Base phi representations and golden mean beta-expansions

2019/06/20 by Dekking, Michel · 1 citation
#11B99 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1906.08437

Abstract

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 kth digit is 1, proving two conjectures for k=0,1. The expressions are all in terms of generalized Beatty sequences.

Cited by

• New properties of the φ-representation of integers

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