cp's OEIS Frontend

A094847 Let p = n-th odd prime. Then a(n) = least positive integer congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.

%I A094847 #29 Feb 21 2019 15:08:40
%S A094847 5,53,173,173,293,437,9173,9173,24653,74093,74093,74093,170957,214037,
%T A094847 214037,214037,2004917,44401013,71148173,154554077,154554077,
%U A094847 163520117,163520117,163520117,261153653,261153653,1728061733
%N A094847 Let p = n-th odd prime. Then a(n) = least positive integer congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.
%C A094847 With an initial a(0) = 5, a(n) is the least fundamental discriminant D > 1 such that the first n + 1 primes are inert in the real quadratic field with discriminant D. See A094841 for the imaginary quadratic field case. - _Jianing Song_, Feb 15 2019
%C A094847 All terms are congruent to 5 mod 24. - _Jianing Song_, Feb 17 2019
%H A094847 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 A094847 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 A094847 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.
%o A094847 (PARI) isok(m, oddpn) = {forprime(q=3, oddpn, if (kronecker(m, q) != -1, return (0));); return (1);}
%o A094847 a(n) = {oddpn = prime(n+1); m = 5; while(! isok(m, oddpn), m += 8); m;} \\ _Michel Marcus_, Oct 17 2017
%Y A094847 Cf. A094848, A094849, A094850.
%Y A094847 Cf. A094841 (the imaginary quadratic field case), A094842, A094843, A094844.
%Y A094847 See A001992, A094851, A094852, A094853 for the case where the terms are restricted to the primes.
%K A094847 nonn
%O A094847 1,1
%A A094847 _N. J. A. Sloane_, Jun 14 2004