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In mathematics and theoretical computer science, an automatic sequence is an infinite sequence of terms characterized by a finite automaton. The n-th term of an automatic sequence a is a mapping of the final state reached in a finite automaton accepting the digits of the number n in some fixed base k.
An automatic set is a set of non-negative integers S for which the sequence of values of its characteristic function χS is an automatic sequence; that is, S is k-automatic if χS is k-automatic, where χS = 1 if n ∈ {\displaystyle \in } S and 0 otherwise.
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