What is the answer to this number sequence 2 4 3 9 8 64 63?

The number sequence appears to be alternating between multiplying by 2 and subtracting 1. Starting with 2, we get 22 = 4, then 4-1 = 3, then 33 = 9, then 9-1 = 8, then 88 = 64, and finally 64-1 = 63. Therefore, the next number in the sequence should be 6363 = 3969.