Hi, I've been trying to work out this puzzle for a while but can't solve it. If you could help me I'd be much appreciated.

Here's a number sequence:
111, 112, 21123, 1312, 2114, 121, 25262, 73123...
Find the rule and post two next numbers in the sequence.

I obviously haven't solved it but I have made some observations about it:

- the first number only uses digits for binary numbers; the second only for base 3 numbers; the n+1th only for base n numbers
- none of the digits is zero
- longer and shorter numbers seem to be mixed