Some considerations on the total stopping time for the Collatz problem - Fabiano, Nicola; Mirkov, Nikola; Radenović, Stojan (Vojnotehnički glasnik / Military Technical Courier, 2024)
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