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

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## Details

### 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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## Cite this paper

Arslan, Abdullah N. (2018). Methods for constructing Collatz numbers. Notes on Number Theory and Discrete Mathematics, 24(2), 47-54, doi: 10.7546/nntdm.2018.24.2.47-54.