Regularly increasing values between X and Y with N number of points between?

[emittim3]

I have the need to create a series of numbers between a starting number and ending number where the numbers between increase gradually but not at regular intervals. I feel it's a function of a logarithm, but I'm not certain.

For example, to help explain further.

The starting number is 1.
The ending number is 125.
I need to have 12 numbers between 1 and 125 that increase gradually and evenly (a curve).

Just dividing 125 by 12 would give me 10.4166, so I could have a series of numbers being:

1
20.8332
31.2498
41.6664
52.083
62.4996
72.9162
83.3328
93.7494
104.166
114.5826
124.9992

But that would end up being linear, and not a gradual (curved) increase between 1 and 125.

What is a good formula that would provide for 12 points between 1 and 125 on a gradually curved increase?

Thanks much in advance!

 

[lev888]

Choose y=f(x), such that it increases per your requirements and passes through y = 1 and 125. E.g. y=x².
Find x for y values of 1 and 125 - minx and maxx. Divide this range by 11 - this gives you 12 x values (minx, minx + increment, minx + 2*increment, etc).
Plug the x values into your function - y values are your numbers.