On Hofstadter's G-sequence
Combinatorics
2023-11-02 v3
Abstract
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 of Hofstadter's G-sequence and the sequence of averages of the swapped Wythoff sequences. In a second part we give some results that hold when one replaces the golden mean by other quadratic algebraic numbers. In a third part we prove a close relationship between Hofstadter's G-sequence and a sequence studied by Avdivpahic and Zejnulahi.
Cite
@article{arxiv.2307.01471,
title = {On Hofstadter's G-sequence},
author = {Michel Dekking},
journal= {arXiv preprint arXiv:2307.01471},
year = {2023}
}