  Adler, Keane, and Smorodinsky showed that if one concatenates the finite
continued fraction expansions of the sequence of rationals \[ \frac{1}{2},
\frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{1}{5},
\cdots \] into an infinite continued fraction expansion, then this new number
is normal with respect to the continued fraction expansion. We show a variety
of new constructions of continued fraction normal numbers, including one
generated by the subsequence of rationals with prime numerators and
denominators: \[ \frac{2}{3}, \frac{2}{5}, \frac{3}{5}, \frac{2}{7},
\frac{3}{7}, \frac{5}{7},\cdots. \]
