GEEK powers test!

[tsudonimh]

Can you tell me what the numbers in each series have in common?

series zro: 0
series one: 1 2 4 8
series two: 3 5 6 9 10 12
series tre: 7 11 13 14
series for: 15

[Update:]
Okay, there's actually a couple series I left out because I'm mean... I've added series zro and for, above.