Well, I at least got the 1 / 1 1 / 2 1 / 1 2 1 1 / 1 1 1 2 2 1 problem - the next lines are 3 1 2 2 1 1 / 1 3 1 1 2 2 2 1 / 1 1 1 3 2 1 3 2 1 1 / 3 1 1 3 1 2 1 1 1 3 1 2 2 1 / 1 3 2 1 1 3 1 1 1 2 3 1 1 3 1 1 2 2 1 1 and so on. I think I can prove that you never get numbers higher than 3.

Another good one is 1 3 7 12 18 26 ...

And so much more at The Online Encyclopaedia of Integer Sequences

Paul