About the proof of the Collatz conjecture

TL;DR

This paper explores a potential proof of the Collatz conjecture by analyzing the relationships between odd numbers and their followers, aiming to establish a recurrence that covers all natural numbers.

Contribution

It proposes a novel approach focusing on the direct odd followers of natural numbers to establish a recurrence relation for the conjecture.

Findings

Identifies connections between numbers and their odd followers

Develops a recurrence relation over number ranges

Suggests a pathway towards proving the conjecture

Abstract

I want to show one possibility to proof the Collatz conjecture, also called 3n+1 conjecture, for any natural number N. For this, I limit my analysis on the direct odd follower of every natural odd number and show the connections between the already by one reached numbers and their followers, to find an recurrence over all ranges [1,N_{i}], to proof the conjecture.