An optimal convergent Collatz algorithm

TL;DR

This paper introduces an optimal algorithm for the Collatz conjecture, demonstrating its convergence and relating it to the classical problem, with validation on the first 600 powers of 3.

Contribution

It presents a new convergent algorithm for the Collatz conjecture and establishes a mathematical relation to the classical problem, supported by empirical validation.

Findings

The algorithm converges for the first 600 powers of 3.

A new equation relating the algorithm to the classical Collatz conjecture.

Empirical validation supports the algorithm's effectiveness.

Abstract

In this research, an optimal algorithm for the Collatz conjecture is presented. Properties such as the convergence of the algorithm and an equation that relates the algorithm to the classical Collatz conjecture are obtained. It is validated that the proposed theory is correct with several examples; as a sector of mathematicians believes that the Collatz conjecture fails in some power of $3$. The algorithm was applied to the first $600$ powers of $3$, where the convergence of the proposed algorithm was verified.