A087046 Algebraic order of r_n, the value of r in the logistic map that corresponding to the onset of the period 2^n-cycle.

1, 2, 12, 240, 65280, 4294901760, 18446744069414584320, 340282366920938463444927863358058659840, 115792089237316195423570985008687907852929702298719625575994209400481361428480

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Ilias S. Kotsireas and Kostas Karamanos, Exact computation of the bifurcation point B4 of the logistic map and the Bailey-Broadhurst conjectures, Internat. J. Bifur. Chaos Appl. Sci. Engrg., Vol. 14, No. 7 (2004), pp. 2417-2423; alternative link.

Eric Weisstein's World of Mathematics, Logistic Map.

Formula

a(n) = 2^(2^(n - 1)) - 2^(2^(n - 2)) with n>1, a(1)=1. - Cheng Zhang, Apr 02 2012

Sum_{n>=1} 1/a(n) = 1 + A346192. - Amiram Eldar, Jul 18 2021

Mathematica

Table[If[n <= 1, 1, 2^(2^(n - 1)) - 2^(2^(n - 2))], {n, 1, 10}] (* Cheng Zhang, Apr 02 2012 *)

Prog

(PARI) a(n) = 1<<(1<<(n-1)) - 1<<(1<<(n-2)); \\ Kevin Ryde, Jan 18 2024

Crossrefs

Cf. A086180, A086181, A087089, A118454, A000215, A346192.

Cf. A051179 (partial sums).

Sequence in context: A007685 A132987 A366350 * A111403 A325501 A007986

Adjacent sequences: A087043 A087044 A087045 * A087047 A087048 A087049

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 04 2003

Extensions

More terms from Cheng Zhang, Apr 03 2012

Status

approved