  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.
