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TopicsNumber theory Probabilistic Collatz dynamics Collatz conjecture

For random odd N, the 2-adic valuation of 3N+1 is geometrically distributed with mean 2.

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Almost all Collatz orbits attain almost bounded valuesSep 10, 2019 Untraced · nothing upstream recorded

any given value {a \in{\bf N}+1} with probability {2^{-a}}. Such a geometric random variable is twice as likely to be odd as to be even

Almost all Collatz orbits attain almost bounded valuesextraction 0.85

number of times 2 divides 3N+1 has geometric distribution of mean 2

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Created by extractor · Sep 13, 2026. Every judgment on this page is accompanied by a reasoning trace.