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May 2020 Arithmetic Sequences and Blocks of Powers of Two in the Collatz Array
Shaun V. Ault, Matthew Cliatt
Missouri J. Math. Sci. 32(1): 32-38 (May 2020). DOI: 10.35834/2020/3201032

Abstract

In this short paper, we examine a curious feature of the Collatz function. When the sequences generated by the Collatz function on consecutive integer initial points are arranged into an array, certain arithmetic sequences show up with common differences given by products of twos and threes. The common differences themselves are further related by a formula that depends on even versus odd input. While we do not solve the Collatz Conjecture by this observation, we present our findings as interesting mathematical results in their own rights.

Citation

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Shaun V. Ault. Matthew Cliatt. "Arithmetic Sequences and Blocks of Powers of Two in the Collatz Array." Missouri J. Math. Sci. 32 (1) 32 - 38, May 2020. https://doi.org/10.35834/2020/3201032

Information

Published: May 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4118648
Digital Object Identifier: 10.35834/2020/3201032

Subjects:
Primary: 11A99
Secondary: 11B25

Rights: Copyright © 2020 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.32 • No. 1 • May 2020
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