A randomized version of the Collatz 3x+1 problem

Aristides V. Doumas and Vassilis G. Papanicolaou

Statistics & Probability Letters, 2016, vol. 109, issue C, 39-44

Abstract: We consider a Markov chain on the positive odd integers, which can be viewed as a stochastic version of the Collatz 3x+1 Problem. We show that, no matter its initial value, the chain visits 1 infinitely often. Its values, however, are unbounded.

Keywords: Collatz 3x+1 problem; Markov chain (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2015.10.017

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