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On the Probabilistic Proof of the Convergence of the Collatz Conjecture

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  • Kamal Barghout

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.

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  • Kamal Barghout, 2019. "On the Probabilistic Proof of the Convergence of the Collatz Conjecture," Journal of Probability and Statistics, Hindawi, vol. 2019, pages 1-11, August.
    • Handle: RePEc:hin:jnljps:6814378
    DOI: 10.1155/2019/6814378
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    Cited by:

    1. Kamal Barghout & Wadii Hajji & Nidal Abu-Libdeh & Mohammad Al-Jamal, 2023. "Statistical Analysis of Descending Open Cycles of Collatz Function," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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