A091514 Primes of the form (2^n + 1)^2 - 2 = 4^n + 2^(n+1) - 1.

2, 7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359, 17180131327, 68720001023, 4398050705407, 70368760954879, 18014398777917439, 18446744082299486207, 5070602400912922109586440191999

Offset

1,1

Comments

Cletus Emmanuel calls these "Kynea primes".

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..30

Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Eric Weisstein's World of Mathematics, Near-Square Prime

Formula

a(n) = (2^A091513(n) + 1)^2 - 2.

Maple

select(isprime, [seq((2^n+1)^2-2, n=0..1000)]); # Robert Israel, Feb 10 2016

Mathematica

lst={}; Do[If[PrimeQ[p=4^n+2^(n+1)-1], (*Print[p]; *)AppendTo[lst, p]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)
Select[Table[(2^n + 1)^2 - 2, {n, 0, 50}], PrimeQ] (* Eric W. Weisstein, Feb 10 2016 *)

Prog

(Magma) [a: n in [0..60] | IsPrime(a) where a is 4^n+2^(n+1)-1]; // Vincenzo Librandi, Dec 13 2011
(PARI) select(isprime, vector(100, n, (2^n+1)^2-2)) \\ Charles R Greathouse IV, Feb 19 2016

Crossrefs

Cf. A093069 (numbers of the form (2^n + 1)^2 - 2).

Cf. A091513 (indices n such that (2^n + 1)^2 - 2 is prime).

Sequence in context: A112657 A007717 A130567 * A143629 A176287 A119371

Adjacent sequences: A091511 A091512 A091513 * A091515 A091516 A091517

Keyword

nonn

Author

Eric W. Weisstein, Jan 17 2004

Extensions

Edited by Ray Chandler, Nov 15 2004

First term (2) added by Vincenzo Librandi, Dec 13 2011

Status

approved