Equation for simple transform

Question

I have an ordinal list that I am trying to represent mathematically. The list is as follows:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000.

So basically, 100, 1000 and 10000 are multiplied by 10. I am visualising a chunk of data and I need an easy way to communicate the distribution without resorting to log. I'd like to formalise this, however.

cheers all,

s

Answer 1

See OEIS sequence A037124: Numbers that contain only one nonzero digit.

Answer 2

If the list stops at $100,000$, you have represented it by listing it. You could say something like $k10^n$ where $k \in \{1,2,3,4,5,6,7,8,9\}$ and $1 \le n \le 4$, but that is pretty complicated and leaves off the last term.