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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
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
Sequence in context: A268667 A330032 A273381 * A259326 A061192 A356136
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.)