On Hofstadter’s G-Sequence

Journal article (2023)

Authors

F.M. Dekking Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2023 F.M. Dekking
Wythoff sequence Hofstadter’s G-sequence Slow Beatty sequence
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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 the second part we give some results that hold when one re-places the golden mean by other quadratic algebraic numbers. In the third part we prove a close relationship between Hofstadter’s G-sequence and a sequence studied by Avdivpahić and Zejnulahi.

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