10, 22, 200, 11202, ______, ______

The next two numbers in the sequence are 20111111 and 21221222212121.  The numbers are a(n+1) = a(n) converted to base 3 from base 8 (written in base 10).

        base-3   base-10     base-8
            10         3          3 
            22         8         10
           200        18         22
         11202       128        200
      20111111      4738      11202
21221222212121   4231753   20111111
           ...       ...        ...