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arXiv · 2003.04615

On the Behavior of Unbounded Collatz Sequences

Jorge Salazar
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Abstract

The aim of this paper is to show a peculiar behavior of a (hypothetical) Collatz sequence going to infinity. We study the associated Syracusa sequence (the odd elements of the former) and show that the limit set of a conveniently normalized sequence is the whole unit interval. In particular, for any positive integer there is a subsequence whose elements' expansions in base 3 begin (from the left) with the expansion of the given number.

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Jorge Salazar. 2020-03-10. On the Behavior of Unbounded Collatz Sequences. https://arxiv.org/abs/2003.04615

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