Mathematical+Series

It is a simple arithmetic progression having common difference, d=1;
 * 1. Let us consider 1 2 3**

**2. Let us consider 1 2 4** It is a simple geometric progression having a ratio, r =2;

**3. Let us consider 1 2 8**

What is it? Would you make it a series of some mathematical function.

I hope you will find a mathematical function, (2)^[{(2)^n}-1] where n stands for 0, 1 and 2 when n=0, then (2)^[{(2)^0}-1] = (2)^[1-1] =2^0=1 when n=1, then (2)^[{(2)^1}-1] = (2)^[2-1] =2^1=2 when n=2, then (2)^[{(2)^2}-1] = (2)^[4-1] =2^3=8. Let us have fun!!!