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A002189
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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)
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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,1
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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).
Jonathan P. Sorenson, Sieving for pseudosquares and pseudocubes in parallel using doubly-focused enumeration and wheel datastructures, http://arxiv.org/abs/1001.3316 [From Jonathan Vos Post and Charles Greathouse, Jan 20 2010]
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).
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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
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MATHEMATICA
| a[n_] := a[n] = (pp = Prime[ Range[2, n+1]]; k = If[ n == 0, 9, a[n-1] - 8]; While[ True, k += 8; If[ ! IntegerQ[ Sqrt[k]] && If[ Scan[ If[ ! (JacobiSymbol[k, #] == 1 ), Return[ False]] & , pp], , False, True], Break[]]]; k); Table[ Print[ an = a[n]]; an, {n, 0, 24}] (* From Jean-François Alcover, Sep 30 2011 *)
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CROSSREFS
| Cf. A018883, A045535, A090983.
Sequence in context: A141972 A161735 A142648 * A002224 A096637 A201610
Adjacent sequences: A002186 A002187 A002188 * A002190 A002191 A002192
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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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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