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

✍ Scribed by Shalom Eliahou

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 607 KB
Volume: 118
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90052-u

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✦ Synopsis

Eliahou,

S., The 3x+ 1 problem: new lower bounds on nontrivial cycle lengths, Discrete Mathematics 118 (1993) 45556.

Let 7': 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.