For further work in this area, see 

J. L. Gerver and L. T. Ramsey, Sets of integers with no long arithmetic
progressions generated by the greedy algorithm, Math. Comp. 33 (1979),
1353-1359.

J. L. Gerver, Irregular sets of integers generated by the greedy algorithm,
Math. Comp. 40 (1983), 667-676.

J. Gerver, J. Propp, and J. Simpson, Greedily partitioning the natural
numbers into sets free of arithmetic progressions, Proc. Amer. Math. Soc.
102 (1988), 765-772.

S. C. Lindhurst, An investigation of several interesting sets of numbers
generated by the greedy algorithm, Bachelor of Arts senior thesis, Dept.
of Mathematics, Princeton University, April 1990.