For anyone else confused by the problem description: A Van der Waerden number is notated as W(r, k). r is the number of colors that can be applied to an integ

For anyone else confused by the problem description: A Van der Waerden number is notated as W(r, k). r is the number of colors that can be applied to an integer (e.g. 2 if you have blue and red beads). A “big evenly spaced sequence” means that at least k integers of the same color form an arithmetic progression. So if n, n+1, n+2, …, or n, n+3, n+6, …, etc. all have the same color, that is considered an “evenly spaced sequence”, . “Big” means this sequence contains at least k integers, so for example, if n, n+1 and n+2 are all red, but n+3 is blue, this sequence would be “big” for a k of 3, but not for a k of 4. The Van der Waerden number W(r, k) is then the smallest integer i such that, coloring the integers starting at 1 and ending at i, will force a “big evenly spaced sequence” to exist as defined above.