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%I #37 Sep 08 2022 08:45:12
%S 2,7,23,79,1087,66047,263167,16785407,1073807359,17180131327,
%T 68720001023,4398050705407,70368760954879,18014398777917439,
%U 18446744082299486207,5070602400912922109586440191999
%N Primes of the form (2^n + 1)^2 - 2 = 4^n + 2^(n+1) - 1.
%C Cletus Emmanuel calls these "Kynea primes".
%H Vincenzo Librandi, <a href="/A091514/b091514.txt">Table of n, a(n) for n = 1..30</a>
%H Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>
%F a(n) = (2^A091513(n) + 1)^2 - 2.
%p select(isprime,[seq((2^n+1)^2-2, n=0..1000)]); # _Robert Israel_, Feb 10 2016
%t 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 *)
%t Select[Table[(2^n + 1)^2 - 2, {n, 0, 50}], PrimeQ] (* _Eric W. Weisstein_, Feb 10 2016 *)
%o (Magma) [a: n in [0..60] | IsPrime(a) where a is 4^n+2^(n+1)-1]; // _Vincenzo Librandi_, Dec 13 2011
%o (PARI) select(isprime, vector(100,n,(2^n+1)^2-2)) \\ _Charles R Greathouse IV_, Feb 19 2016
%Y Cf. A093069 (numbers of the form (2^n + 1)^2 - 2).
%Y Cf. A091513 (indices n such that (2^n + 1)^2 - 2 is prime).
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Jan 17 2004
%E Edited by _Ray Chandler_, Nov 15 2004
%E First term (2) added by _Vincenzo Librandi_, Dec 13 2011
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