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The \(3x+1\) problem: New lower bounds on nontrivial cycle lengths

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Publication:685592
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DOI10.1016/0012-365X(93)90052-UzbMath0786.11012WikidataQ63353519 ScholiaQ63353519MaRDI QIDQ685592

Shalom Eliahou

Publication date: 2 November 1993

Published in: Discrete Mathematics (Search for Journal in Brave)


zbMATH Keywords

cyclestrajectory\(3x+1\)-conjectureCollatz functionone-sided diophantine approximation of \(\log_ 2(3)\)


Mathematics Subject Classification ID

Special sequences and polynomials (11B83)


Related Items (9)

On generalized circuit of the Collatz conjecture ⋮ On a class of 2-adic functions related to the ``\(3x+1\)-problem ⋮ Linear dynamics of an operator associated to the Collatz map ⋮ Is the Syracuse falling time bounded by 12? ⋮ The autoconjugacy of the \(3x+1\) function. ⋮ Unnamed Item ⋮ A Dual-Radix Approach to Steiner’s 1-Cycle Theorem ⋮ The \(3x+1\) problem: a lower bound hypothesis ⋮ Maximum excursion and stopping time record-holders for the problem: Computational results



Cites Work

  • The Collatz problem
  • The 3x + 1 Problem and Its Generalizations
  • Continued Fractions without Tears
  • On the "3x + 1" Problem


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