The structure behind the Collatz algorithm
DOI:
https://doi.org/10.23755/rm.v55i0.1711Keywords:
Collatz algorithm, Collatz conjecture, geometric sequence, moduloAbstract
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.
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
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