Some considerations on Collatz conjecture

TL;DR

This paper explores properties of the Collatz tree and chains, providing new insights that may help understand the conjecture, despite it remaining unproven.

Contribution

It introduces new facts about the Collatz tree and chains, reducing the complexity of the problem's significant elements.

Findings

Reduction in the number of significant elements in the Collatz tree

New facts about chains in the Collatz tree

Potential insights into the Collatz conjecture's nature

Abstract

Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact may cast some light on the nature of the problem.