A091513 Numbers k such that (2^k + 1)^2 - 2 = 4^k + 2^(k+1) - 1 is prime.

0, 1, 2, 3, 5, 8, 9, 12, 15, 17, 18, 21, 23, 27, 32, 51, 65, 87, 180, 242, 467, 491, 501, 507, 555, 591, 680, 800, 1070, 1650, 2813, 3281, 4217, 5153, 6287, 6365, 10088, 10367, 37035, 45873, 69312, 102435, 106380, 108888, 110615, 281621, 369581, 376050, 442052, 621443, 661478

Offset

1,3

Links

Table of n, a(n) for n=1..51.

S. Harvey, Carol and Kynea Primes

M. Rodenkirch, Carol and Kynea Prime Search

Eric Weisstein's World of Mathematics, Integer Sequence Primes

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

Formula

A093069(n) = (2^a(n) + 1)^2 - 2.

Mathematica

Flatten[Position[Table[(2^n + 1)^2 - 2, {n, 0, 10^3}], _?PrimeQ] - 1] (* Eric W. Weisstein, Feb 10 2016 *)
Select[Range[0, 5000], PrimeQ[(2^# + 1)^2 - 2] & ] (* Vincenzo Librandi, Feb 19 2016 *)

Prog

(Magma) [n: n in [0..500] | IsPrime((2^n+1)^2-2)]; // Vincenzo Librandi, Feb 19 2016
(PARI) is(n)=ispseudoprime((2^n+1)^2-2) \\ Charles R Greathouse IV, Feb 19 2016

Crossrefs

Cf. A091514 (primes of the form (2^n + 1)^2 - 2).

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

Sequence in context: A286492 A025033 A122933 * A060138 A139487 A162586

Adjacent sequences: A091510 A091511 A091512 * A091514 A091515 A091516

Keyword

nonn,hard

Author

Eric W. Weisstein, Jan 17 2004

Extensions

a(41) from Eric W. Weisstein, Feb 27 2004

a(42) to a(44) from Eric W. Weisstein, Jun 05 2004

Edited by Ray Chandler, Nov 15 2004

a(46) from Cletus Emmanuel (cemmanu(AT)yahoo.com), Oct 07 2005

a(47)-a(48) from Eric W. Weisstein, Feb 10 2016 (computed by Mark Rodenkirch)

a(49)-a(50) from Eric W. Weisstein, Jun 08 2016 (computed by Mark Rodenkirch)

a(51) from Eric W. Weisstein, Jun 19 2016 (computed by Mark Rodenkirch)

Status

approved