This paper extends the work done by Angela Siegel on subtraction games in
which the subtraction set is N \ X for some finite set X. Siegel proves that
for any finite set X, the G-sequence is ultimately arithmetic periodic, and
that if |X| = 1 or 2, then it is purely arithmetic periodic. This note proves
that if |X| = 3 then the G-sequence is purely arithmetic periodic. It is known
that for |X| \geq 4 the sequence is not always purely arithmetic periodic.Comment: 7 pages, including 2 pages of dat