# Number patterns

I'm going to put in a series just to comply, but I was wondering if anyone had advice for figuring out patterns in numbers. All I hear is that some people are natural at it.

4, 6, 10, 18...

the context here is GED, so don't make answers too complicated.

Thanks

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A standard trick is taking differences of neighboring numbers. In this case we get 2, 4, 8, which looks like the differences double each time. So the series could be $a_n = 2+2^n$. – Henning Makholm Sep 18 '11 at 4:19
Can I make a comment too complicated instead? What comes next in the sequence 0, 1, 2, 720! (that's 720 factorial), ? I think I first saw this in Hofstadter's Fluid Concepts and Creative Analogies, but I'm not positive. – Rahul Sep 18 '11 at 5:48
@Rahul: For $n\in\omega$ define $f_0(n)=n$ and $f_{k+1}(n)=f_k(n)!$. The $n$-th term of the sequence is then $f_n(n)$. – Brian M. Scott Sep 18 '11 at 7:19
If people cannot find the pattern, then perhaps computer can. – Jiri Sep 18 '11 at 12:08
Next in the sequence 0,1,2,720! is 4!!!!. The rule is 0,1!,2!!,3!!!... – Angela Richardson Sep 18 '11 at 14:50

Let's define recursive formula $a_n=a_{n-1}+2^{n-1}$, so the next number is $a_5=18+2^4=34$