On the Probabilistic Proof of the Convergence of the Collatz Conjecture
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-01
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
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 2 that follows a recurrent pattern of the form x,1,x,1…, where x 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.
American Psychological Association (APA)
Barghout, Kamal. 2019. On the Probabilistic Proof of the Convergence of the Collatz Conjecture. Journal of Probability and Statistics،Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1186861
Modern Language Association (MLA)
Barghout, Kamal. On the Probabilistic Proof of the Convergence of the Collatz Conjecture. Journal of Probability and Statistics No. 2019 (2019), pp.1-11.
https://search.emarefa.net/detail/BIM-1186861
American Medical Association (AMA)
Barghout, Kamal. On the Probabilistic Proof of the Convergence of the Collatz Conjecture. Journal of Probability and Statistics. 2019. Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1186861
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186861