Some considerations on the total stopping time for the Collatz problem

Abstract

Introduction/purpose: The Collatz conjecture has been considered and the stopping time needed for the recursive transformation to end has been investigated. Methods: A statistical analysis on the stopping time has been used. Results: The statistical approach shows that the probability of finding an infinite stopping time, that is a violation of the Collatz conjecture, is extremely low. Conclusion: Picking precisely one particular atom in the Universe is still more favorable, by more than 61 orders of magnitude, than encountering an infinite total stopping time.

Keywords

• collatz conjecture
• recurrences
• statistical analysis
• curve fitting