 0^n.
%F A127239 a(n)=A010060(binomial(2n,n))
%Y A127239 Sequence in context: A023533 A010052 A039985 this_sequence A129186 A095901 A087049
%Y A127239 Adjacent sequences: A127236 A127237 A127238 this_sequence A127240 A127241 A127242
%K A127239 easy,nonn
%O A127239 0,1
%A A127239 Paul Barry (pbarry(AT)wit.ie), Jan 10 2007
%I A129186
%S A129186 1,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,
%T A129186 0
%N A129186 Right shift operator generating 1's in shifted spaces.
%C A129186 Let A129186 = M, then M*V, V a vector; shifts V to the right, appending 1's to the shifted spaces. Example: M*V, V = [1,2,3,...] = [1,1,2,3,...].
%F A129186 Infinite lower triangular matrix with (1,0,0,...) in the main diagonal and (1,1,1...) in the subdiagonal.
%e A129186 First few rows of the triangle are:
%e A129186 1;
%e A129186 1, 0;
%e A129186 0, 1, 0;
%e A129186 0, 0, 1, 0;
%e A129186 0, 0, 0, 1, 0;
%e A129186 ...
%Y A129186 Cf. A129184, A129185.
%Y A129186 Sequence in context: A010052 A039985 A127239 this_sequence A095901 A087049 A118009
%Y A129186 Adjacent sequences: A129183 A129184 A129185 this_sequence A129187 A129188 A129189
%K A129186 nonn,tabl
%O A129186 1,1
%A A129186 Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 01 2007
%I A095901
%S A095901 1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,0,0,0,0,1,0,1,
%T A095901 0,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,
%U A095901 0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,0
%N A095901 A004001 (mod 2).
%t A095901 a[1] = a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; Table[ a[n], {n, 105}]
%Y A095901 Cf. A004001. The number of odd entries less than or equal to 2^n is in A095902.
%Y A095901 Sequence in context: A039985 A127239 A129186 this_sequence A087049 A118009 A113429
%Y A095901 Adjacent sequences: A095898 A095899 A095900 this_sequence A095902 A095903 A095904
%K A095901 easy,nonn
%O A095901 1,1
%A A095901 Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 12 2004
%I A087049
%S A087049 1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,
%T A087049 0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,0,
%U A087049 0,0,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1
%N A087049 Characteristic sequence for numbers n>=0 which are squares or have a square>1 as factor.
%C A087049 a(0)=1, a(1)=1, n>=2: a(n)=1 if isquarefree(n)=false else 0.
%C A087049 Except for a(0)=1 and a(1)=1 this is the bit-flipped unsigned Moebius sequence |A008683(n)|, n>=2.
%C A087049 For n>=2: a(n)=1 iff n is from A013929 (not square-free).
%F A087049 a(n)=1 if n is a perfect square (A000290) or has some square > 1 as a factor, else 0.
%e A087049 a(4)=1 because 4 is a square; a(8)=1 because 8=2^2*2.
%Y A087049 Cf. A080733, A000290(squares), A013929(not square-free).
%Y A087049 Sequence in context: A127239 A129186 A095901 this_sequence A118009 A113429 A133100
%Y A087049 Adjacent sequences: A087046 A087047 A087048 this_sequence A087050 A087051 A087052
%K A087049 nonn,easy
%O A087049 0,1
%A A087049 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 08 2003
%I A118009
%S A118009 1,1,0,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,1,1,1,1,1,1,0,1,
%T A118009 0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,
%U A118009 1,1,0,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A118009 a(n) = 1 if at least one of decimal digits n or the concatenation of decimal digits of n is perfect power, otherwise a(n) = 0.
%Y A118009 Sequence in context: A129186 A095901 A087049 this_sequence A113429 A133100 A077606
%Y A118009 Adjacent sequences: A118006 A118007 A118008 this_sequence A118010 A118011 A118012
%K A118009 base,easy,nonn
%O A118009 1,1
%A A118009 Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), May 11 2006
%I A113429
%S A113429 1,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,
%T A113429 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A113429 1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%V A113429 1,-1,0,0,-1,0,0,1,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%W A113429 0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,
%X A113429 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%N A113429 Expansion of f(-x,-x^4) in powers of x.
%F A113429 Euler transform of period 5 sequence [ -1, 0, 0, -1, -1, ...].
%F A113429 |a(n)| is the characteristic function of A085787.
%F A113429 G.f.: Prod_{k>0} (1-x^(5k))(1-x^(5k-1))(1-x^(5k-4)) = Sum_{k} (-1)^k x^((5k^2+3k)/2).
%F A113429 f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
%o A113429 (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1,n, 1-x^k*[1,1,0,0,1][k%5+1], 1+x*O(x^n)), n))}
%Y A113429 Sequence in context: A095901 A087049 A118009 this_sequence A133100 A077606 A004601
%Y A113429 Adjacent sequences: A113426 A113427 A113428 this_sequence A113430 A113431 A113432
%K A113429 sign
%O A113429 0,1
%A A113429 Michael Somos, Oct 31 2005
%I A133100
%S A133100 1,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,
%T A133100 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A133100 1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%N A133100 Expansion of f(x, x^4) in powers of x where f() is Ramanujan's two variable theta function.
%F A133100 The characteristic function of A085787 generalized heptagonal numbers.
%F A133100 Euler transform of period 10 sequence [ 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, ...].
%F A133100 G.f.: Prod_{k>0} (1-x^(5k)) * (1+x^(5k-1)) * (1+x^(5k-4)) = Sum_{k} x^((5*k^2 + 3*k) / 2).
%e A133100 1 + q + q^4 + q^7 + q^13 + q^18 + q^27 + q^34 + q^46 + q^55 + q^70 + ...
%o A133100 (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1,n, 1 + x^k*[ -1,1,0,0,1][k%5+1], 1+x*O(x^n)), n))}
%Y A133100 |A113429(n)| = a(n).
%Y A133100 Sequence in context: A087049 A118009 A113429 this_sequence A077606 A004601 A114915
%Y A133100 Adjacent sequences: A133097 A133098 A133099 this_sequence A133101 A133102 A133103
%K A133100 nonn
%O A133100 0,1
%A A133100 Michael Somos, Sep 11 2007
%I A077606
%S A077606 1,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
%T A077606 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%U A077606 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0
%V A077606 1,-1,0,0,1,0,0,-1,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,
%W A077606 1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
%X A077606 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0
%N A077606 Left differencing matrix, D, by antidiagonals.
%C A077606 If v is a sequence written as a column vector, then Dv is the sequence of first differences of v. The inverse of D is the left summing matrix; the transpose of D is the right differencing matrix.
%H A077606 C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.
%F A077606 D(n, n-1)=-1, D(n, n)=1, else D(n, k)=0.
%F A077606 As a sequence, a(2k^2-2k+1) = 1, a(2k^2) = -1, otherwise a(n) = 0. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 12 2007
%e A077606 Northwest corner:
%e A077606 1 0 0 0 0
%e A077606 -1 1 0 0 0
%e A077606 0 -1 1 0 0
%e A077606 0 0 -1 1 0
%e A077606 0 0 0 -1 1
%Y A077606 Cf. A077605.
%Y A077606 Cf. A001844, A001105.
%Y A077606 Sequence in context: A118009 A113429 A133100 this_sequence A004601 A114915 A074711
%Y A077606 Adjacent sequences: A077603 A077604 A077605 this_sequence A077607 A077608 A077609
%K A077606 easy,sign,tabl
%O A077606 1,1
%A A077606 Clark Kimberling (ck6(AT)evansville.edu), Nov 11 2002
%I A004601
%S A004601 1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0,
%T A004601 0,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0,1,0,0,0,1,1,0,1,0,0,1,1,
%U A004601 0,0,0,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0
%N A004601 Expansion of Pi in base 2.
%D A004601 J. P. Delahaye, Le Fascinant Nombre Pi, "100000 digits of pi in base two", pp. 209-210; Pour la Science, Paris 1997.
%H A004601 Elias's Pi Page, Binary representation of pi with 32768 digits
%H A004601 Steve Pagliarulo, Stu's pi page
%H A004601 A. Brouty, Les decimales de PI en base 2 jusqu'a 1 million
%t A004601 RealDigits[Pi, 2, 75][[1]]
%Y A004601 Cf. A000796., A119017, A068425, A117721, A065987.
%Y A004601 Pi in various bases: A004601 to A004608, A000796, A068436 to A068440, A062964. Cf. A007514.
%Y A004601 Sequence in context: A113429 A133100 A077606 this_sequence A114915 A074711 A004585
%Y A004601 Adjacent sequences: A004598 A004599 A004600 this_sequence A004602 A004603 A004604
%K A004601 nonn,base,cons
%O A004601 2,1
%A A004601 njas
%I A114915
%S A114915 1,1,0,0,1,0,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,
%T A114915 0,0,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,1,1,0,0,1,1,0,1,0,
%U A114915 1,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,1,1,1
%N A114915 Bitwise XOR of pi base 2 (A004601) and e base 2 (A004593).
%e A114915 1.1001001111011110001110111110101000001111010011100010001010111001101...
%Y A114915 Cf. A004601, A004593, A114915.
%Y A114915 Sequence in context: A133100 A077606 A004601 this_sequence A074711 A004585 A133081
%Y A114915 Adjacent sequences: A114912 A114913 A114914 this_sequence A114916 A114917 A114918
%K A114915 base,cons,nonn
%O A114915 1,1
%A A114915 Bryan Jacobs (bryanjj(AT)gmail.com), Jan 06 2006
%I A074711
%S A074711 1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1
%V A074711 1,1,0,0,-1,0,-1,0,0,1,0,0,1,-1,0,0,1,0,-1,0,0,0,1
%N A074711 Moebius function applied to A000461.
%p A074711 Lkst := proc(n): round(evalf(floor(log10(10*n)))); end; Akst := proc(n): n*(10^(n*Lkst(n))-1)/(10^Lkst(n)-1); end; with(numtheory): [seq(mobius(Akst(i)),i=1..23)];
%Y A074711 Cf. A000461.
%Y A074711 Sequence in context: A077606 A004601 A114915 this_sequence A004585 A133081 A125999
%Y A074711 Adjacent sequences: A074708 A074709 A074710 this_sequence A074712 A074713 A074714
%K A074711 easy,sign
%O A074711 0,1
%A A074711 Jani Melik (jani_melik(AT)hotmail.com), Oct 01 2002
%I A004585
%S A004585 1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0,0,1,1,1,0,1,0,1,1,0,1,
%T A004585 1,0,1,0,0,1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,
%U A004585 1,0,0,1,0,1,0,0,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,1
%N A004585 Expansion of sqrt(10) in base 2.
%Y A004585 Sequence in context: A004601 A114915 A074711 this_sequence A133081 A125999 A073784
%Y A004585 Adjacent sequences: A004582 A004583 A004584 this_sequence A004586 A004587 A004588
%K A004585 nonn,base,cons
%O A004585 2,1
%A A004585 njas
%I A133081
%S A133081 1,1,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,
%T A133081 0,0,0,0,0,0,0,0,1,1
%N A133081 An interpolation operator, companion to A133080.
%C A133081 Row sums = A040001: (1, 1, 2, 1, 2, 1, 2, 1,...). A133081 * [1,2,3,...] = A133090: (1, 1, 5, 3, 9, 5, 13, 7, 17,...). A133080: diagonal and subdiagonal are switched.
%F A133081 Infinite lower triangular matrix, (1,0,1,0,...) in the main diagonal and (1,1,1,...) in the subdiagonal.
%e A133081 First few rows of the triangle are:
%e A133081 1;
%e A133081 1, 0;
%e A133081 0, 1, 1;
%e A133081 0, 0, 1, 0;
%e A133081 0, 0, 0, 1, 1;
%e A133081 ...
%Y A133081 Cf. A133080, A133090.
%Y A133081 Sequence in context: A114915 A074711 A004585 this_sequence A125999 A073784 A128130
%Y A133081 Adjacent sequences: A133078 A133079 A133080 this_sequence A133082 A133083 A133084
%K A133081 nonn,tabl
%O A133081 1,1
%A A133081 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 09 2007
%I A125999
%S A125999 1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,1,
%T A125999 1,0,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0,1,0,
%U A125999 1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,0
%N A125999 Square array A(g,h) = 1 if combinatorial game g has value greater than or equal to that of game h, otherwise 0, listed antidiagonally in order A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), ...
%C A125999 Here we use the encoding explained in A106486. A(i,j) = A(A106485(j),A106485(i)).
%H A125999 A. Karttunen, Scheme-program for computing this sequence.
%Y A125999 Row 0 is the characteristic function of A126001 (shifted one step) and similarly, column 0 is the characteristic function of A126002. Cf. tables A126010 and A126000.
%Y A125999 Sequence in context: A074711 A004585 A133081 this_sequence A073784 A128130 A133872
%Y A125999 Adjacent sequences: A125996 A125997 A125998 this_sequence A126000 A126001 A126002
%K A125999 nonn,tabl
%O A125999 0,1
%A A125999 Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Dec 18 2006
%I A073784
%S A073784 1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0,
%T A073784 1,0,0,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,
%U A073784 1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,1,0
%N A073784 Number of primes between successive composite numbers.
%e A073784 a(7) = 0 since there are no primes between the 7th and the 8th composites, (14 and 15).
%t A073784 Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[ PrimePi[Composite[n + 1]] - PrimePi[Composite[n]], {n, 105}] (from Robert G. Wilson v Dec 20 2004)
%Y A073784 a(n) = A073783(n) - 1
%Y A073784 a(n) = A002808(n+1) - A002808(n) - 1
%Y A073784 Also first differences of A073425.
%Y A073784 Sequence in context: A004585 A133081 A125999 this_sequence A128130 A133872 A071026
%Y A073784 Adjacent sequences: A073781 A073782 A073783 this_sequence A073785 A073786 A073787
%K A073784 easy,nonn
%O A073784 1,1
%A A073784 Lior Manor (lior.manor(AT)gmail.com) Aug 11 2002
%I A128130
%S A128130 1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,
%T A128130 0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,
%U A128130 0,0
%V A128130 1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,
%W A128130 0,0,1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,0,0,1,-1,0,0,-1,1,0,0
%N A128130 Expansion of (1-x)/(1+x^4).
%F A128130 a(n)=(sqrt(2)/4+1/2)cos(3*pi*n/4)-sqrt(2)sin(3*pi*n/4)/4+(1/2-sqrt(2)/4)cos(pi*n/4)-sqrt(2)sin(pi*n/4)/4; a(n)=Im{sum{k=0..n, i^(n-k+1)}}, i=sqrt(-1);
%F A128130 a(n)=(1/8)*{-(n mod 8)+[(n+2) mod 8]-2*[(n+3) mod 8]+[(n+4) mod 8]-[(n+6) mod 8]+2*[(n+7) mod 8]}, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Oct 23 2007
%Y A128130 Sequence in context: A133081 A125999 A073784 this_sequence A133872 A071026 A068434
%Y A128130 Adjacent sequences: A128127 A128128 A128129 this_sequence A128131 A128132 A128133
%K A128130 easy,sign
%O A128130 0,1
%A A128130 Paul Barry (pbarry(AT)wit.ie), Feb 15 2007
%I A133872
%S A133872 1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,
%T A133872 0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,
%U A133872 0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1
%N A133872 n modulo 2 twice.
%C A133872 Periodic with length 2^2=4.
%C A133872 Partial sums of A056594.
%C A133872 Let i=sqrt(-1) and S(n)=Sum_{k=0..n-1} exp(2*pi*i*k^2/n) for n>=1 the famouse Gauss sum. Then S(n)=(a(n)+a(n+1)*i)*sqrt(n). - Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Nov 08 2007
%C A133872 For any n>=1 the sequence gives the minimum value m>=0 we can get using addition and subtraction among all the numbers from 1 to n. E.g.: n=1 -> m=1; n=2 -> m=2-1=1; n=3 -> m=3-2-1=0; n=4 -> m=4-3-2+1=0; n=5 -> m=5-4+3-2-1=1; n=6 -> m=6+5-4-3-2-1=6-5+4-3-2+1=1; n=7 -> m=7-6+5-4-3+2-1=7+6-5-4-3-2+1=0; etc. - Paolo P. Lava (ppl(AT)spl.at), Feb 29 2008
%F A133872 a(n)=(1+floor(n/2)) mod 2.
%F A133872 a(n)=A004526(A000035(n+2)).
%F A133872 a(n)=1+floor(n/2)-2*floor((n+2)/4).
%F A133872 a(n)=(((n+2) mod 4)-(n mod 2))/2.
%F A133872 a(n)=((n+2-(n mod 2))/2) mod 2.
%F A133872 a(n)=((2n+3+(-1)^n)/4) mod 2.
%F A133872 a(n)=(1+(-1)^((2n-1+(-1)^n)/4))/2.
%F A133872 a(n)=binomial(n+2,n) mod 2 =binomial(n+2,2) mod 2.
%F A133872 a(n)=A000217(n+1) mod 2.
%F A133872 G.f. g(x)=(1+x)/(1-x^4).
%F A133872 G.f. g(x)=1/((1-x)(1+x^2)).
%F A133872 a(n) = 1/2+(1/2)*cos(Pi*n/2)+(1/2)*sin(Pi*n/2). a(n) = A021913(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 15 2007
%Y A133872 Cf. A056594. A133620-A133625, A133630, A133633-A133636. A021913. A000217.
%Y A133872 Cf. A133882, A133880, A133890, A133900, A133910.
%Y A133872 Sequence in context: A125999 A073784 A128130 this_sequence A071026 A068434 A127015
%Y A133872 Adjacent sequences: A133869 A133870 A133871 this_sequence A133873 A133874 A133875
%K A133872 nonn
%O A133872 0,1
%A A133872 Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Oct 10 2007
%I A071026
%S A071026 1,1,0,0,1,1,0,1,0,1,1,1,1,1,0,0,0,1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,0,1,
%T A071026 1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,1,1,0,0,0,1,
%U A071026 1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0
%N A071026 Triangle read by rows giving successive states of cellular automaton generated by "rule 188".
%C A071026 Row n has length n+1.
%D A071026 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071026 Index entries for sequences related to cellular automata
%Y A071026 Sequence in context: A073784 A128130 A133872 this_sequence A068434 A127015 A068432
%Y A071026 Adjacent sequences: A071023 A071024 A071025 this_sequence A071027 A071028 A071029
%K A071026 nonn,tabl
%O A071026 0,1
%A A071026 Hans Havermann (pxp(AT)rogers.com), May 26 2002
%I A068434
%S A068434 1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,
%T A068434 0,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,1,1,1,1,1,1,0,1,1,
%U A068434 1,1,1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,1,1,0,0,0,0,0,0,1,1,1
%N A068434 Expansion of log(5) in base 2.
%Y A068434 Sequence in context: A128130 A133872 A071026 this_sequence A127015 A068432 A134668
%Y A068434 Adjacent sequences: A068431 A068432 A068433 this_sequence A068435 A068436 A068437
%K A068434 cons,easy,nonn
%O A068434 1,1
%A A068434 Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2002
%I A127015
%S A127015 1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1
%N A127015 Digits of the 2-adic integer lim_{n->infty} A127014(n).
%C A127015 A127014(n) = smallest k such that A(k) == 0 mod 2^n, where A(0) = 1 and A(k) = k*A(k-1) + 1 = A000522(k).
%D A127015 N. Koblitz, p-adic Numbers, p-adic Analysis and Zeta-Functions, 2nd ed., Springer, New York, 1996.
%H A127015 J. Sondow, Which Partial Sums of the Taylor Series for e Are Convergents to e? (and a Link to the Primes $2, 5, 13, 37, 463, ...$) with an Appendix "Periodic Behaviour of Some Recurrence Sequences Related to $e$, Modulo Powers of 2" by Kyle Schalm
%e A127015 In 2-adic notation (aka reverse binary) A127014(26) = 11001110010100010100110001.
%Y A127015 Cf. A000522, A127014.
%Y A127015 Sequence in context: A133872 A071026 A068434 this_sequence A068432 A134668 A092444
%Y A127015 Adjacent sequences: A127012 A127013 A127014 this_sequence A127016 A127017 A127018
%K A127015 nonn
%O A127015 1,1
%A A127015 Kyle Schalm (kschalm(AT)math.utexas.edu), Jan 07 2007
%I A068432
%S A068432 1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,0,1,
%T A068432 1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,1,1,1,0,
%U A068432 0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0
%N A068432 Expansion of golden ratio = (1+sqrt(5))/2 in base 2.
%Y A068432 Sequence in context: A071026 A068434 A127015 this_sequence A134668 A092444 A039963
%Y A068432 Adjacent sequences: A068429 A068430 A068431 this_sequence A068433 A068434 A068435
%K A068432 cons,easy,nonn
%O A068432 1,1
%A A068432 Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2002
%I A134668
%S A134668 1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,
%T A134668 1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,
%U A134668 1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,1,1,0
%V A134668 1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,
%W A134668 -1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,
%X A134668 -1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0,0,-1,1,1,-1,0
%N A134668 Period 6: repeat 1, -1, 0, 0, -1, 1 .
%F A134668 First differences of A134667.
%F A134668 a(n)=(1/6)*{-2*[(n+1) mod 6]+[(n+2) mod 6]-[(n+4) mod 6]+2*[(n+5) mod 6]}, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jan 28 2008
%F A134668 Euler transform of length 6 sequence [ -1, 0, 0, -1, 0, 1]. - Michael Somos Feb 08 2008
%F A134668 a(-1-n) = a(n). - Michael Somos Feb 08 2008
%F A134668 G.f.: (1 - x) * (1 - x^4) / (1 - x^6) = (1 - x) * (1 + x^2) / ((1 - x+ x^2) * (1 + x + x^2)) = (1 - x + x^2 - x^3) / (1 + x^2 + x^4).
%e A134668 1 - x - x^4 + x^5 + x^6 - x^7 - x^10 + x^11 + x^12 - x^13 - x^16 + ...
%o A134668 (PARI) {a(n) = [1, -1, 0, 0, -1, 1][n%6+1]} /* Michael Somos Feb 08 2008 */
%Y A134668 Sequence in context: A068434 A127015 A068432 this_sequence A092444 A039963 A058840
%Y A134668 Adjacent sequences: A134665 A134666 A134667 this_sequence A134669 A134670 A134671
%K A134668 sign,easy
%O A134668 0,1
%A A134668 Paul Curtz (bpcrtz(AT)free;fr), Jan 26 2008
%I A092444
%S A092444 1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0
%N A092444 Duplicate of A039963.
%Y A092444 Sequence in context: A127015 A068432 A134668 this_sequence A039963 A058840 A036987
%Y A092444 Adjacent sequences: A092441 A092442 A092443 this_sequence A092445 A092446 A092447
%K A092444 dead
%O A092444 0,1
%I A039963
%S A039963 1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,
%T A039963 0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,
%U A039963 1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1
%N A039963 The period-doubling sequence A035263 repeated.
%C A039963 An example of a d-perfect sequence.
%C A039963 Motzkin numbers mod 2. - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 23 2004
%C A039963 Let {a, b, c, c, a, b, a, b, a, b, c, c, a, b, ...} be the fixed point of the morphism : a -> ab, b -> cc, c -> ab, starting from a; then the sequence is obtained by taking a = 1, b = 1, c = 0. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 28 2004
%H A039963 D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions
%H A039963 D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions
%F A039963 a(n)=A035263(1+floor(n/2)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 23 2004
%F A039963 a(n) = A040039(n) mod 2 = A002212(n+1) mod 2 . a(0) = a(1) = 1, for n>=2 : a(n) = ( a(n) + sum_{k= 0, (n-2)} a(k)*a(n-2-k)) mod 2 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 26 2004
%F A039963 a(n) = (A(n+2) - A(n)) mod 2, for A = A019300, A001285, A010060, A010059, A000069, A001969. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 28 2004
%F A039963 a(n) = A001006(n) mod 2 = A092444(n) - Christian G. Bower (bowerc(AT)usa.net), Jun 12 2005
%t A039963 Flatten[ Nest[ Function[l, {Flatten[(l /. {a -> {a, b}, b -> {c, c}, c -> {a, b}})]}], {a}, 7] /. {a -> {1}, b -> {1}, c -> {0}}] (from Robert G. Wilson v Feb 26 2005)
%Y A039963 Cf. A081706.
%Y A039963 Sequence in context: A068432 A134668 A092444 this_sequence A058840 A036987 A113430
%Y A039963 Adjacent sequences: A039960 A039961 A039962 this_sequence A039964 A039965 A039966
%K A039963 nonn
%O A039963 0,1
%A A039963 njas
%E A039963 More terms from Christian G. Bower (bowerc(AT)usa.net), Jun 12 2005
%E A039963 Edited by njas at the suggestion of Andrew Plewe and Ralf Stephan, Jul 13 2007
%I A058840
%S A058840 1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,
%T A058840 0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U A058840 1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0
%N A058840 From Renyi's "beta expansion of 1 in base 3/2": sequence gives y(0), y(1), ...
%C A058840 Let r be a real number strictly between 1 and 2, x any real number between 0 and 1; define y = (y(i)) by x(0) = x; x(i+1) = r*x(i)-1 if r*x(i)>1 and r*x(i) otherwise; y(i) = integer part of x(i+1): y = (y(i)) is an infinite word on the alphabet (0,1). Here we take r = 3/2 and x = 1.
%D A058840 A. Renyi (1957), Representation for real numbers and their ergodic properties, Acta. Math. Acad. Sci. Hung., 8, 477-493.
%Y A058840 Cf. A058841, A058842.
%Y A058840 Sequence in context: A134668 A092444 A039963 this_sequence A036987 A113430 A113681
%Y A058840 Adjacent sequences: A058837 A058838 A058839 this_sequence A058841 A058842 A058843
%K A058840 nonn,nice,easy
%O A058840 0,1
%A A058840 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001
%E A058840 More terms from Larry Reeves (larryr(AT)acm.org), Feb 22 2001
%I A036987
%S A036987 1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%T A036987 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A036987 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A036987 Fredholm-Rueppel sequence.
%C A036987 a(n+1) = a(floor(n/2)) * (n mod 2); a(0)=1. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 02 2002
%C A036987 Sum {0..infinity} 1/10^(2^n) = 0.110100010000000100000000000000010...
%C A036987 Binary representation of Kempner-Mahler number sum(k>=0,1/2^(2^k)).
%C A036987 Also a(n) == mod(A(n), 2) where A is any of A001700, A005573, A007854, A026641, A049027, A064063, A064088, A064090, A064092, A064 325, A064327, A064329, A064331, A064613, A076026, A105523, A123273, A126694, A126930, A126931, A126982, A126983, A126987, A127016, A127053, A127358, A127360, A127361, A127363 - Philippe DELEHAM (kolotoko@wanadoo.fr), May 26 2007
%C A036987 a(n) = (product of digits of n; n in binary notation) mod 2. This sequence is a transformation of the Thue-Morse sequence (A010060), since there exists a function f such that f(sum of digits of n) = (product of digits of n). - Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Feb 12 2008
%D A036987 H. Niederreiter and M. Vielhaber, Tree complexity and a doubly ..., J. Complexity, 12 (1996), 187-198.
%H A036987 D. Bailey et al., On the binary expansions of algebraic numbers
%H A036987 Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
%H A036987 D. Kohel, S. Ling and C. Xing, Explicit Sequence Expansions
%H A036987 E. Sheppard, net.math post (1985)
%H A036987 Stephen Wolfram, [Page 1092] A New Kind of Science | Online.
%F A036987 1 followed by a string of 2^k - 1 0's. Also a(n)=1 iff n = 2^m - 1.
%F A036987 Right-shifted sequence is multiplicative with a(2^e) = 1, a(p^e) = 0 otherwise. - Mitch Harris, Apr 19 2005.
%F A036987 1 if n=0, [log2(n+1)]-[log2(n)] else. G.f.: 1/x * Sum(k>=0, x^2^k) = Sum(k>=0, x^(2^k-1)). - Ralf Stephan, Apr 28 2003
%F A036987 a(n)=-sumdiv(n+1, d, mu(2*d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 24 2003
%F A036987 Dirichlet g.f. for right-shifted sequence: 2^(-s)/(1-2^(-s)).
%F A036987 a(n)=mod(A000108(n), 2)=mod(A001405(n), 2) - Paul Barry (pbarry(AT)wit.ie), Nov 22 2004
%F A036987 a(n)=sum{k=0..n, (-1)^(n-k)*C(n,k)*sum{j=0..k, C(k,2^j-1)}}; - Paul Barry (pbarry(AT)wit.ie), Jun 01 2006
%p A036987 A036987 := n -> `if`(((2^floor_log_2(n+1)) = (n+1)),1,0);
%p A036987 floor_log_2 := proc(n) local nn,i; nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi; nn := floor(nn/2); od; end;
%t A036987 RealDigits[ N[ Sum[1/10^(2^n), {n, 0, Infinity}], 110]][[1]]
%o A036987 (PARI) a(n)=if(n<0,0,n++; n==2^valuation(n,2))
%Y A036987 Cf. A007404, A078885, A078585, A078886, A078887, A078888, A078889, A078890.
%Y A036987 The first row of A073346. Occurs for first time in A073202 as the row 6 (and 8).
%Y A036987 Congruent to any of the sequences A000108, A007460, A007461, A007463, A007464, A061922, A068068 reduced modulo 2. Characteristic function of A000225.
%Y A036987 If interpreted with offset=1 instead of 0 (i.e. a(1)=1, a(2)=1, a(3)=0, a(4)=1, ...) then this is the characteristic function of 2^n (A000079) and as such occurs as the first row of A073265. Also, in that case the INVERT transform will produce A023359.
%Y A036987 A043545(n)=1-a(n).
%Y A036987 This is Guy Steele's sequence GS(1,3), also GS(3,1) (see A135416).
%Y A036987 Sequence in context: A092444 A039963 A058840 this_sequence A113430 A113681 A010054
%Y A036987 Adjacent sequences: A036984 A036985 A036986 this_sequence A036988 A036989 A036990
%K A036987 nonn,mult
%O A036987 0,1
%A A036987 njas
%I A113430
%S A113430 1,1,0,1,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,
%T A113430 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,
%U A113430 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%V A113430 1,-1,0,-1,0,0,0,1,1,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,
%W A113430 0,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%X A113430 0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0
%N A113430 Expansion of f(-x)f(-x^10)/f(-x^2,-x^8) in powers of x.
%C A113430 f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function and f(-x):=f(-x,-x^2).
%F A113430 Euler transform of period 10 sequence [ -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, ...].
%F A113430 |a(n)| is the characteristic function of A093722.
%F A113430 G.f.: Prod_{k>0} (1-x^k)/((1-x^(10k-2))(1-x^(10k-8))) = Sum_{k} x^((15k^2+k)/2) -x^((15k^2-11k+2)/2).
%o A113430 (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1,n, 1-x^k*[1,1,0,1,1,1,1,1, 0,1][k%10+1], 1+x*O(x^n)), n))}
%Y A113430 Sequence in context: A039963 A058840 A036987 this_sequence A113681 A010054 A106459
%Y A113430 Adjacent sequences: A113427 A113428 A113429 this_sequence A113431 A113432 A113433
%K A113430 sign
%O A113430 0,1
%A A113430 Michael Somos, Oct 31 2005
%I A113681
%S A113681 1,1,0,1,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,
%T A113681 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,
%U A113681 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%V A113681 1,1,0,-1,0,0,0,-1,-1,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,
%W A113681 0,1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,
%X A113681 0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
%N A113681 Expansion of f(-x^2,-x^3)^2/f(-x,-x^2) in powers of x.
%C A113681 f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
%F A113681 Euler transform of period 5 sequence [1, -1, -1, 1, -1, ...].
%F A113681 G.f.: Sum_{k} (-1)^k(x^((15k^2-k)/2) +x^((15k^2-11k)/2+1)).
%F A113681 G.f.: Product_{k>0} (1-x^(5k))(1-x^(5k-2))(1-x^(5k-3))/((1-x^(5k-1))(1-x^(5k-4))).
%o A113681 (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1,n,(1-x^k)^((k%5==0)-kronecker(5,k)),1+x*O(x^n)), n))}
%o A113681 (PARI) {a(n)=n*=5; if(issquare(24*n+1, &n), kronecker(12, n))}
%Y A113681 Cf. A113430. A010815(5n)=a(n).
%Y A113681 Sequence in context: A058840 A036987 A113430 this_sequence A010054 A106459 A033806
%Y A113681 Adjacent sequences: A113678 A113679 A113680 this_sequence A113682 A113683 A113684
%K A113681 sign
%O A113681 0,1
%A A113681 Michael Somos, Nov 04 2005
%I A010054
%S A010054 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A010054 0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U A010054 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A010054 a(n) = 1 if n is a triangular number else 0.
%C A010054 Ramanujan's theta function f(a,b)=Sum a^{n*(n+1)/2}*b^{n*(n-1)/2}, n=-inf..inf.
%C A010054 Euler transform of period 2 sequence [1,-1,...].
%C A010054 This sequence is the concatenation of the base-b digits in the sequence b^n, for any base b >= 2. - Davis Herring (herring(AT)lanl.gov), Nov 16 2004
%C A010054 Number of partitions of n into distinct parts such that the greatest part equals the number of all parts, see also A047993; a(n)=A117195(n,0) for n>0; a(n)=1-A117195(n,1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Mar 03 2006
%H A010054 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
%F A010054 G.f.: theta2(q)/(2*q^(1/4)) = f(q, q^3) where f is Ramanujan's theta function.
%F A010054 G.f.: Product_{k>0} (1-x^(2*k))/(1-x^(2*k-1)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 02 2002
%F A010054 a(0)=1; for n>0, a(n)=A002024(n+1)-A002024(n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 05 2004
%F A010054 G.f.: sum(j=0, oo, product(k=0, j, x^j)) - Jon Perry (perry(AT)globalnet.co.uk), Mar 30 2004
%F A010054 Expansion of q^(-1/8)eta(q^2)^2/eta(q) in powers of q.
%F A010054 Given g.f. A(x), then B(x)=x*A(x^8) satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1, u2, u3, u6)=u1*u6^3 +u2*u3^3 -u1*u2^2*u6. - Michael Somos Apr 13 2005
%F A010054 a(n)=b(8n+1) where b(n) is multiplicative and b(2^e)=0^e, b(p^e)=(1+(-1)^e)/2 if p>2. - Michael Somos Jun 06 2005
%F A010054 a(n) = floor((1-cos(Pi*sqrt(8*n+1)))/2) - Carl R. White (oeisfan(AT)cyreksoft.yorks.com), Mar 18 2006
%F A010054 a(n)=round(sqrt(2n+1))-round(sqrt(2n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 06 2007
%F A010054 a(n)=ceiling(2*sqrt(2n+1))-floor(2*sqrt(2n))-1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 06 2007
%e A010054 Comment from Philippe DELEHAM, Jan 04 2008: As a triangle this begins:
%e A010054 1;
%e A010054 1, 0;
%e A010054 1, 0, 0;
%e A010054 1, 0, 0, 0;
%e A010054 1, 0, 0, 0, 0;
%e A010054 1, 0, 0, 0, 0, 0 ; ...
%o A010054 (PARI) a(n)=local(X); if(n<0,0,X=x+x*O(x^n); polcoeff(eta(X^2)^2/eta(X),n))
%o A010054 (PARI) a(n)=if(n<0,0,issquare(8*n+1))
%Y A010054 Cf. A000217, A023531.
%Y A010054 a(n) = A035214(n) - 1. Also a(n) = A005369(2n).
%Y A010054 Sequence in context: A036987 A113430 A113681 this_sequence A106459 A033806 A033802
%Y A010054 Adjacent sequences: A010051 A010052 A010053 this_sequence A010055 A010056 A010057
%K A010054 nonn,tabl
%O A010054 0,1
%A A010054 njas
%E A010054 Additional comments from Michael Somos, Apr 27, 2000.
%I A106459
%S A106459 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A106459 0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%U A106459 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0
%V A106459 1,-1,0,-1,0,0,1,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,
%W A106459 0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
%X A106459 0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A106459 Expansion of q^(-1)eta(q^8)eta(q^32)/eta(q^16) in powers of q^8.
%D A106459 D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; p. 53, Exer. 2.2.10
%F A106459 Euler transform of period 4 sequence [ -1, 0, -1, -1, ...].
%F A106459 Given g.f. A(x), then B(x)=x*A(x^8) satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1, u2, u3, u6)=u1^4*u6^4 +u1^3*u2*u3^3*u6 +2*u1*u2^3*u3*u6^3 -u2^4*u3^4.
%F A106459 a(n)=b(8n+1) where b(n) is multiplicative and b(p^e) = kronecker(8, p)^(e/2) if e even, b(p^e) = 0 if e odd.
%F A106459 G.f.: 1/B(x) where B(x)= g.f. A006950.
%F A106459 Expansion of psi(-q)=f(-q,-q^3) in powers of q where f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
%F A106459 G.f.: Product_{k>0} (1-x^k)*(1+x^(2*k)) = Product_{k>0} (1-x^k)*(1-x^(4*k-2)).
%F A106459 G.f.: Product_{k>0} (1-x^(2*k))/(1+x^(2*k-1)) = Product_{k>0} (1-x^(4*k))*(1-x^(2*k-1)).
%F A106459 Sum_{k>=0} a(k)x^(8k+1) = Sum_{k} (-1)^k x^((4k+1)^2).
%F A106459 G.f.: Sum_{k>=0} (-x)^(k*(k+1)/2) = Sum_{k} x^(8k^2+2k) -x^(8k^2+6k+1)
%e A106459 q - q^9 - q^25 + q^49 + q^81 - q^121 - q^169 + q^225 + q^289 -...
%o A106459 (PARI) {a(n)=local(A); if(n<0,0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)/eta(x^2+A), n))}
%o A106459 (PARI) {a(n)=local(x); if(issquare(8*n+1, &x), kronecker(8, x))}
%Y A106459 Sequence in context: A113430 A113681 A010054 this_sequence A033806 A033802 A033800
%Y A106459 Adjacent sequences: A106456 A106457 A106458 this_sequence A106460 A106461 A106462
%K A106459 sign
%O A106459 0,1
%A A106459 Michael Somos, May 02 2005
%I A033806
%S A033806 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A033806 0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0
%N A033806 Product t2(q^d); d | 47, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033806 Sequence in context: A113681 A010054 A106459 this_sequence A033802 A033800 A033796
%Y A033806 Adjacent sequences: A033803 A033804 A033805 this_sequence A033807 A033808 A033809
%K A033806 nonn
%O A033806 0,1
%A A033806 njas
%I A033802
%S A033802 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A033802 0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0
%N A033802 Product t2(q^d); d | 43, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033802 Sequence in context: A010054 A106459 A033806 this_sequence A033800 A033796 A033790
%Y A033802 Adjacent sequences: A033799 A033800 A033801 this_sequence A033803 A033804 A033805
%K A033802 nonn
%O A033802 0,1
%A A033802 njas
%I A033800
%S A033800 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A033800 0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0
%N A033800 Product t2(q^d); d | 41, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033800 Sequence in context: A106459 A033806 A033802 this_sequence A033796 A033790 A033788
%Y A033800 Adjacent sequences: A033797 A033798 A033799 this_sequence A033801 A033802 A033803
%K A033800 nonn
%O A033800 0,1
%A A033800 njas
%I A033796
%S A033796 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A033796 0,1,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0
%N A033796 Product t2(q^d); d | 37, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033796 Sequence in context: A033806 A033802 A033800 this_sequence A033790 A033788 A033782
%Y A033796 Adjacent sequences: A033793 A033794 A033795 this_sequence A033797 A033798 A033799
%K A033796 nonn
%O A033796 0,1
%A A033796 njas
%I A033790
%S A033790 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A033790 0,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0,0
%N A033790 Product t2(q^d); d | 31, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033790 Sequence in context: A033802 A033800 A033796 this_sequence A033788 A033782 A033778
%Y A033790 Adjacent sequences: A033787 A033788 A033789 this_sequence A033791 A033792 A033793
%K A033790 nonn
%O A033790 0,1
%A A033790 njas
%I A033788
%S A033788 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
%T A033788 0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,
%U A033788 0
%N A033788 Product t2(q^d); d | 29, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033788 Sequence in context: A033800 A033796 A033790 this_sequence A033782 A033778 A055088
%Y A033788 Adjacent sequences: A033785 A033786 A033787 this_sequence A033789 A033790 A033791
%K A033788 nonn
%O A033788 0,1
%A A033788 njas
%I A033782
%S A033782 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,
%T A033782 0,1,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0,1,1,0,0,0,0,0
%N A033782 Product t2(q^d); d | 23, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033782 Sequence in context: A033796 A033790 A033788 this_sequence A033778 A055088 A068427
%Y A033782 Adjacent sequences: A033779 A033780 A033781 this_sequence A033783 A033784 A033785
%K A033782 nonn
%O A033782 0,1
%A A033782 njas
%I A033778
%S A033778 1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,1,1,1,1,0,0,1,0,
%T A033778 0,1,1,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,
%U A033778 0
%N A033778 Product t2(q^d); d | 19, where t2 = theta2(q)/(2*q^(1/4)).
%Y A033778 Sequence in context: A033790 A033788 A033782 this_sequence A055088 A068427 A080545
%Y A033778 Adjacent sequences: A033775 A033776 A033777 this_sequence A033779 A033780 A033781
%K A033778 nonn
%O A033778 0,1
%A A033778 njas
%I A055088
%S A055088 1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,
%T A055088 0,1,0,0,1,1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,1,1,
%U A055088 0,0,0,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0,0
%N A055088 Triangle of generalized Legendre symbols L(a/b), with 1's for quadratic residues and 0's for quadratic non-residues.
%C A055088 For every prime of the form 4k+1 (A002144) the row is symmetric and for every prime of the form 4k+3 (A002145) the row is "complementarily symmetric".
%F A055088 [seq(quadres_0_1_array(j), j=1..)]; (See Maple code below)
%e A055088 Terms are L(1/2); L(1/3), L(2/3); L(1/4), L(2/4), L(3/4); L(1/5), ... where L(a/b) is 1 if an integer c exists such that c^2 is congruent to a (mod b) and 0 otherwise.
%e A055088 E.g. the tenth row gives the quadratic residues and non-residues of 11 (see A011582) and the twelfth row gives the same information for 13 (A011583), with -1's replaced by zeros.
%p A055088 with(numtheory,quadres); quadres_0_1_array := (n) -> one_or_zero(quadres((n-((trinv(n-1)*(trinv(n-1)-1))/2)),(trinv(n-1)+1)));
%Y A055088 Cf. A054431 for one_or_zero and trinv. Each row interpreted as a binary number: A055094.
%Y A055088 Sequence in context: A033788 A033782 A033778 this_sequence A068427 A080545 A141735
%Y A055088 Adjacent sequences: A055085 A055086 A055087 this_sequence A055089 A055090 A055091
%K A055088 nonn,tabl
%O A055088 1,1
%A A055088 Antti Karttunen Apr 18 2000
%I A068427
%S A068427 1,1,0,1,0,0,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,1,0,0,
%T A068427 1,1,0,0,0,0,0,1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,1,0,0,0,0,1,1,1,0,0,
%U A068427 1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1
%N A068427 Expansion of zeta(2) in base 2.
%Y A068427 Sequence in context: A033782 A033778 A055088 this_sequence A080545 A141735 A073097
%Y A068427 Adjacent sequences: A068424 A068425 A068426 this_sequence A068428 A068429 A068430
%K A068427 cons,easy,nonn
%O A068427 1,1
%A A068427 Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2002
%I A080545
%S A080545 1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,
%T A080545 0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,
%U A080545 0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0
%N A080545 Characteristic function of {1} union {odd primes}: 1 if n is 1 or an odd prime, else 0.
%Y A080545 Cf. A010051, A080355, A080339, A080567.
%Y A080545 Sequence in context: A033778 A055088 A068427 this_sequence A141735 A073097 A117569
%Y A080545 Adjacent sequences: A080542 A080543 A080544 this_sequence A080546 A080547 A080548
%K A080545 nonn
%O A080545 1,1
%A A080545 njas, Mar 21 2003
%I A141735
%S A141735 1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0,1,1,
%T A141735 0,0,0,1,1,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,1,0,0,1,
%U A141735 0,0,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0,0,1,1,0,1,0,1,1,1,0,0
%N A141735 List of the 0s and 1s digits of triangle A141727 along a boustrophedon path. First case: see example below.
%e A141735 First boustrophedon path:
%e A141735 ................................/1.
%e A141735 .............................../_____
%e A141735 ...............................1.0.1.\
%e A141735 ............................._________\
%e A141735 .........................../.1.0.0.1.0.
%e A141735 .........................../______________
%e A141735 ...........................1.0.1.0.1.0.0.\
%e A141735 .........................__________________\
%e A141735 ......................./.1.0.0.1.1.0.1.1.1
%e A141735 ......................./_____________________
%e A141735 .......................1.0.1.0.0.0.0.0.1.1.0
%Y A141735 Cf. A141727 - A141734, A141736 - A141746.
%Y A141735 Sequence in context: A055088 A068427 A080545 this_sequence A073097 A117569 A135528
%Y A141735 Adjacent sequences: A141732 A141733 A141734 this_sequence A141736 A141737 A141738
%K A141735 easy,nonn
%O A141735 1,1
%A A141735 Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jul 02 2008
%I A073097
%S A073097 1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%T A073097 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U A073097 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1
%V A073097 -1,-1,0,-1,0,1,0,1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,-1,0,1,0,1,0,-1,0,
%W A073097 1,0,1,0,1,0,-1,0,-1,0,1,0,-1,0,-1,0,1,0,1,0,-1,0,-1,0,-1,0,1,0,1,0,-1,0,1,0,1,0,1,0,
%X A073097 -1,0,-1,0,1,0,1,0,-1,0,1,0,1,0,-1,0,-1,0,-1,0,1,0,-1,0,-1
%N A073097 Let x(n) denote the number of 4's among the n first elements of the continued fraction for sum k>=0 1/2^(2^k) (A007400 ), y(n) the number of 6's and z(n) the number of 2's. Then a(n)=x(n)-y(n)-z(n)-1.
%C A073097 The positive sequence has a(n)=mod(A000120(A047849(n)),2)=mod(A000120(A078008(2n)),2) - Paul Barry (pbarry(AT)wit.ie), Jan 13 2005
%C A073097 Cosh(1) in 'reflected factorial' base is 1.10101010101010101010101010101010101010101010... - see A091337 for Sinh(1) (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 04 2005)
%F A073097 It seems that a(2k+1)=0 for k>=1.
%F A073097 The positive sequence (assuming the pattern continues) has g.f. (1+x-x^2)/((1-x)(1-x^2)), with a(n)=(1-(1)^n)/2+0^n=mod((1+A001045(n+1))/2, 2) =mod(A005578, 2). The partial sums are A008619(n+1). - Paul Barry (pbarry(AT)wit.ie), Apr 28 2004
%Y A073097 Cf. A007400.
%Y A073097 Sequence in context: A068427 A080545 A141735 this_sequence A117569 A135528 A071040
%Y A073097 Adjacent sequences: A073094 A073095 A073096 this_sequence A073098 A073099 A073100
%K A073097 sign
%O A073097 0,1
%A A073097 Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 18 2002
%I A117569
%S A117569 1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%T A117569 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U A117569 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
%V A117569 1,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,
%W A117569 0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,
%X A117569 0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0,1,0,-1,0
%N A117569 Expansion of (1+x+x^2)/(1+x^2).
%C A117569 Row sums of A117568.
%F A117569 G.f.: (1-x^3)/((1-x)(1+x^2)); a(n)=0^n+(1-(-1)^n)(cos(pi*n/2)+sin(pi*n/2))/2;
%F A117569 a(n)=A101455(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 10 2008]
%Y A117569 Cf. A073097.
%Y A117569 Sequence in context: A080545 A141735 A073097 this_sequence A135528 A071040 A078387
%Y A117569 Adjacent sequences: A117566 A117567 A117568 this_sequence A117570 A117571 A117572
%K A117569 easy,sign,new
%O A117569 0,1
%A A117569 Paul Barry (pbarry(AT)wit.ie), Mar 29 2006
%I A135528
%S A135528 1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%T A135528 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U A135528 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0
%N A135528 1, then repeat 1,0.
%F A135528 a(n)=(1/2)*[1+(-1)^n]+{C[2*(n-1),(n-1)] mod 2}, with n>=1 - Paolo P. Lava (ppl(AT)spl.at), Mar 03 2008
%p A135528 GS(2,1,200); [see A135416].
%Y A135528 Cf. A135416.
%Y A135528 This is Guy Steele's sequence GS(2,1) (see A135416).
%Y A135528 Sequence in context: A141735 A073097 A117569 this_sequence A071040 A078387 A105470
%Y A135528 Adjacent sequences: A135525 A135526 A135527 this_sequence A135529 A135530 A135531
%K A135528 nonn
%O A135528 1,1
%A A135528 njas, based on a message from Guy Steele and D. E. Knuth, Mar 01 2008
%I A071040
%S A071040 1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%T A071040 1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%U A071040 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0
%N A071040 Triangle read by rows giving successive states of cellular automaton generated by "rule 214".
%C A071040 Row n has length 2n+1.
%D A071040 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.
%H A071040 Index entries for sequences related to cellular automata
%Y A071040 Sequence in context: A073097 A117569 A135528 this_sequence A078387 A105470 A087429
%Y A071040 Adjacent sequences: A071037 A071038 A071039 this_sequence A071041 A071042 A071043
%K A071040 nonn,tabf
%O A071040 0,1
%A A071040 Hans Havermann (pxp(AT)rogers.com), May 26 2002
%I A078387
%S A078387 1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,1,0,1,1,0,1,
%T A078387 0,1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,
%U A078387 1,0,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1
%V A078387 -1,-1,0,1,0,-1,0,1,0,-1,1,0,-1,-1,0,0,0,1,0,1,0,0,-1,0,0,1,-1,1,0,-1,0,-1,1,0,-1,0,1,
%W A078387 1,1,1,0,0,0,1,0,-1,0,-1,1,1,0,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,-1,0,-1,0,0,1,-1,0,-1,0,
%X A078387 -1,0,0,0,0,1,0,0,-1,0,-1,0,0,0,-1,-1,0,1,0,0,-1,1,-1
%N A078387 Moebius' mue of numbers which can be written as sum of a positive square and a positive cube.
%C A078387 a(n)=A008683(A055394(n)).
%Y A078387 Cf. A078386.
%Y A078387 Sequence in context: A117569 A135528 A071040 this_sequence A105470 A087429 A093075
%Y A078387 Adjacent sequences: A078384 A078385 A078386 this_sequence A078388 A078389 A078390
%K A078387 sign
%O A078387 1,1
%A A078387 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 25 2002
%I A105470
%S A105470 1,1,0,1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,0,1,0,
%T A105470 1,1,1,1,1,0,1,0,1,0,1,1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,
%U A105470 1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1
%N A105470 a(n)=1 if there is number of the form 6k+3 with prime(n) <= 6k+3 <= prime(n+1), otherwise 0.
%C A105470 Except for the first pair of primes and for twin primes there is always at least one number of the form 6n+3 between two successive primes.
%e A105470 a(3)=0 because between prime(3) and prime(4) there are no numbers of the form 6k+3;
%e A105470 a(4)=1 because between prime(4) and prime(5) there is one number of the form 6k+3: 9.
%t A105470 f[n_] := Count[Table[Mod[k, 6], {k, Prime[n], Prime[n + 1]}], 3];Table[If[f[n] == 0, 0, 1], {n, 120}] (*Chandler*)
%Y A105470 Cf. A100810, A106002.
%Y A105470 Sequence in context: A135528 A071040 A078387 this_sequence A087429 A093075 A104120
%Y A105470 Adjacent sequences: A105467 A105468 A105469 this_sequence A105471 A105472 A105473
%K A105470 easy,nonn
%O A105470 1,1
%A A105470 Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), May 02 2005
%E A105470 Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 17 2006
%I A087429
%S A087429 1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,
%T A087429 1,0,0,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,
%U A087429 0,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1
%N A087429 a(n) = if gpf(n) < gpf(n+1) then 1 else 0, where gpf=A006530 (greatest prime-factor).
%C A087429 Equivalently, a(n) = 1 iff A061395(n+1) > A061395(n), otherwise a(n) = 0. - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Jan 03 2008
%C A087429 a(n) = A057427(1+A057427(A070221(n)));
%C A087429 for primes p: a(p-1)=1 and a(p)=0;
%C A087429 a(A070089(n)) = 1, a(A070087(