Article
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Calculation of the Number of Transactions for Collatz Conjecture
Version 1
: Received: 15 July 2024 / Approved: 16 July 2024 / Online: 16 July 2024 (09:24:14 CEST)
How to cite: Gocgen, A. F.; Buyukyayla, E. M. Calculation of the Number of Transactions for Collatz Conjecture. Preprints 2024, 2024071312. https://doi.org/10.20944/preprints202407.1312.v1 Gocgen, A. F.; Buyukyayla, E. M. Calculation of the Number of Transactions for Collatz Conjecture. Preprints 2024, 2024071312. https://doi.org/10.20944/preprints202407.1312.v1
Abstract
In this article we have constructed a basic methodology from which important perspectives for both the Collatz conjecture and Beal's conjecture can be derived. We falsified the conjecture we previously developed on Beal's conjecture and made the falsified conjecture usable for Collatz conjecture. In this regard, we have clearly expressed the numbers that can reach 1 in the Collatz conjecture. Then, using this, we created a limit for the numbers that should be considered for the Collatz conjecture. Thanks to the analysis of this limit, we have clearly expressed the recursive Collatz function in an equation. Using this structure, we wrote a function that indicates how many times the Collatz function repeats certain numbers to reach 1.
Keywords
collatz conjecture; beal’s conjecture; composite numbers; recursive structure; number of transactions
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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