To expand on that last paragraph: If x is the smallest coefficient, it makes sense that once you find x number of consecutive solutions, you will have ability to create all solutions after that, since doing so merely requires that you add x to each of the previous solutions. Whether you need at leastx number is what I haven't formally proven, but using an equation where the smallest coefficient is greater than 6 and the largest one is relatively large by comparison shows that it requires more than 6 consecutive solutions to find the last number that doesn't have one.
no subject
To expand on that last paragraph: If x is the smallest coefficient, it makes sense that once you find x number of consecutive solutions, you will have ability to create all solutions after that, since doing so merely requires that you add x to each of the previous solutions. Whether you need at least x number is what I haven't formally proven, but using an equation where the smallest coefficient is greater than 6 and the largest one is relatively large by comparison shows that it requires more than 6 consecutive solutions to find the last number that doesn't have one.