Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Proof the Collatz Conjecture in Binary Strings

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)

How to cite: Feng, J. Proof the Collatz Conjecture in Binary Strings. Preprints 2023, 2023040931. Feng, J. Proof the Collatz Conjecture in Binary Strings. Preprints 2023, 2023040931.


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

Comments (1)

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 
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