• 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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5 Citations
Background Citations
3
Methods Citations
1

5 Citations

How to add two natural numbers in base phi

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…

The sum of digits functions of the Zeckendorf and the base phi expansions

On the representation of the natural numbers by powers of the golden mean

In a base phi representation a natural number is written as a sum of powers of the golden mean φ. There are many ways to do this. Well known is the standard representation, introduced by George…

Points of increase of the sum of digits function of the base phi expansion

We prove that the sequence of first differences of the points of increase of the sum of digits function of the phi expansions of the natural numbers is a morphic sequence. We also show that it is the…

The sum of digits function of the base phi expansion of the natural numbers

In the base phi expansion any natural number is written uniquely as a sum of powers of the golden mean with digits 0 and 1, where one requires that the product of two consecutive digits is always 0.…

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