1, 2, 4, 8, 16 seconds is the same doubling each time as 2.8, 5.6, 11, 22 seconds. The advantage is in using it for test strips. If you use the traditional method of 10 second steps then at the start going from 10 to 20 is quite a difference. At the other end of the strip e.g. 50 to 60 is not much of a change.
Using the 'f stop' sequence gives an equal percentage change per step. You don't have to use the actual numbers used in f stops. 10, 20, 40, 80, etc. is equally valid.