Generalized Schur Numbers for x_1 + x_2 + c = 3x_3 - Kézdy, André E.; Snevily, Hunter S.; White, Susan C. (The Electronic Journal of Combinatorics, 2009)
Let r(c) be the least positive integer n such that every two coloring of the integers 1,…,n contains a monochromatic solution to x_1 + x_2 + c = 3x_3. Verifying a conjecture of Martinelli and Schaal, we prove that r(c) = 22+c3 ceil + c3ceil, for all c 13, and r(c) = 33-c2 ceil - c2ceil, for all c -4.