The structure behind the Collatz algorithm

Michael O'Loughlin

Abstract


The Collatz algorithm gives the operations to apply to both even and odd numbers so that starting with any natural number and applying these operations repeatedly, the number one is eventually reached. The Collatz conjecture claims that this is true no matter what starting number is used. It happens that the natural numbers can be organised into a hierarchical structure of infinite geometric sequences and the Collatz algorithm is the means of ascending through this hierarchy.


Keywords


Collatz algorithm; Collatz conjecture; geometric sequence; modulo

Full Text:

PDF

References


Lagarias J. C., The 3x + 1 problem: An annotated bibliography (1963– 1999), arXiv:math/0309224v13 [math.NT], 2011. Available at https:// doi.org/10.48550/arXiv.math/0309224




DOI: http://dx.doi.org/10.23755/rm.v55i0.1711

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Michael O'Loughlin

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.