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Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$ L ~=~ \{ a^n ~:~ n \text{ is divisible by 2 or by 3 } \} $$
This is an infinite language with, for example, the following words:$$ L ~=~ \{ aa, aaa, aaaaaa, aaaaaaa, ~.... \} $$