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

1,1

References

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A007519, A002224, A144294, A269704.

Subsequence of A094929.

Sequence in context: A014780 A216199 A073081 * A178984 A065507 A182731

Adjacent sequences: A094925 A094926 A094927 * A094929 A094930 A094931

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 19 2004

Extensions

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

Status

approved