A Solution of The Collatz Conjecture Problem

Baoyuan Duan

doi:10.20944/preprints202301.0541.v15

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preprints.org > computer science and mathematics > signal processing > doi: 10.20944/preprints202301.0541.v15

Preprint Article Version 15 Preserved in Portico This version is not peer-reviewed

A Solution of The Collatz Conjecture Problem

Baoyuan Duan

Version 1 : Received: 30 January 2023 / Approved: 30 January 2023 / Online: 30 January 2023 (06:21:02 CET)
Version 2 : Received: 11 February 2023 / Approved: 13 February 2023 / Online: 13 February 2023 (02:53:06 CET)
Version 3 : Received: 4 March 2023 / Approved: 6 March 2023 / Online: 6 March 2023 (04:14:16 CET)
Version 4 : Received: 11 March 2023 / Approved: 13 March 2023 / Online: 13 March 2023 (03:05:38 CET)
Version 5 : Received: 28 March 2023 / Approved: 28 March 2023 / Online: 28 March 2023 (05:32:08 CEST)
Version 6 : Received: 3 April 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (07:22:34 CEST)
Version 7 : Received: 10 April 2023 / Approved: 11 April 2023 / Online: 11 April 2023 (03:28:27 CEST)
Version 8 : Received: 22 June 2023 / Approved: 25 June 2023 / Online: 25 June 2023 (04:40:44 CEST)
Version 9 : Received: 20 July 2023 / Approved: 21 July 2023 / Online: 21 July 2023 (08:53:32 CEST)
Version 10 : Received: 10 August 2023 / Approved: 10 August 2023 / Online: 11 August 2023 (03:01:11 CEST)
Version 11 : Received: 19 September 2023 / Approved: 20 September 2023 / Online: 21 September 2023 (03:25:23 CEST)
Version 12 : Received: 14 October 2023 / Approved: 17 October 2023 / Online: 17 October 2023 (07:08:50 CEST)
Version 13 : Received: 28 October 2023 / Approved: 30 October 2023 / Online: 30 October 2023 (09:47:16 CET)
Version 14 : Received: 19 November 2023 / Approved: 21 November 2023 / Online: 21 November 2023 (10:43:13 CET)
Version 15 : Received: 9 April 2024 / Approved: 9 April 2024 / Online: 10 April 2024 (09:37:50 CEST)
Version 16 : Received: 20 April 2024 / Approved: 22 April 2024 / Online: 23 April 2024 (09:43:39 CEST)
Version 17 : Received: 2 October 2024 / Approved: 2 October 2024 / Online: 2 October 2024 (14:50:39 CEST)

How to cite: Duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v15 Duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v15

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MDPI and ACS Style

Duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v15

APA Style

Duan, B. (2024). A Solution of The Collatz Conjecture Problem. Preprints. https://doi.org/10.20944/preprints202301.0541.v15

Chicago/Turabian Style

Duan, B. 2024 "A Solution of The Collatz Conjecture Problem" Preprints. https://doi.org/10.20944/preprints202301.0541.v15

Abstract

Research Collatz odd sequence, change (*3+1)/2^k operation in Collatz Conjecture to (*3+2^m-1)/2^k operation. Build a (*3+2^m-1)/2^k odd tree and a transform position model, prove if (*3+2^m-1)/2^k odd sequence can not converge after infinite steps of (*3+2^m-1)/2^k operation, the sequence must walk out of boundary of the tree.

Keywords

Collatz conjecture; (*3+1)/2^k odd sequence; (*3+2^m-1)/2^k odd sequence; (*3+2^m-1)/2^k odd tree.

Subject

Computer Science and Mathematics, Signal Processing

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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Comments (1)

Comment 1

Received: 12 April 2024
Commenter:

baoyuan duan

Commenter's Conflict of Interests: I am one of the author

Comment: Modify Lemma 4.6: There is no self convergence Collatz odd except 1.

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