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A002189 Pseudo-squares: a(n) = the least nonsquare positive integer which is 1 mod 8 and is a (nonzero) quadratic residue modulo the first n odd primes.
(Formerly M5039 N2175)
+0
3
17, 73, 241, 1009, 2641, 8089, 18001, 53881, 87481, 117049, 515761, 1083289, 3206641, 3818929, 9257329, 22000801, 48473881, 48473881, 175244281, 427733329, 427733329, 898716289, 2805544681, 2805544681, 2805544681 (list; graph; listen)
OFFSET

0,1

REFERENCES

D. H. Lehmer, A sieve problem on "pseudo-squares", Math. Tables Other Aids Comp., 8 (1954), 241-242.

D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.

R. F. Lukes, C. D. Patterson and H. C. Williams, "Some results on pseudosquares", Mathematics of Computation 65:213 (1996), pp. 361-372.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. C. Williams and J. O. Shallit, Factoring integers before computers, pp. 481-531 of Mathematics of Computation 1943-1993 (Vancouver, 1993), Proc. Symp. Appl. Math., Vol. 48, Amer. Math. Soc. 1994.

Kjell Wooding and H. C. Williams, "Doubly-focused enumeration of pseudosquares and pseudocubes". Proceedings of the 7th International Algorithmic Number Theory Symposium (ANTS VII, 2006).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n=0..73 (from Bernstein link)

D. J. Bernstein, Doubly focused enumeration of locally square polynomial values

Eric Weisstein's World of Mathematics, Pseudosquare

CROSSREFS

Cf. A018883, A045535, A090983.

Sequence in context: A141972 A161735 A142648 this_sequence A002224 A096637 A146658

Adjacent sequences: A002186 A002187 A002188 this_sequence A002190 A002191 A002192

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

The PSAM reference gives a table through p = 223.

More terms from Don Reble (djr(AT)nk.ca), Nov 14 2006

Additional references from Charles R Greathouse IV, Oct 13 2008

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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