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 replaces 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.