What is this sequence?

This is a sequence of numbers with a certain logic that I thought of. Try to figure out the logic behind it:

4, 8, 7, 5, 10, 11, 13, 8, 7, 14, 19, 20, 22

If you’re having a hard time you can consult the hint below and the solution below it.

Hint

The sequence actually begins with 1 and 2 before the 4. So the complete sequence is:

1, 2, 4, 8, 7, 5, 10, 11, 13, 8, 7, 14, 19, 20, 22

Can you now determine what it is?

Solution

This is the sequence of the decimal digits’ sum of the powers of whole powers of 2. 1,2,4,8 are single digit numbers so that’s the start of the sequence. Later on 16 yields 7, 32 yields 5, 64 yields 10, 128 yields 11 and so forth.

I came up with this riddle back in high school and after I got an Internet connection I found this sequence in the On-Line Encyclopedia of Integer Sequences.