

A102847


a(0)=1, a(n) = a(n1)*a(n1) + 2.


2




OFFSET

0,2


COMMENTS

The Mandelbrotprocess is z:=z*z+c, where z and c is complex. In our case c=2 and the initial z is 1. The process is very quickly increasing.
Prime for a(1)=3, a(2)=11, a(4)=15131; semiprime for a(3) = 123 = 3 * 41, a(5) = 228947163 = 3 * 76315721. a(6), added by Jonathan Vos Post, has 4 prime factors. a(7) = 41 * 811^2 * 106693969 * 317171188688357726699 * 8272236925540996054440172449761. When is the next prime in the sequence?  Jonathan Vos Post, Feb 28 2005
Composite for a(8), a(9), ..., a(19). a(20) is roughly 2^909982 and its primality is unknown.  Russ Cox, Apr 02 2006


LINKS

Table of n, a(n) for n=0..8.


FORMULA

a(n) ~ c^(2^n), where c = 1.8249111600523655937123650418390169034...  Vaclav Kotesovec, Sep 20 2013


EXAMPLE

a(2)=11, a(3)=11*11+2=123.


MAPLE

a[0]:=1: for n from 1 to 10 do a[n]:=a[n1]^2+2 od: seq(a[n], n=0..9); # Emeric Deutsch


MATHEMATICA

a[0] := 1; a[n_] := a[n  1]^2 + 2; Table[a[n], {n, 0, 10}] (* Stefan Steinerberger, Apr 08 2006 *)


PROG

(PARI) a(n)=if(n<1, n==0, 2+a(n1)^2) /* Michael Somos, Mar 25 2006 */


CROSSREFS

Bisection of A065653.
Sequence in context: A209107 A015047 A339326 * A113258 A113848 A287429
Adjacent sequences: A102844 A102845 A102846 * A102848 A102849 A102850


KEYWORD

easy,nonn


AUTHOR

Miklos Kristof, Feb 28 2005


EXTENSIONS

a(7) from Jonathan Vos Post, Feb 28 2005
a(8) from Emeric Deutsch, Jun 13 2005


STATUS

approved



