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

This research introduces <b>FAR-1 (Faizan Ali Reduction – Version 1)</b>, a novel integer reduction algorithm designed to outperform traditional <b>Collatz</b> and <b>Half-Collatz</b> approaches in step efficiency.The method follows a simple rule:<br>If <b>n % 3 == 0</b> → n = n / 3<br>Else → n = n - 1In benchmarking across integers from <b>1 to 100,000,000</b>, FAR-1 is faster than Half-Collatz in over <b>95% of cases</b> and significantly faster than Collatz on average. The algorithm consistently reduces integers to 1 in fewer steps, with a simpler and more efficient structure.<br><br>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.<br><br><br>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:<br>https://github.com/Faizanali412/FAR-1-Integer-ReductionAlso<br><br>https://doi.org/10.5281/zenodo.15851417