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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.

%I A001988 M4333 N1888 #35 Feb 04 2022 02:01:57
%S A001988 7,7,127,463,463,487,1423,33247,73327,118903,118903,118903,454183,
%T A001988 773767,773767,773767,773767,86976583,125325127,132690343,788667223,
%U A001988 788667223,1280222287,2430076903,10703135983,10703135983,10703135983
%N 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.
%C A001988 Numbers so far are all congruent to 7 (mod 24). - _Ralf Stephan_, Jul 07 2003
%D A001988 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001988 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001988 D. H. Lehmer, E. Lehmer and D. Shanks, <a href="https://doi.org/10.1090/S0025-5718-1970-0271006-X">Integer sequences having prescribed quadratic character</a>, Math. Comp., 24 (1970), 433-451.
%H A001988 D. H. Lehmer, E. Lehmer and D. Shanks, <a href="/A002189/a002189.pdf">Integer sequences having prescribed quadratic character</a>, Math. Comp., 24 (1970), 433-451 [Annotated scanned copy]
%o A001988 (PARI) isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -kronecker(-1, q), return (0));); return (1);}
%o A001988 a(n) = {oddpn = prime(n+1); forprime(p=3, , if ((p%8) == 7, if (isok(p, oddpn), return (p));););} \\ _Michel Marcus_, Oct 18 2017
%o A001988 (Python)
%o A001988 from sympy import legendre_symbol as L, primerange, prime, nextprime
%o A001988 def isok(p, oddpn):
%o A001988     for q in primerange(3, oddpn + 1):
%o A001988         if L(p, q)!=-L(-1, q): return 0
%o A001988     return 1
%o A001988 def a(n):
%o A001988     oddpn=prime(n + 1)
%o A001988     p=3
%o A001988     while True:
%o A001988         if p%8==7:
%o A001988             if isok(p, oddpn): return p
%o A001988         p=nextprime(p) # _Indranil Ghosh_, Oct 23 2017, after PARI code by _Michel Marcus_
%Y A001988 Cf. A001990.
%K A001988 nonn
%O A001988 1,1
%A A001988 _N. J. A. Sloane_
%E A001988 Better name and more terms from _Sean A. Irvine_, Mar 06 2013
%E A001988 Name and offset corrected by _Michel Marcus_, Oct 18 2017