An Exploration Into the Collatz Conjecture with Changed Parameters

TL;DR

This paper investigates the behavior of a modified Collatz-like problem with different parameters, revealing diverse patterns such as convergence, divergence, and cycles, and exploring connections between different variants.

Contribution

It introduces new parameter variations of the Collatz problem and analyzes their behaviors, highlighting patterns and relationships not previously documented.

Findings

Some numbers converge to one under 5n+1

Others escape to infinity or form cycles

Connections between 3n+1 and 3n+5 variants are identified

Abstract

Exploring the Collatz Conjecture and changing the expression from 3n + 1 to 5n + 1, we found patterns in different sets of numbers. Some numbers reduce to one (as stated in the Collatz Conjecture), some might escape to infinity, and some get stuck in repeating cycles. To further explore the patterns involved in Collatz-like expressions, we changed the expression to 3n+5 and found connections between 3n+1 and 3n+5.