A145508 a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 8.

8, 78, 6238, 38925118, 1515164889164158, 2295724641355838227053650177278, 5270351628928392053240255925779522360603268430188068127843838

Offset

1,1

Comments

See A145502 for a formula for a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = k-1.

Links

Jason Yuen, Table of n, a(n) for n = 1..11

Formula

From Peter Bala, Nov 12 2012: (Start)

a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha = (9 + sqrt(77))/2.

a(n) == 1 (mod 7).

Recurrence: a(n) = 10*(Product_{k = 1..n-1} a(k)) - 2 with a(1) = 8.

Product_{n >= 1} (1 + 1/a(n)) = 10/sqrt(77).

Product_{n >= 1} (1 + 2/(a(n) + 1)) = sqrt(11/7). (End)

Mathematica

aa = {}; k = 8; Do[AppendTo[aa, k]; k = k^2 + 2 k - 2, {n, 1, 10}]; aa
(* or *)
k = 9; Table[Floor[((k + Sqrt[k^2 - 4])/2)^(2^(n - 1))], {n, 1, 7}]
NestList[#^2+2#-2&, 8, 8] (* Harvey P. Dale, Sep 20 2013 *)

Crossrefs

Cf. A145502-A145510.

Sequence in context: A071556 A316203 A303507 * A266090 A366214 A061425

Adjacent sequences: A145505 A145506 A145507 * A145509 A145510 A145511

Keyword

nonn,easy

Author

Artur Jasinski, Oct 11 2008

Status

approved