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

%I A091515 #43 Feb 16 2025 08:32:52
%S A091515 2,3,4,6,7,10,12,15,18,19,21,25,27,55,129,132,159,171,175,315,324,358,
%T A091515 393,435,786,1459,1707,2923,6462,14289,39012,51637,100224,108127,
%U A091515 110953,175749,185580,226749,248949,253987,520363,653490,688042,695631
%N A091515 Numbers k such that (2^k - 1)^2 - 2 = 4^k - 2^(k+1) - 1 is prime.
%H A091515 Steven Harvey, <a href="http://harvey563.tripod.com/Carol_Kynea.txt">Carol and Kynea Primes</a>
%H A091515 M. Rodenkirch, <a href="http://www.mersenneforum.org/rogue/ckps.html">Carol and Kynea Prime Search</a>
%H A091515 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>
%H A091515 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%t A091515 lst={};Do[p=(2^n-1)^2-2;If[PrimeQ[p],AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2009 *)
%o A091515 (PARI) is(n)=ispseudoprime((2^n - 1)^2 - 2) \\ _Charles R Greathouse IV_, Feb 19 2016
%Y A091515 Cf. A093112, A091516.
%K A091515 nonn,hard
%O A091515 1,1
%A A091515 _Eric W. Weisstein_, Jan 17 2004
%E A091515 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
%E A091515 a(36)=175749 from Cletus Emmanuel (cemmanu(AT)yahoo.com), Oct 08 2004
%E A091515 a(37)=185580 from Cletus Emmanuel (cemmanu(AT)yahoo.com), Nov 03 2004
%E A091515 Edited by _Ray Chandler_, Nov 15 2004
%E A091515 a(38)=226749 from _Steven Harvey_, Jan 11 2005 and subsequently confirmed as next term
%E A091515 a(39) from _Eric W. Weisstein_, Mar 31 2006
%E A091515 a(40) = 253987 from Cletus Emmanuel (cemmanu(AT)yahoo.com), May 03 2007
%E A091515 a(41) = 520363 from _Eric W. Weisstein_, Jun 08 2016 (computed by Mark Rodenkirch)
%E A091515 a(42) = 653490 from _Eric W. Weisstein_, Jun 15 2016 (computed by Mark Rodenkirch)
%E A091515 a(43) = 688042 from _Mark Rodenkirch_, Jul 05 2016
%E A091515 a(44) = 695631 from _Mark Rodenkirch_, Jul 16 2016