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arXiv · 2105.07955

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

Fabian S. Reid
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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.

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Fabian S. Reid. 2021-05-13. The Visual Pattern in the Collatz Conjecture and Proof of No Non-Trivial Cycles. https://arxiv.org/abs/2105.07955

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