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A094928 Let p = n-th prime == 1 mod 8 (A007519); a(n) = smallest prime q such that p is not a square mod q.

%I A094928 #13 May 06 2019 09:55:14
%S A094928 3,3,5,3,5,3,3,5,3,7,3,3,5,5,3,3,7,5,3,5,3,3,5,3,7,3,3,5,3,7,3,3,3,3,
%T A094928 5,3,3,11,5,3,3,11,5,3,11,3,7,3,5,7,3,3,3,3,7,3,3,7,5,3,3,5,5,11,5,3,
%U A094928 3,5,5,3,7,5,3,5,3,7,3,7,3,5,3,3,3,5,11,5,3,5,3,3,13,5,3,3,3,3,5,5,3,5,3,7
%N A094928 Let p = n-th prime == 1 mod 8 (A007519); a(n) = smallest prime q such that p is not a square mod q.
%D A094928 M. Kneser, Quadratische Formen, Springer, 2002; see Hilfssatz 18.3.
%H A094928 Robert Israel, <a href="/A094928/b094928.txt">Table of n, a(n) for n = 1..10000</a>
%F A094928 a(n) = A094929(A269704(n)). - _Robert Israel_, May 06 2019
%e A094928 n=3, p = 73, a(3) = q = 5: Legendre(73,5) = -1.
%p A094928 f:= proc(p) local q;
%p A094928      q:= 3:
%p A094928      do
%p A094928       if numtheory:-quadres(p,q) = -1 then return q fi;
%p A094928       q:= nextprime(q);
%p A094928      od;
%p A094928 end proc:
%p A094928 map(f, select(isprime, [seq(p,p=1..10000,8)])); # _Robert Israel_, May 06 2019
%t A094928 f[n_] := Prime[ Position[ JacobiSymbol[n, Select[Range[3, n - 1], PrimeQ[ # ] &]], -1][[1, 1]] + 1]; f /@ Select[ Prime[ Range[435]], Mod[ #, 8] == 1 &] (* _Robert G. Wilson v_, Jun 23 2004 *)
%Y A094928 Cf. A007519, A002224, A144294, A269704.
%Y A094928 Subsequence of A094929.
%K A094928 nonn,easy
%O A094928 1,1
%A A094928 _N. J. A. Sloane_, Jun 19 2004
%E A094928 More terms from _Robert G. Wilson v_, Jun 23 2004