Apparently everyone else also remembered this one and chose to leave it for someone who hadn't already seen it. But it's sitting here holding up the show, so:
111221 (one 1, one 2, two 1s)
312211 (three 1s, two 2s, one 1)
13112221 (one 3, one 1, two 2s, two 1s)
...and so on. Each number just describes the previous one.
I didn't take it much further than this. Would it ever produce a 4 or 5?