• Corpus ID: 195218850

Base phi representations and golden mean beta-expansions

@article{Dekking2019BasePR,
title={Base phi representations and golden mean beta-expansions},
author={Michel Dekking},
journal={arXiv: Number Theory},
year={2019}
}
• M. Dekking
• Published 20 June 2019
• Mathematics
• arXiv: Number Theory
In the base phi representation any natural number is written uniquely as a sum powers of the golden mean with digits 0 and 1, where one requires that the product of two consecutive digits is always 0. In this paper we give precise expressions for the those natural numbers for which the $k$th digit is 1, proving two conjectures for $k=0,1$. The expressions are all in terms of generalized Beatty sequences.
5 Citations
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• 2021
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In the base phi representation any natural number is written uniquely as a sum of powers of the golden mean with coefficients 0 and 1, where it is required that the product of two consecutive digits

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Editors' Note: This article was written by the author when he was a 12-year old student at Junior High School 246 in Brooklyn, New York. Here he explores using the golden mean, which he calls τ, more

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