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The Ultimate Challenge: The $3x+1$ Problem


About this Title

Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, Editor

Publication: Miscellaneous Books
Publication Year: 2010; Volume 78
ISBNs: 978-0-8218-4940-8 (print); 978-1-4704-1813-7 (online)
DOI: https://doi.org/10.1090/mbk/078

This volume is not part of this online collection.

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Table of Contents


Part I. Overview and introduction

  • 1. The $3x+1$ problem: An overview
  • 2. The $3x+1$ problem and its generalizations

Part II. Survey papers

  • 3. A $3x+1$ Survey: Number theory and dynamical systems
  • 4. Generalized $3x+1$ mappings: Markov chains and ergodic theory
  • 5. Generalized $3x+1$ functions and the theory of computation

Part III. Stochastic modelling and computation papers

  • 6. Stochastic models for the $3x+1$ and $5x+1$ problems and related problems
  • 7. Empirical verification of the $3x+1$ and related conjectures

Part IV. Reprinted early papers

  • 8. Cyclic sequences and Frieze patterns (The Fourth Felix Behrend Memorial Lecture)
  • 9. Unpredictable iterations
  • 10. Iteration of the number-theoretic function $f(2n)=n,f(2n+1)=3n+2$
  • 11. Don’t try to solve these problems!
  • 12. On the motivation and origin of the $(3n+1)$-problem
  • 13. FRACTRAN: A simple universal programming language for arithmetic

Part V. Annotated bibliography

  • 14. The $3x+1$ problem: An annotated bibliography (1963–1999)