The greedy algorithm was used to generate sets of positive integers containing no subset of the form {x, x + y, x + 2y), {x, x + y, x + 3y), {x, x + 2y, x + 3y), {x, x + 2y, x + 4y), {x, x + 3y, x + 5y), and {x, x + y, x + 2y, x + 3y}, respectively. All of these sets have peaks of density in roughly geometric progression.