A263726 Least prime p such that p^2 + A263977(n)^2 is prime.

2, 3, 2, 5, 2, 5, 2, 3, 3, 7, 2, 11, 2, 5, 2, 5, 3, 5, 5, 5, 2, 5, 11, 3, 2, 5, 2, 5, 2, 3, 3, 5, 19, 2, 5, 2, 13, 7, 3, 11, 11, 2, 3, 13, 3, 11, 2, 29, 2, 5, 3, 5, 2, 5, 5, 7, 7, 3, 11, 2, 11, 2, 3, 11, 7, 5, 2, 5, 2, 3, 3, 5, 2, 11, 5, 5, 3, 3, 59, 2, 11, 2, 3, 7, 13, 5, 2, 5, 7

Offset: 1

Author

Jonathan Sondow and Robert G. Wilson v, Oct 30 2015

Keywords

• nonn

Comments

The least k, such that prime(n) is the smallest prime p for which k^2 + p^2 is also prime, is in A263466.

Examples

			A263977(1) = 1, and 2 and 2^2 + 1^2 = 5 are prime, so a(1) = 2.
		

Links

• Stephan Baier and Liangyi Zhao, On Primes Represented by Quadratic Polynomials, Anatomy of Integers, CRM Proc. & Lecture Notes, Vol. 46, Amer. Math. Soc. 2008, pp. 169 - 166.
• Étienne Fouvry and Henryk Iwaniec, Gaussian primes, Acta Arithmetica 79:3 (1997), pp. 249-287.

Crossrefs

Cf. A240130, A240131, A263466, A263722, A263977.

Programs

Mathematica

f[n_] := Block[{p = 2}, While[! PrimeQ[n^2 + p^2] && p < 1500, p = NextPrime@ p]; If[p > 1500, 0, p]]; lst = {}; k = 1; While[k < 130, If[f@ k > 0, AppendTo[lst, f@ k]]; k++]; lst