A092419 Let k = n-th nonsquare = A000037(n); then a(n) = smallest prime p such that the Kronecker-Jacobi symbol K(k,p) = -1.

3, 2, 2, 7, 5, 3, 7, 2, 5, 2, 3, 13, 3, 5, 2, 3, 2, 5, 3, 7, 3, 2, 5, 2, 11, 7, 3, 5, 7, 2, 2, 3, 11, 7, 3, 5, 2, 3, 2, 11, 3, 5, 3, 2, 5, 2, 7, 7, 3, 5, 5, 2, 13, 2, 3, 5, 3, 7, 2, 3, 2, 13, 3, 5, 5, 3, 2, 7, 2, 5, 11, 3, 5, 2, 11, 2, 3, 5, 5, 3, 7, 2, 3, 2, 7, 3, 7, 5, 3, 2, 2, 5, 5, 3, 11, 11, 2, 5, 2, 3, 7

Offset: 1

Author

N. J. A. Sloane, Oct 16 2008

Keywords

• nonn

Comments

Maple calls K(k,p) the Legendre symbol.

The old entry with this sequence number was a duplicate of A024356.

References

• H. Cohen, A Course in Computational Number Theory, Springer, 1996 (p. 28 defines the Kronecker-Jacobi symbol).

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000037. Records: A067073, A070040. See A144294 for another version.

Programs

Maple

with(numtheory); f:=proc(n) local M,i,j,k; M:=100000; for i from 1 to M do if legendre(n,ithprime(i)) = -1 then RETURN(ithprime(i)); fi; od; -1; end;

PARI

a(n)=my(k=n+(sqrtint(4*n)+1)\2); forprime(p=2,, if(kronecker(k,p)<0, return(p))) \\ Charles R Greathouse IV, Aug 28 2016

Extensions

Definition corrected Dec 03 2008