An optimal convergent Collatz algorithm

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.