On a generalization of the \(3x+1\) problem

DOI10.1006/AAMA.1996.0496zbMath0886.11009OpenAlexW2463169724MaRDI QIDQ5906835

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Publication date: 23 April 1998

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.1996.0496

zbMATH Keywords

integer-valued polynomialsbijectivity\(3n+1\) problemdensity one resultsgeneralized Collatz mappingsiterations of periodically linear functionslinear recurrence functions

Mathematics Subject Classification ID

Recurrences (11B37) Polynomials over commutative rings (13B25)

Related Items (3)

Injectivity and surjectivity of Collatz functions ⋮ Visualizing generalized \(3x+1\) function dynamics based on fractal ⋮ A remark about the density of the orbits of the Collatz permutation

Cites Work

• A generalization of Everett's result on the Collatz \(3x+1\) problem
• Iteration of the number-theoretic function \(f(2n)=n\), \(f(2n+1)=3n+2\)
• A Markov process underlying the generalized Syracuse algorithm
• A Markov approach to the generalized Syracuse algorithm
• The 3x + 1 Problem and Its Generalizations
• A generalization of Hasse's generalization of the Syracuse algorithm
• A stopping time problem on the positive integers
• Unsolved problems in number theory
• On the \(3x+1\) problem

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