Guess the rules of the set

[Legend]

I'm thinking of a set of numbers. You may ask if a number is in the set, or you may guess what the rules are.

Here are some numbers in the set to get you started:

1, 2, 8, 16

[SWORDF1SH]

Is there a 4?

[Legend]

Is there a 4?

Yes

[the-pi-guy]

The rule is clearly:
1/24*(n^4-6n^3+23n^2-18n+24)

[Dr. Pezus]

n=2(n/2)

Lol

[Legend]

The rule is clearly:
1/24*(n^4-6n^3+23n^2-18n+24)

n=2(n/2)

Lol

It's a set, not a sequence. Order doesn't matter.

[Cute Pikachu]

Buncha of nerds in here  

[Legend]

Buncha of nerds in here  

You don't do math as a hobby?

[the-pi-guy]

It's a set, not a sequence. Order doesn't matter.

Well the natural numbers are a set.  
Defining sets like X={n in N | n^2} is a perfectly acceptable way to define a set.  


Is 3 in the set?  

[Legend]

Well the natural numbers are a set.  
Defining sets like X={n in N | n^2} is a perfectly acceptable way to define a set.  


Is 3 in the set?  

3 is in it.

[the-pi-guy]

3 is in it.

What about 6 and 7?  

If yes, then is it the set of natural numbers?  

[Legend]

What about 6 and 7?  

If yes, then is it the set of natural numbers?  

Yes

[SWORDF1SH]

Yes

Ha, you tricked me. That's why I asked if there's a 4 because I though it was multiplied by 2. I also through it was too simple and you were going to introduce gradually difficult rules to guess after each one was correctly guessed.

[the-pi-guy]

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.  

[Cute Pikachu]

You don't do math as a hobby?

I try to avoid classes like Calculas and College Algwbra with a passion.