What come next sequence 1 247?

Answer 1

Any number can be the next number. It is easy to find a rule based on a polynomial of order 2 such that the first two numbers are 1 and 247, and followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.

So, if you want the next number to be 1, use the rule t(n) = -246n^2 + 984n - 737

You want 9, use the rule t(n) = -242n^2 + 972n - 729

You want 99, use the rule t(n) = -197n^2 + 837n - 639

You want 765, use the rule t(n) = 136n^2 - 162n + 27

and so on.