Infinity increasing steps on the Collatz sequences

Abstract

We intend to contribute to the Collatz dynamics problem by seeking to analyze the Collatz conjecture from the tree of numbers sequences. First, we show numerically that the distribution of odd numbers has an initial transient, and proceeds to a power law growth to its maximum. Second, using the formulation that uses only odd numbers, we present analytically a set of odd number sequences that is always increasing and can have an infinite number of terms.