On linear forms whose coefficients are in arithmetic progression

Let Ω be the set of positive integers that are omitted values of the form where thea _i are fixed positive integers with g.c.d. 1 and thex _i are variable nonnegative integers. Set ω=|Ω| and κ=max Ω+1. Using an expression of Roberts 4] for κ when thea _i form an arithmetic progression, we determine ω in this case.