A puzzle

What is the sequence that begins like this?

0, 1, 2, 4, 5, 8, 12, 16, 17, 18, 24, 32, 34, 40, 48, 50, 56, 64, 65, 72, 80, 81, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200

Hint: it is connected with Rado’s explicit description of the Erdős–Rényi countable random graph. There is another clue in the tag.