3 7 14 23 36 49 66 83 What number comes next?

[BicycleTree]

Probably not easy:

3 7 14 23 36 49 66 83

What number comes next?

 

[Jimmy Snyder]

These are the smallest 8 roots of a 9th degree polynomial whose 9th root is 123456789

 

[BicycleTree]

It's not quite that arbitrary.

Here's a hint: if I continued the sequence for 20 more terms then it would be much easier to figure out. In fact, from looking at the 10th and 20th terms you could get it almost immediately.

 

[Moo Of Doom]

Are you sure 67 is correct for slot 7? I have a formula that gives all of them except it generates 66 for the 7th term.

EDIT: To check, my formula generates 104 for the 9th term.

 

[t!m]

I agree with Moo, and assume the next term to be 104 [in white].

 

[BicycleTree]

You're right, I did make a mistake. 104 is the answer! Congratulations.

 

[Gale]

is someone going to show how to do it?

 

[BicycleTree]

Explanation in white: It's the sum of the squares 1, 4, 9, ... with the corresponding primes 2, 3, 5, ...[/color]