Article
Version 1
Preserved in Portico This version is not peer-reviewed
Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?
Version 1
: Received: 2 May 2023 / Approved: 2 May 2023 / Online: 2 May 2023 (08:10:49 CEST)
How to cite: Allame, M.; Hadi-Vencheh, A. Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?. Preprints 2023, 2023050071. https://doi.org/10.20944/preprints202305.0071.v1 Allame, M.; Hadi-Vencheh, A. Does the Collatz Sequence Eventually Reach 1 for All Positive Integer Initial Values?. Preprints 2023, 2023050071. https://doi.org/10.20944/preprints202305.0071.v1
Abstract
This study focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The Collatz conjecture or 3x + 1 Problem is perhaps today's most enigmatic unsolved mathematical problem. It is named after Lothar Collatz, who rst proposed it in 1937. It may be stated as as follow: Take any positive integer n. If n is even then divide it by 2, else do \triple plus one" and get 3n + 1. The conjecture is that this process will eventually reach the number 1, regardless of which positive integer is chosen initially. In this paper, we present a simple proof for the Collatz conjecture.
Keywords
Collatz Conjecture; 3x + 1 Conjecture; base-2 numeral system
Subject
Computer Science and Mathematics, Algebra and Number Theory
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.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment