1, -3, -7
Any three numbers that you choose can be the next number. It is easy to find a rule based on a polynomial of order 6 such that the first four numbers are as listed in the question followed by the chosen three numbers. 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. Having said that, based on the simplest rule, the next three are 2, 7 and 12.
1 5 9 13 17 21
They appear to be 13 and 17
This sequence is an arithmetic series that makes use of another series. This sequence advances by adding the series 4, 11, 21, 34, and 50 to the initial terms. This secondary series has a difference of 7, 10, 13 and 16 which advance by terms of 3. So the next three numbers in the primary sequence are 190, 281 and 397.
1, -3, -7
They are 40, 53 and 68 and the pattern is 5 7 9 11 13 15
125 13 23 43 53...
13 is not a polynomial.
Any three numbers that you choose can be the next number. It is easy to find a rule based on a polynomial of order 6 such that the first four numbers are as listed in the question followed by the chosen three numbers. 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. Having said that, based on the simplest rule, the next three are 2, 7 and 12.
It's an algebraic expression containing three terms.
1 5 9 13 17 21
They appear to be 13 and 17
34, 41
11, 13, 17
13 21 34 55
As of December 13, 2013, Ash will be going to the Kalos region next in terms of the U.S. broadcast however in terms of the Japanese airing schedule, he's already in the Kalos region.