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TopicsCollatz conjecture Number theory Logarithmic density

For almost all N, Col_min(N) is below N^θ for any fixed θ greater than log3/log4 ≈ 0.7924.

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

extended later by Korec to cover all {\theta > \frac{\log 3}{\log 4} \approx 0.7924}

Almost all Collatz orbits attain almost bounded valuesextraction 0.93

improvement of the exponent for almost all N

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