A091515 Numbers n such that (2^n - 1)^2 - 2 = 4^n - 2^(n+1) - 1 is prime.

2, 3, 4, 6, 7, 10, 12, 15, 18, 19, 21, 25, 27, 55, 129, 132, 159, 171, 175, 315, 324, 358, 393, 435, 786, 1459, 1707, 2923, 6462, 14289, 39012, 51637, 100224, 108127, 110953, 175749, 185580, 226749, 248949, 253987, 520363, 653490, 688042, 695631

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Steven Harvey, Carol and Kynea Primes

M. Rodenkirch, Carol and Kynea Prime Search

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

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Mathematica

lst={}; Do[p=(2^n-1)^2-2; If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)

Prog

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

Crossrefs

Cf. A093112, A091516.

Sequence in context: A158381 A163180 A341270 * A036405 A051424 A308632

Adjacent sequences: A091512 A091513 A091514 * A091516 A091517 A091518

Keyword

nonn,hard

Author

Eric W. Weisstein, Jan 17 2004

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004

a(36)=175749 from Cletus Emmanuel (cemmanu(AT)yahoo.com), Oct 08 2004

a(37)=185580 from Cletus Emmanuel (cemmanu(AT)yahoo.com), Nov 03 2004

Edited by Ray Chandler, Nov 15 2004

a(38)=226749 from Steven Harvey, Jan 11 2005 and subsequently confirmed as next term

a(39) from Eric W. Weisstein, Mar 31 2006

a(40) = 253987 from Cletus Emmanuel (cemmanu(AT)yahoo.com), May 03 2007

a(41) = 520363 from Eric W. Weisstein, Jun 08 2016 (computed by Mark Rodenkirch)

a(42) = 653490 from Eric W. Weisstein, Jun 15 2016 (computed by Mark Rodenkirch)

a(43) = 688042 from Mark Rodenkirch, Jul 05 2016

a(44) = 695631 from Mark Rodenkirch, Jul 16 2016

Status

approved