A145505 a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 5.

5, 33, 1153, 1331713, 1773462177793, 3145168096065837266706433, 9892082352510403757550172975146702122837936996353

Offset

1,1

Comments

See A145502 for a general 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 = 3 + 2*sqrt(2).

a(n) = (1 + sqrt(2))^(2^n) + (sqrt(2) - 1)^(2^n) - 1.

a(n) = A003423(n-1) - 1.

a(n) = 2*A001601(n) - 1.

a(n) = 4*A190840(n-1) + 1.

Recurrence: a(n) = -2 + 7*Product_{k=1..n-1} a(k) with a(1) = 5.

Product_{n>=1} (1 + 1/a(n)) = (7/8)*sqrt(2).

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

Mathematica

NestList[#^2+2#-2&, 5, 7]  (* Harvey P. Dale, Mar 19 2011 *)

Crossrefs

Cf. A145502-A145510, A003423, A001601, A190840.

Sequence in context: A268296 A212296 A276160 * A276126 A193325 A303693

Adjacent sequences: A145502 A145503 A145504 * A145506 A145507 A145508

Keyword

nonn

Author

Artur Jasinski, Oct 11 2008

Status

approved