ChristopherCoy,
You're very close. The f/stop number is the focal length of the lens divided by the diameter of the aperture. The amount of light that passes through an aperture per unit time is proportional to the square of the radius. Thus stepping from 2.8 to 4 halves the amount of light (because 2.8 * (square root of 2) = 4), stepping from 4 to 5.6 halves the light again.

If you want to go by full stops, you should do 2.8-5.6-11-22 second exposures. If you want to go by half stops, then the 2.8-4-5.6-8-11-16 seconds will give you half stops instead.