Count up in a somewhat complex way

So we have hex. We have binary. We have base 110. How could I make it more complex?

By changing the bases dependant on the digit.

The base will be (distance from decimal place + 1). So the ones place will count up in base 2, the tens place will be base 3, the hundreds will be base 4, etc.

Here's an example of the first ten posts:

1
10
11
20
21
100
101
110
111
120

etc.

I shall start:

1


Yes, this will be complicated. The first digit of the number is in base 2, second in base 3, third in base 4, etc.