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arXiv · 2504.07970

Collatz Representations With Bounded Partial Quotients

Franciszek Kobus
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Abstract

We define Collatz representations for a subset of rational numbers and prove that each real number \( x \notin (-1,1) \) can be approximated arbitrarily well by rational numbers which have only \( 2 \)'s and \( 1 \)'s in their Collatz representation.

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Franciszek Kobus. 2025-03-21. Collatz Representations With Bounded Partial Quotients. https://arxiv.org/abs/2504.07970

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