Vortex base Mathematics?

1 ---> 1
2 ----> 2
4 ----> 4
8 ----> 8
16 ----> 7
32 ------> 5
64 -----> 1
128 -----> 2
256 -----> 4
512---- > 8
1024 ----> 7
.
.
.

Do you know another, more common, use for the sum of digits of a number?

The sum of digits, when divided by 9, has the same remainder as the original number. Therefore, the sequence we're looking at is actually the sequence of reminders of the powers of 2.
Since the reminder of 2^n determines the reminder of 2^(n+1), the sequence has to repeat itself after a short while.

I agree wholeheartedly.