A remark about the density of the orbits of the Collatz permutation

DOI10.1016/j.disc.2013.05.003zbMath1350.11014OpenAlexW2070090016MaRDI QIDQ390288

Mohammad Hasan, H. S. Yoon

Publication date: 23 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.disc.2013.05.003

zbMATH Keywords

Collatz original functioniteration number-theoretic functions

Mathematics Subject Classification ID

Recurrences (11B37) Special sequences and polynomials (11B83) Density, gaps, topology (11B05)

Cites Work

• Density of sets of natural numbers and the Lévy group
• Density of natural numbers and the Lévy group
• Iteration of the number-theoretic function \(f(2n)=n\), \(f(2n+1)=3n+2\)
• Lévy group and density measures
• The 3x + 1 Problem and Its Generalizations
• A generalization of Hasse's generalization of the Syracuse algorithm
• Iterates of Number Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x+ 1 Problem)
• Lévy group action and invariant measures on 𝛽{ℕ}
• Finitely additive measures on \(\mathbb{N}\)
• On a generalization of the \(3x+1\) problem
• Unsolved problems in number theory