• 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. 

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