English

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}
}
R2 v1 2026-06-28T11:21:28.109Z