Base phi representations and golden mean beta-expansions
Journal Article
(2020)
Author(s)
F.Michel Dekking (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Research Group
Applied Probability
URL related publication
https://www.fq.math.ca/58-1.html
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https://resolver.tudelft.nl/uuid:fac7a684-c0f1-4b4c-8a9f-1065c947d59e
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Publication Year
2020
Language
English
Research Group
Applied Probability
Journal title
Fibonacci Quarterly
Issue number
1
Volume number
58
Pages (from-to)
38-48
Downloads counter
168
Abstract
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 is always 0. In this paper, we give precise expressions for those natural numbers for which the kth digit is 1, proving two conjectures for k = 0,1. The expressions are all in terms of generalized Beatty sequences.