  It is well known that if $0.a_1a_2a_3\dots$ is the base-$b$ expansion of a
number normal to base-$b$, then the numbers $0.a_ka_{m+k}a_{2m+k}\dots$ for
$m\ge 2$, $k\ge 1$ are all normal to base-$b$ as well.
  In contrast, given a continued fraction expansion $\langle
a_1,a_2,a_3,\dots\rangle$ that is normal (now with respect to the continued
fraction expansion), we show that for any integers $m\ge 2$, $k\ge 1$, the
continued fraction $\langle a_k, a_{m+k},a_{2m+k},a_{3m+k},\dots\rangle$ will
never be normal.
