5 citations · 38 across the 26 of their papers we have counts for
12 papers · 1 filter
On Hofstadter's G-sequence
Michel Dekking
We characterize the entries of Hofstadter's G-sequence in terms of the lower and upper Wythoff sequences. This can be used to give a short and comprehensive proof of the equality o…
The Thue-Morse sequence in base 3/2
Michel Dekking
We discuss the base 3/2 representation of the natural numbers. We prove that the sum of digits function of the representation is a fixed point of a 2-block substitution on an infin…
Two-block substitutions and morphic words
Michel Dekking, Mike Keane
We consider in general two-block substitutions and their fixed points. We prove that some of them have a simple structure: their fixed points are morphic sequences. Others are intr…
The structure of Zeckendorf expansions
Michel Dekking
In this paper we classify the Zeckendorf expansions according to their digit blocks. It turns out that if we consider these digit blocks as labels on the Fibonacci tree, then the n…
The sum of digits functions of the Zeckendorf and the base phi expansions
Michel Dekking
We consider the sum of digits functions for both base phi, and for the Zeckendorf expansion of the natural numbers. For both sum of digits functions we present morphisms on infinit…
Morphic words, Beatty sequences and integer images of the Fibonacci language
Michel Dekking
Morphic words are letter-to-letter images of fixed points of morphisms on finite alphabets. There are situations where these letter-to-letter maps do not occur naturally, but h…