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 A091513 Numbers n such that (2^n + 1)^2 - 2 = 4^n + 2^(n+1) - 1 is prime. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 FORMULA A093069(n) = (2^a(n) + 1)^2 - 2. MATHEMATICA lst={}; Do[p=4^n+2^(n+1)-1; If[PrimeQ[p], AppendTo[lst, n]], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *) 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 *) PROG (MAGMA) [n: n in [0..500] | IsPrime((2^n+1)^2-2)]; // Vincenzo Librandi, Feb 19 2016 (PARI) is(n)=ispseudoprime((2^n+1)^2-2) \\ Charles R Greathouse IV, Feb 19 2016 CROSSREFS Cf. A091514 (primes of the form (2^n + 1)^2 - 2). Cf. A093069 (numbers of the form (2^n + 1)^2 - 2). Sequence in context: A286492 A025033 A122933 * A060138 A139487 A162586 Adjacent sequences:  A091510 A091511 A091512 * A091514 A091515 A091516 KEYWORD nonn,hard AUTHOR Eric W. Weisstein, Jan 17 2004 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) STATUS approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)