A096634 Let p = n-th prime == 5 (mod 8) (A007521); a(n) = smallest prime q such that p is not a square mod q.

3, 5, 3, 5, 3, 7, 3, 11, 3, 5, 3, 7, 3, 7, 3, 5, 3, 3, 7, 5, 3, 5, 13, 3, 3, 11, 3, 5, 3, 7, 3, 3, 13, 5, 5, 3, 3, 3, 7, 5, 5, 3, 5, 3, 7, 3, 7, 5, 3, 5, 3, 5, 3, 5, 3, 3, 3, 11, 11, 5, 3, 13, 5, 3, 17, 3, 7, 5, 3, 3, 7, 11, 7, 3, 3, 5, 3, 3, 3, 7, 5, 3, 3, 3, 11, 3, 13, 5, 3, 3, 7, 3, 3, 11, 5, 3, 3, 5, 3

Offset: 1

Author

Robert G. Wilson v, Jun 24 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A094928, A096633, A096635, A096638.

Programs

Maple

g:= proc(n) local p;
  p:= 1;
  do
    p:= nextprime(p);
    if numtheory:-quadres(n,p) = -1 then return p fi
  od
end proc:
map(g, select(isprime, [seq(i,i=5..10000,8)])); # Robert Israel, Apr 17 2023

Mathematica

f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; f /@ Select[ Prime[ Range[435]], Mod[ #, 8] == 5 &]