The 3x+1 problem : new lower bounds on nontrivial cycle lengths

Eliahou, Shalom

doi:10.1016/0012-365x(93)90052-u

Scientific article

English

The 3x+1 problem : new lower bounds on nontrivial cycle lengths

ContributorsEliahou, Shalom

Published inDiscrete mathematics, vol. 118, no. 1-3, p. 45-56

Publication date1993

Abstract

Let T: N → N be the function defined by T(n) = n/2 if n is even, T(n) = (3n + 1)/2 if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration of T must contain at least 17 087 915 elements.

Affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

ELIAHOU, Shalom. The 3x+1 problem : new lower bounds on nontrivial cycle lengths. In: Discrete mathematics, 1993, vol. 118, n° 1-3, p. 45–56. doi: 10.1016/0012-365x(93)90052-u

Identifiers

PID : unige:12087
DOI : 10.1016/0012-365x(93)90052-u

Journal ISSN0012-365X

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The 3x+1 problem : new lower bounds on nontrivial cycle lengths

Let T: N → N be the function defined by T(n) = n/2 if n is even, T(n) = (3n + 1)/2 if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration of T must contain at least 17 087 915 elements.

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