A176616 Primes of the form x^2 + 7*y^2, where x and y=x+1 are consecutive natural numbers.

7, 29, 67, 191, 277, 379, 631, 947, 1129, 1327, 2017, 2557, 2851, 4561, 4951, 5779, 6217, 8647, 9181, 12721, 13367, 14029, 15401, 16111, 17579, 20707, 21529, 22367, 24091, 24977, 31627, 36857, 37951, 42487, 43661, 44851, 47279, 53629, 58997

Offset: 1

Author

Giovanni Teofilatto, Apr 22 2010

Keywords

• nonn

Comments

Primes of the form 8*n^2+14*n+7 = (2*n+2)*(4*n+3)+1 = A000384(2*n+2)+1. - Vincenzo Librandi, Apr 25 2010

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A176608.

A285790 is an almost identical sequence.

Programs

Magma

[ a: n in [0..250] | IsPrime(a) where a is 8*n^2+14*n+7 ] // Vincenzo Librandi, Apr 25 2010

Mathematica

Select[Table[x^2+7(x+1)^2,{x,0,100}],PrimeQ] (* Harvey P. Dale, May 03 2024 *)

Extensions

Definition made more accurate by R. J. Mathar, May 04 2010

Corrected (inserted 7) and extended by Vincenzo Librandi, Apr 25 2010

Offset corrected by Mohammed Yaseen, May 20 2023