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 A085613 a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2). 1
 2, 3, 5, 11, 17, 41, 65, 155, 257, 593, 1025, 2291, 4097, 8921, 16385, 34955, 65537, 137633, 262145, 543971, 1048577, 2156201, 4194305, 8565755, 16777217, 34085873, 67108865, 135812051, 268435457, 541653881, 1073741825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Extends Euler's 6-term sequence. In Euler's 6-term sequence we have noticed that e(1) = 2 = 2^0 + 1; e(2) = 3 = 2^1 + 3^0; e(3) = 5 = 2^2 + 1; e(4) = 11 = 2^3 + 3^1; e(5) = 17 = 2^4 + 1; e(6) = 41 = 2^5 + 3^2, which of course immediately leads to our formula above. Note: For m>0, we take m^(1/2) to be the unique positive square root of m. a(2^n + 1), n=0,1,2,... are the Fermat numbers. LINKS Index entries for linear recurrences with constant coefficients, signature (2,4,-8,-3,6). PROG (PARI) a(n) = 2^(n-1) + (2 + (-1)^n)^((n-2)/2) \\ Charles R Greathouse IV, Jan 29 2013 CROSSREFS Cf. A082605. Sequence in context: A203074 A014556 A062737 * A082605 A007755 A060611 Adjacent sequences:  A085610 A085611 A085612 * A085614 A085615 A085616 KEYWORD nonn,easy AUTHOR Ben de la Rosa & Johan Meyer (MeyerJH.sci(AT)mail.uovs.ac.za), Jul 09 2003 EXTENSIONS More terms from Neven Juric, Apr 10 2008 STATUS approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)