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Collatz Representations With Bounded Partial Quotients

2025/03/21 by Franciszek Kobus, Kobus, Franciszek
Mathematics · Social Sciences · #Benford’s Law and Fraud Detection #Academic integrity and plagiarism

paper · pdf · doi:10.48550/arxiv.2504.07970

Abstract

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

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