Faculty Publications

The Pure Numbers Generated By The Collatz Sequence

Document Type

Article

Journal/Book/Conference Title

Fibonacci Quarterly

Volume

44

Issue

3

First Page

194

Last Page

201

Abstract

The Collatz Conjecture has been vexing mathematicians for over seventy years. It is the only mathematics problem that is comprehensible to a fourth-grader, yet has caused Paul Erdos to say, "Mathematics is not yet ready for such a problem." This paper divides the integers into "pure" and "impure" numbers, where the "impure" numbers occur in the trajectories of smaller numbers. It develops an infinite set of theorems characterizing the "impure" numbers, and establishes bounds on their density in the integers.

Department

Department of Mathematics

Original Publication Date

8-1-2006

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