Expressions using generalized Beatty sequences characterize the natural numbers with a 1 at the kth digit in the base-phi representation, proving conjectures for k=0 and 1.
Fraenkel and C, Kimberling, Generalized Wythoff arrays, shuffles and interspersions,
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Base phi representations and golden mean beta-expansions
Expressions using generalized Beatty sequences characterize the natural numbers with a 1 at the kth digit in the base-phi representation, proving conjectures for k=0 and 1.