Guess the rules of the set

[Legend]

I expected a trick.  I just wasn't sure which one.  

There was the one {1,2,4,8,16,31,...}
Where 31 breaks the doubling streak, and is described the equation above.  

So what's after the 31?

[the-pi-guy]

So what's after the 31?

57, 99

[Xevross]

Ewwwww sets. Get it away

[SWORDF1SH]

6, 21, 12, 5, 7, 5, 15, 4
Work the rule out. This is the set of numbers in its entirety.

[Legend]

6, 21, 12, 5, 7, 5, 15, 4
Work the rule out. This is the set of numbers in its entirety.

The rule is that the set is {6, 21, 12, 5, 7, 5, 15, 4}