A062013 a(1) = 3, a(n) = a(n-1)^2 + 1.

3, 10, 101, 10202, 104080805, 10832813969448026, 117349858496668297583751115296677, 13770989289188072635789270799554901596999795308252284177727242330

Offset

1,1

Comments

Define f(n, c) := x - Sum_{k>=0} A088674(k)/(2*x)^(2*k+1) where x = c^(2^n). Then a(n) = f(n, 1.78050350...). - Michael Somos, Jun 07 2021

Links

Harry J. Smith, Table of n, a(n) for n = 1..11

Formula

a(n) ~ c^(2^n), where c = 1.78050350352842911667602268320603615359... - Vaclav Kotesovec, Sep 20 2013

Example

a(4) = a(3)^2 +1 = 101^2 +1 =10202

Mathematica

NestList[#^2+1&, 3, 10] (* Harvey P. Dale, Feb 21 2013 *)
a[ n_] := If[n < 2, 3 Boole[n == 1], A062013[n - 1]^2 + 1]; (* Michael Somos, Jun 07 2021 *)

Prog

(PARI) { for (n=1, 11, if (n==1, a=3, a=a^2 + 1); write("b062013.txt", n, " ", a) ) } [Harry J. Smith, Jul 29 2009]

Crossrefs

Cf. A003095, A088674.

Sequence in context: A015487 A326428 A260813 * A023372 A025541 A203903

Adjacent sequences: A062010 A062011 A062012 * A062014 A062015 A062016

Keyword

nonn

Author

Amarnath Murthy, Jun 01 2001

Extensions

More terms from Jason Earls, Jun 02 2001

Offset changed from 0,1 to 1,1 by Harry J. Smith, Jul 29 2009

Typo in a(8) corrected by N. J. A. Sloane, Aug 31 2009 using the b-file.

Status

approved