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arXiv · 2512.13760

Counting the Collatz numbers

Chunlei Liu
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Abstract

The counting function for the numbers satisfying the Collatz conjecture is studied. A related exponential congruence equation is investigated, yielding a method to construct its solutions from free variables, and enabling us to find at least $x^{0.3227}$ Collatz numbers in the interval $[1,x]$. The historical record is 0.84.

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Chunlei Liu. 2025-12-15. Counting the Collatz numbers. https://arxiv.org/abs/2512.13760

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