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
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Authors and affiliations

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


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.


  • 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.

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