Function to estimate the total stopping time distribution of the Collatz problem based on the stochastic approach.
This repository contains a code implementing a function that approximates the total stopping time distribution of the Collatz (3x+1) problem [1] based on the Brownian motion model.
We derived this distribution function in a similar approach described in [2], [3]. The longest total stopping time can be estimated by using the distribution function.
| folder name | explanation |
|---|---|
| doc | Mathematical details on this approach. |
| results | Comparison results of the Collatz sequences and estimation by the distribution function. |
| src | A Code implementing the distribution function. |
The results folder containts
- the total stopping time distribution of the Collatz sequences (3-point moving average) for numbers in [1, 10^6] and estimation results.
- the longest total stopping time of the Collatz sequences [4] and predictions of it for numbers less than 10^50.
This project is licensed under the terms of the MIT license.
- [1] Lagarias, Jeffrey C., ed. The ultimate challenge: The 3x+ 1 problem. American Mathematical Soc., 2010.
- [2] Kontorovich, Alex V., and Jeffrey C. Lagarias. "Stochastic Models for the 3x+ 1 and 5x+ 1 Problems." arXiv preprint arXiv:0910.1944 (2009).
- [3] Borovkov, Konstantin Aleksandrovich, and Dietmar Pfeifer. "Estimates for the Syracuse problem via a probabilistic model." Theory of Probability & Its Applications 45.2 (2001): 300-310.
- [4] Roosendaal, Eric. "3x+1 Delay Records". http://www.ericr.nl/wondrous/delrecs.html