0,2

The Mandelbrot-process 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 (jvospost2(AT)yahoo.com), Feb 28 2005

Composite for a(8), a(9), ..., a(19). a(20) is roughly 2^909982, and its primality is unknown. - Russ Cox (rsc(AT)swtch.com), Apr 2 2006

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

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

a[0] := 1; a[n_] := a[n - 1]^2 + 2; Table[a[n], {n, 0, 10}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006

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

Bisection of A065653.

Sequence in context: A068693 A036930 A015047 this_sequence A113258 A113848 A088075

Adjacent sequences: A102844 A102845 A102846 this_sequence A102848 A102849 A102850

easy,nonn

Miklos Kristof (kristmikl(AT)freemail.hu), Feb 28 2005

a(7) from Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 28 2005

a(8) from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 13 2005