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 A094680 a(n+1) = 4*a(n)^3 - 3*a(n), with a(0) = 2. 1
 2, 26, 70226, 1385331749802026, 10634604778476758291777057017318241822792488226 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Smallest positive integer x satisfying the Pell equation x^2 - 3^(2*n-3) * y^2 = 1. - A.H.M. Smeets, Sep 29 2017 Term a(5) has 139 decimal digits and a(6) has 417 decimal digits. - Andrew Howroyd, Feb 25 2018 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..6 FORMULA a(n) = cosh(3^n*arccosh(2)). a(n) = ChebyshevT(3^n, 2). - Vladeta Jovovic, Jun 11 2004 From A.H.M. Smeets, Oct 02 2017: (Start) a(n) = A001075(3^(n-2)) a(n) = A002350(3^(2n-3)). (End) MATHEMATICA NestList[4 #^3 - 3 # &, 2, 5] (* Michael De Vlieger, Oct 02 2017 *) PROG (PARI) a(n) = if (n==0, 2, 4*a(n-1)^3 - 3*a(n-1)); \\ Michel Marcus, Oct 03 2017 (PARI) a(n) = polchebyshev(3^n, 1, 2); \\ Michel Marcus, Oct 03 2017 CROSSREFS Cf. A001075, A002812. Sequence in context: A268667 A330032 A273381 * A259326 A061192 A356136 Adjacent sequences: A094677 A094678 A094679 * A094681 A094682 A094683 KEYWORD nonn,easy AUTHOR Jose Eduardo Blazek, Jun 07 2004 EXTENSIONS More terms from Vladeta Jovovic, Jun 11 2004 Offset corrected by Michel Marcus, Oct 03 2017 STATUS approved

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Last modified April 13 11:28 EDT 2024. Contains 371640 sequences. (Running on oeis4.)