Problem of The Week: Due Friday, September 24

On the ancient island of Circulus, archaeologists found a series of caves.  In the first cave they found a circle with 560 stones.  In the 2nd cave they found a circle with 8 fewer stones than in the first cave.  Each new cave had a circle with twice as many stones missing from the circle than in the previous cave.  For example, there were 16 fewer stones in the 3rd cave than in the 2nd cave.  If the stone circles continue in this way, which cave would have the last stone circle?