User blog comment:Alemagno12/How strong is this function?/@comment-1605058-20171028095436/@comment-33478904-20171029073214

In the first case you are talking about [|cube-free words]. The [|Thue–Morse sequence] identifies just two symbols will here lead to an undefined (infinite) output. Intuitively f(1) = 2. See [|this] which prove infinite cube free words exist. Hence f(n) is undefined for the cases you propose when n > 1.