A Solution of The Collatz Conjecture Problem

baoyuan duan

doi:10.20944/preprints202301.0541.v9

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preprints.org > computer science and mathematics > signal processing > doi: 10.20944/preprints202301.0541.v9

Preprint Article Version 9 Preserved in Portico This version is not peer-reviewed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)

How to cite: duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v9 duan, B. A Solution of The Collatz Conjecture Problem. Preprints 2023, 2023010541. https://doi.org/10.20944/preprints202301.0541.v9

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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.v9

APA Style

duan, B. (2023). A Solution of The Collatz Conjecture Problem. Preprints. https://doi.org/10.20944/preprints202301.0541.v9

Chicago/Turabian Style

duan, B. 2023 "A Solution of The Collatz Conjecture Problem" Preprints. https://doi.org/10.20944/preprints202301.0541.v9

Abstract

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, change the operation to (*3+2^m-1)/2^k, and get a solution for this equation, give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build a complement weight function model, prove it increase to its convergence state. Build a (*3+2^m-1)/2^k odd tree, prove if odd in (*3+2^m-1)/2^k long huge odd sequence can not converge, the sequence must outstep the boundary of the tree after infinite steps of (*3+2^m-1)/2^k operation.

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; weight function

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 (3)

Comment 1

Received: 21 July 2023
Commenter: baoyuan duan
Commenter's Conflict of Interests: Author

Comment: make the proof stronger

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Comment 2

Received: 21 July 2023
Commenter:

baoyuan duan

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

Comment: If we rebuild sequence as this: do not change the first step and last step, move all other downward steps next to the first step, following all other forward steps and upward steps, then merge last step, upward steps, forward steps and the last downward step in front of forward steps to one step, the new sequence must have a slower transform position increment speed and has a increment ratio>3/4 only according to the ratio formula which indicates that (downward, downward, downward...) sequence has a transform position increment ratio>3/4.

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Comment 3

Received: 23 July 2023
Commenter:

baoyuan duan

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

Comment: If we merge upward steps, forward steps and the last downward step before the forward steps of the new sequence to one step, the new sequence already has a increment ratio>3/4 only according to the ratio formula which indicates that (upward, downward), (forward, downward), (downward, downward) have a transform position increment ratio>3/4.

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