 Van der Waerden number

Van der Waerden's theorem states that for any positive integers "r" and "k" there exists a positive integer "N" such that if the integers {1, 2, ..., "N"} are colored, each with one of "r" different colors, then there are at least "k" integers in arithmetic progression all of the same color.The smallest such "N" is the van der Waerden number "W"("r", "k").