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

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

Table of n, a(n) for n=0..9.

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

Wikipedia, Herbrand Structure

Damiano Zanardini, Computational Logic, UPM European Master in Computational Logic (EMCL) School of Computer Science Technical University of Madrid, 2009-2010.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

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

Adjacent sequences: A072188 A072189 A072190 * A072192 A072193 A072194

Keyword

easy,nonn

Author

Miklos Kristof, Jul 02 2002

Extensions

Edited by Robert G. Wilson v, Jul 03 2002

Status

approved