Novel Theorems and Algorithms Relating to the Collatz Conjecture

Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between t...

Full description

Saved in:
Bibliographic Details
Main Authors: Michael R. Schwob, Peter Shiue, Rama Venkat
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2021/5754439
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.
ISSN:0161-1712
1687-0425