Decimation
Fix k > 1. For a sequence w we define the k-decimations of w for r=0,1,...,k-1 to be the subsequences consisting of the letters in positions congruent to r modulo k. The decimation kernel of w consists of the set of words obtained by all possible repeated decimations of w. A sequence is k-automatic if an only if the k-decimation kernel is finite.
Read more about this topic: Automatic Sequence