Forgive me if I have attached the wrong title to this problem but I don’t know a Sucint way to describe it.
Imagine a geometric series x of base r and starting point n and p progressions. For example, if n is 4, r is 1.41, and p is 5 then the sequence is approximately 4, 5.6, 8, 11.3, 16.
Now here is the fun part. I want to be able to generate a sequence F of numbers of length p such that for the pth value of the geometric series x the sum of sequence F will equal the pth value, the p-1 value of x will equal the sum of F from 1 to p-1.
The purpose of this is that I am doing calculations for photography and I want to expose photographic paper in such a way that as I uncover ever wider sections of it and shine light on it at various times, the cumulative amount of time each section of paper is exposed to light will equal the geometric sequence I have described.