Open Problem

This post is just a story which is not mine.

When I met R.B.M at "his place", he gave me a sequence of number

1 11 21 1211 111221 ... 

and asked me what is the next number?
I spent 6 months to get the answer with help from some friends.
How long will it take you to solve this open problem? ;-)

Feel free to ask for hints. I will tell you story of R.B.M once you answer it right!