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A001992 Let p = n-th odd prime. Then a(n) = least prime congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.

%I A001992 M4012 N1663 #33 Feb 21 2019 15:07:42
%S A001992 5,53,173,173,293,2477,9173,9173,61613,74093,74093,74093,170957,
%T A001992 360293,679733,2004917,2004917,69009533,138473837,237536213,384479933,
%U A001992 883597853,1728061733,1728061733,1728061733,1728061733
%N A001992 Let p = n-th odd prime. Then a(n) = least prime congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.
%C A001992 All terms are congruent to 5 mod 24. - _Jianing Song_, Feb 17 2019
%C A001992 Also a(n) is the least prime r congruent to 5 mod 8 such that the first n odd primes are quadratic nonresidues modulo r. Note that r == 5 (mod 8) implies 2 is a quadratic nonresidue modulo r. See A001986 for the case where r == 3 (mod 8). - _Jianing Song_, Feb 19 2019
%D A001992 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001992 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001992 Michael John Jacobson, Jr., <a href="http://hdl.handle.net/1993/18862">Computational Techniques in Quadratic Fields</a>, Master's thesis, University of Manitoba, Winnipeg, Manitoba, 1995.
%H A001992 Michael John Jacobson Jr. and Hugh C. Williams, <a href="https://doi.org/10.1090/S0025-5718-02-01418-7">New quadratic polynomials with high densities of prime values</a>, Math. Comp. 72 (2003), 499-519.
%H A001992 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. [There is an error in the table given in this paper.]
%H A001992 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 A001992 (PARI) isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(p, q) != -1, return (0));); return (1);}
%o A001992 a(n) = {my(oddpn = prime(n+1)); forprime(p=3, , if ((p%8) == 5, if (isok(p, oddpn), return (p));););} \\ _Michel Marcus_, Oct 17 2017
%Y A001992 Cf. A094851, A094852, A094853.
%Y A001992 Cf. A001986 (the congruent to 3 mod 8 case), A001987, A094845, A094846.
%Y A001992 See A094847, A094848, A094849, A094850 for the case where the terms are not restricted to the primes.
%K A001992 nonn
%O A001992 1,1
%A A001992 _N. J. A. Sloane_
%E A001992 Corrected and extended by _N. J. A. Sloane_, Jun 14 2004