# Illustration DFA - length divisible by 2 or 3, but not by 6

Sketch of a deterministic finite automaton (DFA) for the following regular language (type 3):$$L ~=~ \{ a^n ~:~ n \equiv 0 ~\text{mod}~2 ~\text{or}~3, ~~ \text{not}~6 \}$$
This is an infinite language with, for example, the following words $$w$$:$$L ~=~ \{aa, aaa, aaaa, aaaaaa,~.... \}$$
This automaton accepts all words $$w$$ whose length is divisible by two or by three, but not by six.