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Search: id:A003188
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| A003188 |
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Decimal equivalent of Gray code for n.
(Formerly M2250)
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+0
37
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| 0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Inverse of sequence A006068 considered as a permutation of the nonnegative integers, i.e. A006068(A003188(n)) = n = A003188(A006068(n)). - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
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REFERENCES
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M. W. Bunder et al., On binary reflected Gray codes and functions, Discr. Math., 308 (2008), 1690-1700.
M. Gardner, Mathematical Games, Sci. Amer. Vol. 227 (No. 2, Feb. 1972), p. 107.
M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 15.
J. A. Oteo and J. Ros, A Fractal Set from the Binary Reflected Gray Code, J. Phys. A: Math Gen. 38 (2005) 8935-8949.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..1000
Joerg Arndt, Fxtbook
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = 2*a([n/2])+A021913(n-1) - Henry Bottomley (se16(AT)btinternet.com), Apr 05 2001
a(n) = n XOR floor(n/2), where XOR is the binary exclusive OR operator. - Paul D. Hanna (pauldhanna(AT)juno.com), Jun 04 2002
G.f.: 1/(1-x) * sum(k>=0, 2^k*x^2^k/(1+x^2^(k+1))). - Ralf Stephan, May 06 2003
a(0)=0, a(2n) = 2a(n) + [n odd], a(2n+1) = 2a(n) + [n even]. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 20 2003
a(n) = sum(k=1, n, 2^A007814(k) * (-1)^((k/2^A007814(k)-1)/2)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 29 2003
a(0) = 0, a(n+1) = a(n) XOR 2^A007814(n) - Jaume Simon Gispert (jaume(AT)nuem.com), Sep 11 2004
Inverse of sequence A006068. - Philippe DELEHAM, Apr 29 2005
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MAPLE
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with(combinat); graycode(6); # to produce first 64 terms
printf(cat(` %.6d`$64), op(map(convert, graycode(6), binary))); lprint(); # to produce binary strings
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PROGRAM
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(PARI) a(n)=sum(k=1, n, (-1)^((k/2^valuation(k, 2)-1)/2)*2^valuation(k, 2))
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CROSSREFS
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a(2*A003714(n)) = 3*A003714(n) for all n. - Antti Karttunen, Apr 26 1999
Same sequence in binary: A014550, bisection: A048724. Cf. A038554, A048641, A048642.
Sequence in context: A083362 A153142 A154447 this_sequence A154435 A006042 A100280
Adjacent sequences: A003185 A003186 A003187 this_sequence A003189 A003190 A003191
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (Larryr(AT)acm.org), Sep 05 2000
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