Considerations on the Collatz Conjecture

Abstract

Part of the scientific community has spent considerable time and resources to somehow validate Collatz's conjecture, countless efforts have achieved considerable progress in this direction, however this conjecture lacked definitive confirmation that choosing any odd number xi ∈ N∗, we will obtain x(i+1) = 3xi + 1, this being an even number x(i+1), divide it by the number two (successively) until another odd number ∈ N∗ is obtained, the process is repeated xn = 3x(n−1) + 1 and divisions by two until a number equal to 1 finally results.
This work presents deductions, algorithms and equations that corroborate this proposition, supporting this perception and conclusion that Collatz's conjecture points to the final cycle 4 → 2 → 1.