A001990 - OEIS

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.
(Formerly M3953 N1632)

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..26.

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) 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

CROSSREFS

Cf. A001988.

Sequence in context: A057713 A124987 A002584 * A043062 A321701 A243012

Adjacent sequences: A001987 A001988 A001989 * A001991 A001992 A001993

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Better name from Sean A. Irvine, Mar 06 2013

Name and offset corrected by Michel Marcus, Oct 18 2017

STATUS

approved