Base phi representations and golden mean beta-expansions
Number Theory
2019-06-21 v1
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 th digit is 1, proving two conjectures for . The expressions are all in terms of generalized Beatty sequences.
Keywords
Cite
@article{arxiv.1906.08437,
title = {Base phi representations and golden mean beta-expansions},
author = {Michel Dekking},
journal= {arXiv preprint arXiv:1906.08437},
year = {2019}
}