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 A118558 a(n) = (2^n-1)^4 - 2. 0
 -2, -1, 79, 2399, 50623, 923519, 15752959, 260144639, 4228250623, 68184176639, 1095222947839, 17557851463679, 281200199450623, 4501401006735359, 72040003462430719, 1152780773560811519, 18445618199572250623, 295138898083176775679, 4722294425687923097599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Exponent-4 analog of what for exponent 2 is A093112 (2^n-1)^2 - 2 = 4^n - 2^{n+1} - 1 and exponent 3 is A098878 (2^n - 1)^3 - 2. Primes include a(n) for n = 0, 2, 3, 11, 57; a type of "near-biquadratic primes." No more primes through (2^100-1)^4 - 2. Semiprimes include a(n) for n = 5, 6, 8, 10, 13, 14, 19, 20, 21, 25, 33, 35, 36, 40, 43, 51, 53, 63. LINKS Eric Weisstein's World of Mathematics, Near-Square Prime. Index entries for linear recurrences with constant coefficients, signature (31,-310,1240,-1984,1024). FORMULA a(n) = (2^n - 1)^4 - 2. G.f.: x*(1984*x^4-2120*x^3+510*x^2-61*x+2) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(16*x-1)). - Colin Barker, Apr 30 2013 EXAMPLE a(0) = (2^0 - 1)^4 - 2 = 0^4 - 2 = -2. a(1) = (2^1 - 1)^4 - 2 = 1^4 - 2 = -1. a(2) = (2^2 - 1)^4 - 2 = 3^4 - 2 = 79 (prime). a(3) = (2^3 - 1)^4 - 2 = 7^4 - 2 = 2399 (prime). a(11) = (2^11 - 1)^4 - 2 = 17557851463679 (prime). a(57) = (2^57 - 1)^4 - 2 = 431359146674410224742050828377557509468732765984721170947417969786879 (prime). PROG (PARI) a(n)=(2^n-1)^4-2 \\ Charles R Greathouse IV, Feb 19 2016 CROSSREFS Cf. A091516, A091515, A098878, A091514. Sequence in context: A247793 A067276 A118580 * A095837 A095835 A147805 Adjacent sequences:  A118555 A118556 A118557 * A118559 A118560 A118561 KEYWORD easy,sign AUTHOR Jonathan Vos Post, May 03 2006 STATUS approved

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Last modified October 7 14:13 EDT 2022. Contains 357271 sequences. (Running on oeis4.)