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

1. Apr 4, 2005

### BicycleTree

Probably not easy:

3 7 14 23 36 49 66 83

What number comes next?

Last edited: Apr 4, 2005
2. Apr 4, 2005

### Jimmy Snyder

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

3. Apr 4, 2005

### 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.

Last edited: Apr 4, 2005
4. Apr 4, 2005

### 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.

Last edited: Apr 4, 2005
5. Apr 4, 2005

### t!m

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

6. Apr 4, 2005

### BicycleTree

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

Last edited: Apr 4, 2005
7. Apr 4, 2005

### Gale

is someone going to show how to do it?

8. Apr 4, 2005

### BicycleTree

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