count numbers in a weird weird way | a

So this is how it works: a. then aa. then aaa. And then 4 a's collapse into a b. then ba. then baa. then baaa. then it collapses again into bb. and so on. Once you have exhausted a-z. Start with A-Z while using a-z as well. zzzz turns into A. then Aa then Aaa then Aaaa. 4 a's collapse into a b. Ab and so on. Count by 1 a and then once you reach bbbaaa. Remember that once you add one. It's not bbbb. It's c! Next goal is f (eeee or dddddddddddddddd or cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc and so on) b - 4 a's c - 16 a's d - 64 a's e - 256 a's f - 1024 a's