In reply to ablackett:
> (In reply to itsThere) Reminds me of a question I was asked once. What comes next in this sequence,
>
> 1, ....
>
> There is a pretty convincing answer which probably isn't what you first think of.
All sequence questions are normally answered with the simplest (lowest power) function which satisfies the initial conditions. In the case of 4, 8, 12 you can use the linear function 4n to fit the bill, but there are an infinite number of higher power solutions which have the same initial 3 terms. In the case of 1, 2, ... most people would say that the next term is 3 again ignoring the infinite higher power solutions such as f(n) = 2^(n-1)
Following this train of logic the lowest power function which fits 1, ... is f(n) = 1, so the sequence is 1, 1, 1, 1,