Collatz Conjecture

Asset Durmagambetov; Aniyar Durmagambetova

doi:10.20944/preprints202401.0227.v11

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preprints.org > computer science and mathematics > analysis > doi: 10.20944/preprints202401.0227.v11

Preprint Article Version 11 Preserved in Portico This version is not peer-reviewed

Collatz Conjecture

Asset Durmagambetov

^* and

Aniyar Durmagambetova

Version 1 : Received: 30 December 2023 / Approved: 3 January 2024 / Online: 4 January 2024 (03:23:16 CET)
Version 2 : Received: 5 January 2024 / Approved: 6 January 2024 / Online: 8 January 2024 (06:22:04 CET)
Version 3 : Received: 8 January 2024 / Approved: 8 January 2024 / Online: 8 January 2024 (10:32:51 CET)
Version 4 : Received: 10 January 2024 / Approved: 11 January 2024 / Online: 11 January 2024 (07:17:52 CET)
Version 5 : Received: 12 January 2024 / Approved: 12 January 2024 / Online: 15 January 2024 (03:45:13 CET)
Version 6 : Received: 21 January 2024 / Approved: 22 January 2024 / Online: 22 January 2024 (10:11:28 CET)
Version 7 : Received: 23 January 2024 / Approved: 23 January 2024 / Online: 23 January 2024 (09:59:20 CET)
Version 8 : Received: 24 January 2024 / Approved: 24 January 2024 / Online: 24 January 2024 (09:02:39 CET)
Version 9 : Received: 25 January 2024 / Approved: 26 January 2024 / Online: 29 January 2024 (04:21:12 CET)
Version 10 : Received: 1 February 2024 / Approved: 2 February 2024 / Online: 2 February 2024 (06:12:54 CET)
Version 11 : Received: 5 February 2024 / Approved: 5 February 2024 / Online: 5 February 2024 (08:16:07 CET)
Version 12 : Received: 5 February 2024 / Approved: 6 February 2024 / Online: 6 February 2024 (05:13:21 CET)
Version 13 : Received: 6 February 2024 / Approved: 7 February 2024 / Online: 7 February 2024 (06:25:43 CET)
Version 14 : Received: 7 February 2024 / Approved: 8 February 2024 / Online: 8 February 2024 (07:39:16 CET)
Version 15 : Received: 8 February 2024 / Approved: 8 February 2024 / Online: 10 February 2024 (05:58:49 CET)
Version 16 : Received: 18 February 2024 / Approved: 20 February 2024 / Online: 20 February 2024 (11:29:01 CET)
Version 17 : Received: 20 February 2024 / Approved: 22 February 2024 / Online: 22 February 2024 (11:40:27 CET)
Version 18 : Received: 3 March 2024 / Approved: 4 March 2024 / Online: 4 March 2024 (09:50:10 CET)
Version 19 : Received: 4 March 2024 / Approved: 5 March 2024 / Online: 5 March 2024 (05:59:39 CET)
Version 20 : Received: 17 March 2024 / Approved: 17 March 2024 / Online: 18 March 2024 (10:20:10 CET)
Version 21 : Received: 24 March 2024 / Approved: 24 March 2024 / Online: 25 March 2024 (08:12:10 CET)

How to cite: Durmagambetov, A.; Durmagambetova, A. Collatz Conjecture. Preprints 2024, 2024010227. https://doi.org/10.20944/preprints202401.0227.v11 Durmagambetov, A.; Durmagambetova, A. Collatz Conjecture. Preprints 2024, 2024010227. https://doi.org/10.20944/preprints202401.0227.v11

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MDPI and ACS Style

Durmagambetov, A.; Durmagambetova, A. Collatz Conjecture. Preprints 2024, 2024010227. https://doi.org/10.20944/preprints202401.0227.v11

APA Style

Durmagambetov, A., & Durmagambetova, A. (2024). Collatz Conjecture. Preprints. https://doi.org/10.20944/preprints202401.0227.v11

Chicago/Turabian Style

Durmagambetov, A. and Aniyar Durmagambetova. 2024 "Collatz Conjecture" Preprints. https://doi.org/10.20944/preprints202401.0227.v11

Abstract

This paper presents an analysis of the number of zeros in the binary representation of natural numbers. The primary method of analysis involves the use of the concept of the fractional part of a number, which naturally emerges in the determination of binary representation. This idea is grounded in the fundamental property of the Riemann zeta function, constructed using the fractional part of a number. Understanding that the ratio between the fractional and integer parts of a number, analogous to the Riemann zeta function, reflects the profound laws of numbers becomes the key insight of this work. The findings suggest a new perspective on the interrelation between elementary properties of numbers and more complex mathematical concepts, potentially opening new directions in number theory and analysis.

Keywords

binary representation; Collatz conjecture

Subject

Computer Science and Mathematics, Analysis

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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