A225225 Second smallest prime quadratic non-residue modulo the n-th prime.

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

Offset

1,1

Comments

See comments, references and links in A053760 = Smallest positive quadratic nonresidue modulo the n-th prime.

Links

Table of n, a(n) for n=1..100.

Kevin J. McGown, On the second smallest prime non-residue, J. Number Theory, 133 (2013), 1289-1299.

Example

The positive quadratic non-residues modulo prime(5) = 11 are 2, 6, 7, 8, 10, 11, ... and the second smallest prime among them is 7, so a(5) = 7.

Mathematica

Table[p = Prime[n]; Part[ Select[ Range[p+1], JacobiSymbol[#, p] != 1 &], 2], {n, 1, 100}]

Crossrefs

Cf. A053760.

Sequence in context: A318203 A282243 A214748 * A290562 A346476 A307446

Adjacent sequences: A225222 A225223 A225224 * A225226 A225227 A225228

Keyword

nonn

Author

Jonathan Sondow, May 02 2013

Status

approved