This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A072191 a(n) = a(n-1)^2 + 2. 2
 0, 2, 6, 38, 1446, 2090918, 4371938082726, 19113842599189892819591078, 365338978906606237729724396156395693696687137202086, 133472569508521677503139972517335009022889462418844369330479463819154657319297609174034202576402751398 (list; graph; refs; listen; history; text; internal format)
 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. 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. 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: A006536 A057297 A005530 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)