  In the base phi representation any natural number is written uniquely as a
sum powers of the golden mean with digits 0 and 1, where one requires that the
product of two consecutive digits is always 0. In this paper we give precise
expressions for the those natural numbers for which the $k$th digit is 1,
proving two conjectures for $k=0,1$. The expressions are all in terms of
generalized Beatty sequences.
