 Last nonzero digit coloring

For a prime number $p$, write a positive integer as $x=p^{v_p(x)}u$ with $p\nmid u$. Its last nonzero base-$p$ digit is $u\mathrm{mod}p$, an element of $\{1,\dots ,p-1\}$. Assigning this digit as the color gives the last nonzero digit coloring used in the necessity proof of Rado's theorem.