Given the set:  {1, 4, 9, 16, 25, ...} And asked to identify the next number, the answer is:  156 For the sequence is obviously generated by the following formula:  ((n - 1) * (n - 2) * (n - 3) * (n - 4) * (n - 5)) + (n ^ 2)

It is left to the reader to manipulate the formula into an unreadable form, so that it's hard to see how it works. Especially fun is adding an irrational multiplier to the '(n - 1) * ... * (n - 5)' part.

And notice this method works for any sequence given to a finite number of elements, for, indeed, there are an infinite number of fully-specified sequences that fit.

That's what I call beauty.