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 - 1In 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 Figshare record includes:The full research paper (PDF)Python scripts for testing and analysisZipped CSV benchmark datasets (split into 4 parts)Visual step comparison plotsAll files and source code are also hosted on GitHub:https://github.com/Faizanali412/FAR-1-Integer-ReductionAlsohttps://doi.org/10.5281/zenodo.15851417