Treffer: FAR-1: A Fast Integer Reduction Algorithm Compared to Collatz and Half-Collatz

This research introduces FAR-1 (Faizan Ali Reduction – Version 1), a novel integer reduction algorithm designed to outperform traditional Collatz and Half-Collatz approaches in step efficiency. The method follows a simple rule:If n % 3 == 0 → n = n / 3Else → n = n - 1 In benchmarking across integers from 1 to 100,000,000, FAR-1 is faster than Half-Collatz in over 95% of cases and significantly faster than Collatz on average. The algorithm consistently reduces integers to 1 in fewer steps, with a simpler and more efficient structure. This submission includes a detailed research paper, Python source code, CSV results for inputs from 1 to 100 million, and step-count comparison graphs. Key findings: FAR-1 is faster than Half-Collatz in 95.38% of cases. FAR-1 averages 30.91 steps to reach 1. Half-Collatz averages 38.17 steps. Classic Collatz averages 179.23 steps. This Zenodo record includes: The full research paper (PDF) Python scripts for testing and analysis Zipped CSV benchmark datasets (split into 4 parts) Visual step comparison plots All files and source code are also hosted on GitHub:https://github.com/Faizanali412/FAR-1-Integer-Reduction