A079138 Primes of the form k^2 + 7.

7, 11, 23, 43, 71, 107, 151, 263, 331, 491, 683, 907, 1031, 1163, 1303, 1451, 1607, 2311, 2711, 3371, 3607, 3851, 4363, 5483, 5783, 6091, 10007, 11243, 12107, 13003, 13463, 13931, 14407, 14891, 15383, 17431, 18503, 19051, 20743, 21323, 21911

Offset

1,1

Comments

The sum of the reciprocals converges to 0.350314... Are there infinitely many primes of this form?

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..6800

Mathematica

Intersection[Table[n^2+7, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=7, i<=7, a={}; Do[If[PrimeQ[n^2+i], AppendTo[a, n^2+i]], {n, 0, 100}]; Print["n^2+", i, ", ", a]; i++ ] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
Select[Table[n^2+7, {n, 0, 70000}], PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

Prog

(PARI) nsqpm(n) = {sr=0; forstep(x=0, n, 2, y = x*x+7; if(isprime(y), print1(y" "); sr+=1.0/y; ); ); print(); print(sr); } \\ Primes of the form n^2 + 7 and the sum of the reciprocals.
(Magma) [a: n in [0..700] | IsPrime(a) where a is n^2+7]; // Vincenzo Librandi, Nov 30 2011

Crossrefs

Sequence in context: A294074 A228227 A107133 * A163848 A111671 A213895

Adjacent sequences: A079135 A079136 A079137 * A079139 A079140 A079141

Keyword

easy,nonn

Author

Cino Hilliard, Dec 26 2002

Status

approved