I have a sequence of positive integers. They were created using geometric progression: initial_value x (ratio^(nth-1))
For example; if initial_value=1 , ratio=2 , and nth begins at 1 and increases +1 every iteration; I end up with a sequence of 1,2,4,8,16,32,64,...
If, just for example, three integers from the above sequence were taken at random and added together, lets say they equaled 25(1+8+16).
Given the sum, is there an equation that can give me the integers that were taken?
For my particular situation, I will always have access to the initial_value, the ratio, and the nths used to create the sequence, the final maximum value of the sequence, and the sum of the integers taken.
Thank you for your time.