Hmmmm... First, you joined AT forums just to post that homework question?
Before I bother thinking about it, I'd like to know what level of mathematics this problem arose in.
Then, I'd probably have little trouble finding a solution.
But, if you're going to offer the first person to find the solution $$$ or something.... then I'll search without you narrowing it down 🙂
(that is, am I looking for a "purely mathematical" solution, as opposed to patterns like this: 3,3,5,4,4,3,5,5,4,3,6,... which would correspond to the number of letters in one,two,three,four,...)
And, that'd help me narrow down the search for a solution - am I looking for some simple pattern? Or am I looking for a some recursive formula with bifurcation heading toward chaos?