Methods for constructing Collatz numbers

Abdullah N. Arslan
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 47–54
DOI: 10.7546/nntdm.2018.24.2.47-54
Full paper (PDF, 136 Kb)

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Authors and affiliations

Abdullah N. Arslan
Department of Computer Science, Texas A&M University-Commerce
Commerce, TX 75428, USA

Abstract

The Collatz conjecture is among the unsolved problems in mathematics. It says that if we take any natural number x; divide it by two if x is even, and multiply it by 3 and add 1 if x is odd; and repeat this rule on the resulting numbers, eventually we obtain 1. For a given positive integer x, we say that x is a Collatz number if the claim of the conjecture is true for x. Computer verification reveals a large range of Collatz numbers. We develop methods by which we construct sets of Collatz numbers.

Keywords

• Collatz conjecture
• Collatz sequence

2010 Mathematics Subject Classification

• 11B83
• 11Y55
• 11A99
• 11B99

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