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.
Original language | English |
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Number of pages | 11 |
Journal | Journal of Integer Sequences |
Volume | 26 |
Issue number | 9 |
Publication status | Published - 2023 |
Keywords
- Hofstadter’s G-sequence
- slow Beatty sequence
- Wythoff sequence