Explanation

Given the series is:

1, 2, 2, 4, 4, 6, 8, 8, 16

Let's break it down:

Powers of 2 are interspersed with repetitions: 1 (2^0), 2 (2^1), 2, 4 (2^2), 4, 8 (2^3), 8, 16 (2^4)

If the pattern continues with repetitions after powers of 2:

The next number would logically be 16 (a repetition of the last number, 16).