A001988 Let p be the n-th odd prime. a(n) is the least prime congruent to 7 modulo 8 such that Legendre(-a(n), q) = -Legendre(-1, q) for all odd primes q <= p. (Formerly M4333 N1888)

7, 7, 127, 463, 463, 487, 1423, 33247, 73327, 118903, 118903, 118903, 454183, 773767, 773767, 773767, 773767, 86976583, 125325127, 132690343, 788667223, 788667223, 1280222287, 2430076903, 10703135983, 10703135983, 10703135983

Offset

1,1

Comments

Numbers so far are all congruent to 7 (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..27.

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(-1, q), return (0)); ); return (1); }
a(n) = {oddpn = prime(n+1); forprime(p=3, , if ((p%8) == 7, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 18 2017
(Python)
from sympy import legendre_symbol as L, primerange, prime, nextprime
def isok(p, oddpn):
    for q in primerange(3, oddpn + 1):
        if L(p, q)!=-L(-1, q): return 0
    return 1
def a(n):
    oddpn=prime(n + 1)
    p=3
    while True:
        if p%8==7:
            if isok(p, oddpn): return p
        p=nextprime(p) # Indranil Ghosh, Oct 23 2017, after PARI code by Michel Marcus

Crossrefs

Cf. A001990.

Sequence in context: A065240 A178708 A072399 * A099739 A261128 A353583

Adjacent sequences: A001985 A001986 A001987 * A001989 A001990 A001991

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Better name and more terms from Sean A. Irvine, Mar 06 2013

Name and offset corrected by Michel Marcus, Oct 18 2017

Status

approved