The Number Game Closed; making new version

You can only use 2 digits in your numbers. Once a number gets to 100000 (5 zeros) or slightly over, we restart.

For example, if our starting digits were 1 and 0, then the first player could start posting 0. The next player 1, then 10, then 11, then 100, then 101, etc. So we are going up, but only using those digits, and finding the closest number with these digits.

Another example:

If our digits were 2 and 5 -
P1 - 2
P2 - 5
P3 - 22
P4 - 25
P5 - 52
P6 - 55

and so on.