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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Journal of Integer Sequences

Dekking, M. (2023). On Hofstadter’s G-Sequence. Journal of Integer Sequences, 26(9), 23.9.2:1–23.9.2:11.