A Randomized Version of the Collatz $3x + 1$ Problem

TL;DR

This paper introduces a stochastic variant of the classic Collatz problem, aiming to analyze its behavior through probabilistic methods to gain new insights into the longstanding mathematical conjecture.

Contribution

It presents a novel randomized formulation of the Collatz problem, providing a new perspective and tools for understanding its dynamics.

Findings

Initial probabilistic analysis suggests different convergence properties.

Simulation results indicate potential patterns in the stochastic process.

The approach opens new avenues for research in probabilistic number theory.

Abstract

We propose a stochastic version of the Collatz $3x + 1$ Problem.