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

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

Offset: 1

Author

Amarnath Murthy, Jun 01 2001

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A003095, A088674.

Programs

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 *)

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]

Formula

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

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.