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

• BicycleTree
In summary, the sequence of numbers given are the smallest 8 roots of a 9th degree polynomial, with the 9th root being 123456789. The next number in the sequence is 104 and can be found by summing the squares of numbers 1, 4, 9, etc. with the corresponding primes 2, 3, 5, etc. There is a formula to generate all the numbers except for the 7th term, which is mistakenly given as 66 instead of 67.
BicycleTree
Probably not easy:

3 7 14 23 36 49 66 83

What number comes next?

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

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.

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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.

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

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

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is someone going to show how to do it?

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

1. What is the pattern in the sequence?

The pattern in the sequence is that each number is increasing by 4, 7, 10, 13, 16, 19, and 22, respectively. This means that the next number in the sequence would increase by 25, making it 108.

2. How do you calculate the next number in the sequence?

To calculate the next number in the sequence, you can use the formula n = n + (3 + 3x), where n is the current number and x is the position of the number in the sequence. In this case, since the given number is the 8th number in the sequence, x = 8. Therefore, the next number would be 83 + (3 + 3x8) = 83 + 27 = 110.

3. Is there a specific formula for this sequence?

Yes, there is a specific formula for this sequence. It is n = n + (3 + 3x), where n is the current number and x is the position of the number in the sequence. This formula can be used to calculate any number in the sequence.

4. Are there any other patterns in the sequence?

Aside from the increasing pattern by 4, 7, 10, 13, 16, 19, and 22, there is also a pattern in the digits of each number. The digits of each number are increasing by 3, starting from 7. For example, 7, 14 (1+3=4), 23 (2+3=5), 36 (3+6=9), and so on.

5. Can this sequence be extended indefinitely?

Yes, this sequence can be extended indefinitely. As long as the pattern of increasing by 4, 7, 10, 13, 16, 19, and 22 and the pattern of increasing digits by 3 continue, the sequence can go on infinitely.

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