1 research outputs found
On the regularity of
Let be real numbers and be an integer. Allouche and
Shallit showed that the sequence is
-regular if and only if is rational. In this paper, using a
base-independent regular language, we prove a similar result that the sequence
is -regular if and only
if is rational. In particular, when and
, we answer the question of Allouche and Shallit that the sequence
is not -regular, which has
been proved by Bell, Moshe and Rowland respectively.Comment: 10 page