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

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Jun 19 2004

Keywords

• nonn
• easy

Examples

			n=3, p = 73, a(3) = q = 5: Legendre(73,5) = -1.
		

References

• M. Kneser, Quadratische Formen, Springer, 2002; see Hilfssatz 18.3.

Links

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

Crossrefs

Cf. A007519, A002224, A144294, A269704.

Subsequence of A094929.

Programs

Maple

f:= proc(p) local q;
     q:= 3:
     do
      if numtheory:-quadres(p,q) = -1 then return q fi;
      q:= nextprime(q);
     od;
end proc:
map(f, select(isprime, [seq(p,p=1..10000,8)])); # Robert Israel, May 06 2019

Mathematica

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 *)

Formula

a(n) = A094929(A269704(n)). - Robert Israel, May 06 2019

Extensions

More terms from Robert G. Wilson v, Jun 23 2004