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
Keywords
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
Crossrefs
Programs
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Magma
[a: n in [0..60] | IsPrime(a) where a is 4^n+2^(n+1)-1]; // Vincenzo Librandi, Dec 13 2011
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Maple
select(isprime,[seq((2^n+1)^2-2, n=0..1000)]); # Robert Israel, Feb 10 2016
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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 *) -
PARI
select(isprime, vector(100,n,(2^n+1)^2-2)) \\ Charles R Greathouse IV, Feb 19 2016
Formula
a(n) = (2^A091513(n) + 1)^2 - 2.
Extensions
Edited by Ray Chandler, Nov 15 2004
First term (2) added by Vincenzo Librandi, Dec 13 2011
Comments