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URL: https://oeis.org/A072191

⇱ A072191 - OEIS

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A072191
a(n) = a(n-1)^2 + 2.
4
0, 2, 6, 38, 1446, 2090918, 4371938082726, 19113842599189892819591078, 365338978906606237729724396156395693696687137202086, 133472569508521677503139972517335009022889462418844369330479463819154657319297609174034202576402751398
OFFSET
0,2
COMMENTS
This shows that in the Mandelbrot set (with z^2 + c), the point c = 2 escapes to infinity. - Alonso del Arte, Apr 08 2016
REFERENCES
Mordechai Ben-Ari, Mathematical Logic for Computer Science, Third edition, 173-203
LINKS
Samuel R. Buss, Herbrand's Theorem, University of California, San Diego La Jolla, California 92093-0112, U.S.A.
Neil J. Calkin, Eunice Y. S. Chan, and Robert M. Corless, Some Facts and Conjectures about Mandelbrot Polynomials, Maple Trans., Vol. 1, No. 1, Article 1 (July 2021).
Alessandro Farinelli, Herbrand Universe
Eric Weisstein's World of Mathematics, Weakly Binary Tree
Damiano Zanardini, Computational Logic, UPM European Master in Computational Logic (EMCL) School of Computer Science Technical University of Madrid, 2009-2010.
FORMULA
a(n) ~ c^(2^n), where c = 1.57583423499194129500626808486999436507... - Vaclav Kotesovec, Sep 20 2013
a(n) mod 2 = 0. - Altug Alkan, Oct 04 2015
EXAMPLE
0^2 + 2 = 2, 2^2 + 2 = 6, 6^2 + 2 = 38 ...
MATHEMATICA
NestList[#^2 + 2 &, 0, 10] (* Harvey P. Dale, Jan 23 2011 *)
PROG
(PARI) a(n)=if(n<1, 0, 2+a(n-1)^2) /* Michael Somos, Mar 25 2006 */
(Magma) [n le 1 select 0 else Self(n-1)^2+2: n in [1..10]]; // Vincenzo Librandi, Oct 05 2015
CROSSREFS
Cf. A001566 (a(n-1)^2-2), A003095 (a(n-1)^2+1).
Sequence in context: A057297 A005530 A353535 * A118324 A060421 A054970
KEYWORD
easy,nonn
AUTHOR
Miklos Kristof, Jul 02 2002
EXTENSIONS
Edited by Robert G. Wilson v, Jul 03 2002
STATUS
approved