What is the smallest $k$ such that $\mathbb{R}^2$ can be red/blue coloured with no pair of red points unit distance apart, and no $k$-term arithmetic progression of blue points with distance 1?

Old and new problems and results in combinatorial number theory by Erdős & Graham (Page 15):

How small can $M$ be made? The only estimate currently known is that $M \le 10000000$ (more or less). In the other direction, it has just been shown by R. Juhász [Ju (79)] that we must have $M \ge 5$.