/sci/ - Science & Math

The recent Prject Euler problem is interesting, but so hard:
https://projecteuler.net/problem=870

Here's what I got:
>for each r, the sequence of L(r) EVENTUALLY follows a linear recurrence
>each term equals the last term, plus some previous element in the sequence (how far back is fixed)
So for L(1), you get {1,2,4,8,...} the powers of 2, which has the recurrence a(n) = a(n-1) + a(n-1), so you have to go 1 element back.
For L(2), you get {1,2,3,5,...} the Fibonacci numbers, which has the recurrence a(n) = a(n-1) + a(n-2), so you have to go 2 elements back.
Again: The recurrence might not hold immediately. You could have 20 terms not following the pattern (even if you need to go like 6 elements back), and then after that it starts following it.

These are the first 22 values of T (or q):
>1, 2, 5/2, 3, 7/2, 11/3, 43/11, 4, 13/3, 31/7, 9/2, 14/3, 33/7, 5, 51/10, 41/8, 27/5, 11/2, 45/8, 65/11, 6, 145/23