On the Probabilistic Proof of the Convergence of the Collatz Conjecture

Kamal Barghout

Journal of Probability and Statistics, 2019, vol. 2019, 1-11

Abstract:

A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by that follows a recurrent pattern of the form , where represents divisions by 2 more than once. The sequence presents a probability of 50:50 of division by 2 more than once as opposed to division by 2 once over the even natural numbers. The sequence also gives the same 50:50 probability of consecutive Collatz even elements when counted for division by 2 more than once as opposed to division by 2 once and a ratio of 3:1. Considering Collatz function producing random numbers and over sufficient number of iterations, this probability distribution produces numbers in descending order that lead to the convergence of the Collatz function to 1, assuming that the only cycle of the function is 1-4-2-1.

Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/JPS/2019/6814378.pdf (application/pdf)
http://downloads.hindawi.com/journals/JPS/2019/6814378.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:6814378

DOI: 10.1155/2019/6814378

Access Statistics for this article

More articles in Journal of Probability and Statistics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().