I can see that the length of each missing subsequence is greater by one than the length of the previous one. But I can't figure out how to determine its start number.
The next values would be
21, 22, 28, 29, 30....
The reason for this
the pattern that repeats is i+pn, i+pn, 1+pn, 1+pn, i+pn, 1+pn, 1+pn repeat
where pn = previous number in the sequence
i's value in the sequence constantly increases by 1 so the next sequence would be
4+pn, 5+pn, 1+pn, 1+pn, 6+pn, 1+pn, 1+pn
15, 20, 21, 22, 28, 29, 30