A001990 Let p be the n-th odd prime. a(n) is the least prime congruent to 5 modulo 8 such that Legendre(-a(n), q) = -Legendre(-2, q) for all odd primes q <= p.

5, 29, 29, 29, 29, 29, 29, 29, 23669, 23669, 23669, 23669, 23669, 23669, 1508789, 5025869, 9636461, 9636461, 9636461, 37989701, 37989701, 37989701, 37989701, 37989701, 240511301, 240511301

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Numbers so far are all congruent to 5 (mod 24). - Ralf Stephan, Jul 07 2003

References

• 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]

Crossrefs

Cf. A001988.

Programs

PARI

isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -kronecker(-2, q), return (0));); return (1);}
a(n) = {oddpn = prime(n+1); forprime(p=3, , if ((p%8) == 5, if (isok(p, oddpn), return (p));););} \\ Michel Marcus, Oct 18 2017

Extensions

Better name from Sean A. Irvine, Mar 06 2013

Name and offset corrected by Michel Marcus, Oct 18 2017