A045535 Least negative pseudosquare modulo the first n odd primes.

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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

Crossrefs

Cf. A002189, A062241.

Programs

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

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