Proof the Collatz Conjecture in Binary Strings

Jishe Feng

doi:10.20944/preprints202304.0931.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 24 April 2023 / Approved: 26 April 2023 / Online: 26 April 2023 (03:01:31 CEST)
Version 2 : Received: 19 May 2023 / Approved: 19 May 2023 / Online: 19 May 2023 (16:16:49 CEST)

The following is the Collatz Conjecture: Suppose we begin with a positive number, multiply it by 3 and add 1 if it is odd, and divide it by 2 if it is even. Then continue doing this as long as you can. Will it matter where you start, whether you end up at the number 1? The Collatz conjecture has been studied for around 85 years. We transform the Collatz function from decimal to binary, then use the binary string's character to prove the Collatz conjecture. In addition, we use mathematics to give another interpretation to chaos, which is the ultimately periodic positive integer sequence.

Collatz conjecture; binary number; ultimately periodic; chaos

Computer Science and Mathematics, Algebra and Number Theory

Comment 1

Received: 19 May 2023
Commenter: Jishe Feng
Commenter's Conflict of Interests: Author

Comment: In page 4, we recorrect the formula (6) and other

+ Respond to this comment

Not displayed online.

Please leave your comment to this article below.

Mathematical equations can be typed in either LaTeX formats \\[ ... \\] or $$ ... $$, or MathML format <math> ... </math>. Try the LaTeX or MathML example.

Type equation:

Preview:

Copy equation into message below

Close menu

Please click a symbol to insert it into the message box below:

Please enter the link here:

Optionally, you can enter text that should appear as linked text:

Copy link into message below

Close menu

Please enter or paste the URL to the image here (please only use links to jpg/jpeg, png and gif images):

Copy image into message below

Close menu

Type author name or keywords to filter the list of references in this group (you can add a new citation under Bibliography):

No existing citations in Discussion Group

Wikify editor is a simple editor for wiki-style mark-up. It was written by MDPI for Sciforum in 2014. The rendering of the mark-up is based on Wiky.php with some tweaks. Rendering of mathematical equations is done with MathJax. Please send us a message for support or for reporting bugs.

Close menu

Please declare any conflicts of interest you may have with this paper, financial or otherwise.

I do not have a conflict of interest

I would like to declare a conflict of interest

Display my name on the website

Captcha

Renew

I accept the following conditions:

Comments must follow the standards of professional discourse and should focus on the scientific content of the article. Insulting or offensive language, personal attacks and off-topic remarks will not be permitted. Comments must be written in English. Preprints reserves the right to remove comments without notice. Readers who post comments are obliged to declare any competing interests, financial or otherwise.

* All users must log in before leaving a comment

Notify me about updates to this article or when a peer-reviewed version is published.

Proof the Collatz Conjecture in Binary Strings

Abstract

Keywords

Subject

Comments (1)