English

The Visual Pattern in the Collatz Conjecture and Proof of No Non-Trivial Cycles

General Mathematics 2021-05-18 v1

Abstract

We present the long sought visual pattern in the Collatz problem with the aid of a logarithmic spiral. Using this newly discovered pattern, we show that the Collatz problem is linked to primes via Jacobsthal numbers. We then prove that no non-trivial cycles exist on the spiral and by extension in the Collatz problem.

Keywords

Cite

@article{arxiv.2105.07955,
  title  = {The Visual Pattern in the Collatz Conjecture and Proof of No Non-Trivial Cycles},
  author = {Fabian S. Reid},
  journal= {arXiv preprint arXiv:2105.07955},
  year   = {2021}
}

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22 pages