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  1. Home > Articles & Issues >
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  3. Walking Cautiously I ...
Conference paper

Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

Edward G. Belaga (1), Maurice Mignotte (1)
(1) Institut de Recherche Mathématique Avancée
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Imported on
May 10, 2017
Published on
December 31, 2005
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Proceedings
DOI
10.46298/dmtcs.3512
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https://about.hal.science/hal-authorisation-v1
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Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

Edward G. Belaga (1), Maurice Mignotte (1)
(1) Institut de Recherche Mathématique Avancée
Abstract
Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: \emphalgorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their \emphcyclic and divergent properties.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • Diophantine approximations
  • exponential Diophantine equations
  • algorithmic decidability
  • pseudo-rundom walks
  • 3n+1
  • or Collatz problem
  • Collatz and Conway transforms
  • discrete dynamical systems
Cited by

Source: OpenCitations

  • A Novel Theoretical Framework Formulated for Information Discovery from Number System and Collatz Conjecture Data

    Procedia Computer Science

    Authors : Michael A. Idowu

    Journal reference : Volume 61, 2015, pp. 105-111

    DOI : 10.1016/j.procs.2015.09.165

  • Two Remarks on the Collatz Cycle Conjecture

    The Fibonacci Quarterly

    Authors : Masayoshi Kaneda ORCID

    Journal reference : Volume 53, 2015, pp. 168-174

    DOI : 10.1080/00150517.2015.12428279
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