This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A102847 #22 Mar 27 2023 09:01:37
%S A102847 1,3,11,123,15131,228947163,52416803445748571,
%T A102847 2747521283470239265968814548542043,
%U A102847 7548873203121950871924356140057489033996373873303512592376938613851
%N A102847 a(0)=1, a(n) = a(n-1)*a(n-1) + 2.
%C A102847 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.
%C A102847 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
%C A102847 Composite for a(8), a(9), ..., a(19). a(20) is roughly 2^909982 and its primality is unknown. - _Russ Cox_, Apr 02 2006
%F A102847 a(n) ~ c^(2^n), where c = 1.8249111600523655937123650418390169034... - _Vaclav Kotesovec_, Sep 20 2013
%e A102847 a(2)=11, a(3)=11*11+2=123.
%p A102847 a[0]:=1: for n from 1 to 10 do a[n]:=a[n-1]^2+2 od: seq(a[n],n=0..9); # _Emeric Deutsch_
%t A102847 a[0] := 1; a[n_] := a[n - 1]^2 + 2; Table[a[n], {n, 0, 10}] (* _Stefan Steinerberger_, Apr 08 2006 *)
%t A102847 NestList[#^2+2&,1,10] (* _Harvey P. Dale_, Mar 27 2023 *)
%o A102847 (PARI) a(n)=if(n<1, n==0, 2+a(n-1)^2) /* _Michael Somos_, Mar 25 2006 */
%Y A102847 Bisection of A065653.
%K A102847 easy,nonn
%O A102847 0,2
%A A102847 _Miklos Kristof_, Feb 28 2005
%E A102847 a(7) from _Jonathan Vos Post_, Feb 28 2005
%E A102847 a(8) from _Emeric Deutsch_, Jun 13 2005