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A045535
Least negative pseudosquare modulo the first n odd primes.
(Formerly M4381 N2226)
14
7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 118271, 366791, 366791, 2155919, 2155919, 2155919, 6077111, 6077111, 98538359, 120293879, 131486759, 131486759, 508095719, 2570169839, 2570169839, 2570169839, 2570169839, 2570169839, 2570169839, 328878692999, 328878692999, 513928659191, 844276851239
OFFSET
0,1
COMMENTS
a(n) is the smallest positive integer m such that m == 7 (mod 8) and for the first n odd primes p, -m is a (nonzero) quadratic residue mod p.
REFERENCES
N. D. Bronson and D. A. Buell, Congruential sieves on FPGA computers, pp. 547-551 of Mathematics of Computation 1943-1993 (Vancouver, 1993), Proc. Symp. Appl. Math., Vol. 48, Amer. Math. Soc. 1994.
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).
LINKS
D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.
D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451 [Annotated scanned copy]
PROG
(PARI) {A045535 = (n, m=7)->until(!m+=8, for(i=2, n+1, m%prime(i)||next(2); issquare(Mod(-m, prime(i)))||next(2)); return(m))} \\ Starting value (e.g., a(n-1); must be in 7+8Z) may be given as 2nd arg. - M. F. Hasler, Oct 24 2013
CROSSREFS
Sequence in context: A139852 A141194 A198644 * A001984 A147972 A002223
KEYWORD
nonn,nice
EXTENSIONS
The Bronson-Buell reference gives terms through 227. The Math. Comp. version is erroneous.
Edited by Don Reble, Nov 14 2006
Corrected link to OEIS index, following a remark by Don Reble. Values a(0..21) double-checked. - M. F. Hasler, Oct 24 2013
a(27)-a(28) from Jinyuan Wang, Mar 24 2020
More terms from Bert Dobbelaere, Feb 28 2021
STATUS
approved