1-automatic Sequences
k-automatic sequences are normally only defined for k ≥ 2. The concept can be extended to k = 1 by defining a 1-automatic sequence to be a sequence whose n-th term depends on the unary notation for n, that is (1)n. Since a finite state automaton must eventually return to a previously visited state, all 1-automatic sequences are eventually periodic.
Read more about this topic: Automatic Sequence