A generalization of Hasse's generalization of the Syracuse algorithm
K. R. Matthews,A. M. Watts +1 more
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This article is published in Acta Arithmetica.The article was published on 1984-01-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Generalization & Ergodic theory.read more
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THE 3x + 1 PROBLEM: TWO STOCHASTIC MODELS
Jeffrey C. Lagarias,A. Weiss +1 more
TL;DR: In this paper, two kinds of stochastic models that mimic the behavior of the $3x + 1$ conjecture are described. But they are not the same as the branching random walk model.
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Stochastic Models for the 3x+1 and 5x+1 Problems
TL;DR: In this article, stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x + 1 problem are presented.
Generalized 3x+1 mappings: Markov chains and ergodic theory
TL;DR: In this paper, the authors review connections of the 3x+1 mapping and its generalizations with ergodic theory and Markov chains, and describe the observed limiting frequencies of divergent trajectories in the congruence classes (mod m).
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Iterates of Number Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x + 1 Problem)
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Some Borel measures associated with the generalized Collatz mapping
TL;DR: In this article, the authors extended T to a mapping of polyadic numbers and constructed finitely many ergodic Borel measures on the polyadic number Ẑ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.