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

Author

Eric W. Weisstein, Jan 17 2004

Keywords

• nonn
• hard

Links

• 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

Crossrefs

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

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

Programs

Magma

[n: n in [0..500] | IsPrime((2^n+1)^2-2)]; // Vincenzo Librandi, Feb 19 2016

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 *)

PARI

is(n)=ispseudoprime((2^n+1)^2-2) \\ Charles R Greathouse IV, Feb 19 2016

Formula

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

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)