What Happens in the Collatz Iteration
Abstract
We give a direct and explicit arithmetic description of the behavior of theCollatz map on odd integers.All odd steps are shown to pass through a single affine progression beforedivision by powers of two.An exhaustive table describes how this progression decomposes under repeateddivision by $2$ and returns to odd values.No probabilistic, asymptotic, or heuristic arguments are used.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic Number Theory Research
Advanced Mathematical Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 18 January 2026
- Language
- EN