So, being a baby wonk, I constructed a table:
So, I doubt if one can find such a number.
Unless, on simple adds the number of digits as in this table:
I haven't looked at the answer. I'm probably wrong. In which case, I will slink away.
Ah, Ha! The Wizard across the pond shows me up. Of course I didn't extend my calculations beyond 100. If I had, I would have gotten the following graph of the difference:
What appeared from 1 to 99 as a dull, monotonically increasing pattern was part of a bigger pattern going the other way. (I should take it beyond 1000.)
When the difference is taken gives this graph:
So, I slink away.