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 A091514 Primes of the form (2^n + 1)^2 - 2 = 4^n + 2^(n+1) - 1. 9
 2, 7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359, 17180131327, 68720001023, 4398050705407, 70368760954879, 18014398777917439, 18446744082299486207, 5070602400912922109586440191999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Cletus Emmanuel calls these "Kynea primes". LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..30 Eric Weisstein's World of Mathematics, Near-Square Prime FORMULA a(n) = (2^A091513(n) + 1)^2 - 2. MAPLE select(isprime, [seq((2^n+1)^2-2, n=0..1000)]); # Robert Israel, Feb 10 2016 MATHEMATICA 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 *) Select[Table[(2^n + 1)^2 - 2, {n, 0, 50}], PrimeQ] (* Eric W. Weisstein, Feb 10 2016 *) PROG (MAGMA) [a: n in [0..60] | IsPrime(a) where a is 4^n+2^(n+1)-1]; // Vincenzo Librandi, Dec 13 2011 (PARI) select(isprime, vector(100, n, (2^n+1)^2-2)) \\ Charles R Greathouse IV, Feb 19 2016 CROSSREFS Cf. A093069 (numbers of the form (2^n + 1)^2 - 2). Cf. A091513 (indices n such that (2^n + 1)^2 - 2 is prime). Sequence in context: A112657 A007717 A130567 * A143629 A176287 A119371 Adjacent sequences:  A091511 A091512 A091513 * A091515 A091516 A091517 KEYWORD nonn AUTHOR Eric W. Weisstein, Jan 17 2004 EXTENSIONS Edited by Ray Chandler, Nov 15 2004 First term (2) added by Vincenzo Librandi, Dec 13 2011 STATUS approved

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)