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%I M4333 N1888 #35 Feb 04 2022 02:01:57
%S 7,7,127,463,463,487,1423,33247,73327,118903,118903,118903,454183,
%T 773767,773767,773767,773767,86976583,125325127,132690343,788667223,
%U 788667223,1280222287,2430076903,10703135983,10703135983,10703135983
%N 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 Numbers so far are all congruent to 7 (mod 24). - _Ralf Stephan_, Jul 07 2003
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H 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 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 (PARI) isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -kronecker(-1, q), return (0));); return (1);}
%o 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 (Python)
%o from sympy import legendre_symbol as L, primerange, prime, nextprime
%o def isok(p, oddpn):
%o for q in primerange(3, oddpn + 1):
%o if L(p, q)!=-L(-1, q): return 0
%o return 1
%o def a(n):
%o oddpn=prime(n + 1)
%o p=3
%o while True:
%o if p%8==7:
%o if isok(p, oddpn): return p
%o p=nextprime(p) # _Indranil Ghosh_, Oct 23 2017, after PARI code by _Michel Marcus_
%Y Cf. A001990.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Better name and more terms from _Sean A. Irvine_, Mar 06 2013
%E Name and offset corrected by _Michel Marcus_, Oct 18 2017
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