An improved algorithm for checking the Collatz conjecture for all n < 2^N
Abstract
We describe a new algorithm for verifying the Collatz conjecture for all n < 2^N for some fixed N. The algorithm takes less than twice as long to verify convergence for all n < 2^{N+1} as it does to verify convergence for all n < 2^N. We also discuss verification of the analogue of the Collatz conjecture for negative numbers.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Dynamics and Fractals
Advanced Mathematical Theories
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 February 2026
- Language
- EN
- Document type
- Preprint