3.7.215. Schur number

Denotes the fact that a constraint was used for solving Schur problems. Given a non -negative integer $k$, the Schur number $S\left(k\right)$ is the largest integer $n$ for which the set $\left\{1,2,...,n\right\}$ can be partitioned into $k$ sets ${S}_{1},{S}_{2},...,{S}_{k}$ such that $\forall i\in \left[1,k\right]:i\in {S}_{i}⇒i+i\notin {S}_{i}$.