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A072191 a(n) = a(n-1)^2 + 2.

%I A072191 #67 Feb 16 2025 08:32:46
%S A072191 0,2,6,38,1446,2090918,4371938082726,19113842599189892819591078,
%T A072191 365338978906606237729724396156395693696687137202086,
%U A072191 133472569508521677503139972517335009022889462418844369330479463819154657319297609174034202576402751398
%N A072191 a(n) = a(n-1)^2 + 2.
%C A072191 This shows that in the Mandelbrot set (with z^2 + c), the point c = 2 escapes to infinity. - _Alonso del Arte_, Apr 08 2016
%D A072191 Mordechai Ben-Ari, Mathematical Logic for Computer Science, Third edition, 173-203
%H A072191 Samuel R. Buss, <a href="http://math.ucsd.edu/~sbuss/ResearchWeb/herbrandtheorem/paper.pdf">Herbrand's Theorem</a>, University of California, San Diego La Jolla, California 92093-0112, U.S.A.
%H A072191 Neil J. Calkin, Eunice Y. S. Chan, and Robert M. Corless, <a href="https://ojs.lib.uwo.ca/index.php/maple/article/view/14037">Some Facts and Conjectures about Mandelbrot Polynomials</a>, Maple Trans., Vol. 1, No. 1, Article 1 (July 2021).
%H A072191 Alessandro Farinelli, <a href="http://profs.sci.univr.it/~farinelli/courses/ar/slides/herbrand.pdf">Herbrand Universe</a>
%H A072191 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WeaklyBinaryTree.html">Weakly Binary Tree</a>
%H A072191 Wikipedia, <a href="https://en.wikipedia.org/wiki/Herbrand_structure">Herbrand Structure</a>
%H A072191 Damiano Zanardini, <a href="http://costa.fdi.ucm.es/~damiano/teaching/emcl/cl_08_09/slides/12lprog.pdf">Computational Logic</a>, UPM European Master in Computational Logic (EMCL) School of Computer Science Technical University of Madrid, 2009-2010.
%H A072191 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A072191 a(n) ~ c^(2^n), where c = 1.57583423499194129500626808486999436507... - _Vaclav Kotesovec_, Sep 20 2013
%F A072191 a(n) mod 2 = 0. - _Altug Alkan_, Oct 04 2015
%e A072191 0^2 + 2 = 2, 2^2 + 2 = 6, 6^2 + 2 = 38 ...
%t A072191 NestList[#^2 + 2 &, 0, 10]  (* _Harvey P. Dale_, Jan 23 2011 *)
%o A072191 (PARI) a(n)=if(n<1, 0, 2+a(n-1)^2) /* _Michael Somos_, Mar 25 2006 */
%o A072191 (Magma) [n le 1 select 0 else Self(n-1)^2+2: n in [1..10]]; // _Vincenzo Librandi_, Oct 05 2015
%Y A072191 Cf. A001566 (a(n-1)^2-2), A003095 (a(n-1)^2+1).
%K A072191 easy,nonn
%O A072191 0,2
%A A072191 _Miklos Kristof_, Jul 02 2002
%E A072191 Edited by _Robert G. Wilson v_, Jul 03 2002