English

Counting the Collatz numbers

General Mathematics 2025-12-18 v2

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 x0.3227x^{0.3227} Collatz numbers in the interval [1,x][1,x]. The historical record is 0.84.

Cite

@article{arxiv.2512.13760,
  title  = {Counting the Collatz numbers},
  author = {Chunlei Liu},
  journal= {arXiv preprint arXiv:2512.13760},
  year   = {2025}
}
R2 v1 2026-07-01T08:25:59.397Z