Base phi representations and golden mean beta-expansions

Journal article (2020)

Authors

F.M. Dekking Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.

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