A072191 a(n) = a(n-1)^2 + 2.
0, 2, 6, 38, 1446, 2090918, 4371938082726, 19113842599189892819591078, 365338978906606237729724396156395693696687137202086, 133472569508521677503139972517335009022889462418844369330479463819154657319297609174034202576402751398
Offset: 0
Examples
0^2 + 2 = 2, 2^2 + 2 = 6, 6^2 + 2 = 38 ...
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
- 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 + ...
Programs
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Magma
[n le 1 select 0 else Self(n-1)^2+2: n in [1..10]]; // Vincenzo Librandi, Oct 05 2015
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Mathematica
NestList[#^2 + 2 &, 0, 10] (* Harvey P. Dale, Jan 23 2011 *)
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PARI
a(n)=if(n<1, 0, 2+a(n-1)^2) /* Michael Somos, Mar 25 2006 */
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
Extensions
Edited by Robert G. Wilson v, Jul 03 2002
Comments