Generalized Arithmetic Progression Free Sequence

For given two positive integers a and b let's construct the sequence x[1], x[2], ... by the following rules. For k=1 we put x[1]=1. Now let k >= 2. Then x[k] is the least positive integer such that the following two conditions hold - x[k] > x[k - 1]; - for all i, j we have x[k] is not equal to a * x[i] - b * x[j]. You need to find the first n terms of this sequence. Remark. Let a=2 and b=1. Th