Number Theory

    

Rearranging the Perfect Binary Tree: a Proof of the Collatz Conjecture

Authors: Wiroj Homsup, Nathawut Homsup

The Collatz conjecture considers recursively sequences of positive integers where n is succeeded by n/2 , if n is even, or (3n+1)/2 , if n is odd. The conjecture states that for all starting positive integers n the sequence eventually reaches the trivial cycle 1, 2, 1, 2u2026u2026The inverted Collatz sequences can be represented as a Collatz tree with 1 as its root node. In order to prove the Collatz conjecture, one must demonstrate that a Collatz tree covers all positive integers. In this paper, we construct a Collatz tree with 1 as its root node by rearranging the perfect binary tree. We prove that a Collatz tree is a connected tree and covers all positive integers.

Comments: 6 Pages.

Download: PDF

Submission history

[v1] 2025-01-16 20:35:58

Unique-IP document downloads: 253 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus