Yes, there are tons of these sorts of circuits. It's something that is often needed, and these sorts of circuits have been used before ultra-cheap microcontrollers were a thing. A turing-complete computer is serious overkill for this sort of application.

I'm not sure if there is a single-chip solution (although I'd be a bit surprised if there isn't), but the fundamental circuit isn't that ambitious. Using a very low-end microcontroller is likely less expensive, though.