On the Probabilistic Proof of the Convergence of the Collatz Conjecture
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 sequenc...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2019/6814378 |
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| author | Kamal Barghout |
| author_facet | Kamal Barghout |
| author_sort | Kamal Barghout |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-aefddd41937a4f08bd1f3179f0f68a2b |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-aefddd41937a4f08bd1f3179f0f68a2b2025-02-03T01:23:45ZengWileyJournal of Probability and Statistics1687-952X1687-95382019-01-01201910.1155/2019/68143786814378On the Probabilistic Proof of the Convergence of the Collatz ConjectureKamal Barghout0Prince Mohammad Bin Fahd University, Al Khobar, Saudi ArabiaA 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.http://dx.doi.org/10.1155/2019/6814378 |
| spellingShingle | Kamal Barghout On the Probabilistic Proof of the Convergence of the Collatz Conjecture Journal of Probability and Statistics |
| title | On the Probabilistic Proof of the Convergence of the Collatz Conjecture |
| title_full | On the Probabilistic Proof of the Convergence of the Collatz Conjecture |
| title_fullStr | On the Probabilistic Proof of the Convergence of the Collatz Conjecture |
| title_full_unstemmed | On the Probabilistic Proof of the Convergence of the Collatz Conjecture |
| title_short | On the Probabilistic Proof of the Convergence of the Collatz Conjecture |
| title_sort | on the probabilistic proof of the convergence of the collatz conjecture |
| url | http://dx.doi.org/10.1155/2019/6814378 |
| work_keys_str_mv | AT kamalbarghout ontheprobabilisticproofoftheconvergenceofthecollatzconjecture |