Bottom-up Approach to the Collatz Conjecture

The Collatz conjecture states that, by following two specific arithmetic operations, every positive integer can be transformed into 1. The rules are that each even number must be divided by 2, while odd numbers are multiplied by 3 and then 1 is added to them. Despite its simplicity, the conjecture has not been proven. For this, an inverted version of the Collatz conjecture, in which it is possible to start from n1=1 to later produce any number, was used to standardize the behavior that the sequence follows. Consequently, formulas were made to describe the observed sequences, and a proof of the tendency of every integer to reach the expected outcome, was developed.