A045535 Least negative pseudosquare modulo the first n odd primes. (Formerly M4381 N2226)

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

Bert Dobbelaere, Table of n, a(n) for n = 0..50

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]

OEIS Index entries for sequences related to pseudo-squares

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

Cf. A002189, A062241.

Sequence in context: A139852 A141194 A198644 * A001984 A147972 A002223

Adjacent sequences: A045532 A045533 A045534 * A045536 A045537 A045538

Keyword

nonn,nice

Author

N. J. A. Sloane

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