Regularity in the G-Sequences of Octal Games with a Pass

Finite octal games are not arithmetic periodic. By adding a single pass move to precisely one heap, however, we show that arithmetic periodicity can occur. We also show a new regularity: games whose G−sequences are partially arithmetic periodic and partially periodic. We give a test to determine when an octal game with a pass has such regularity and as special cases when the G−sequence has become periodic or arithmetic periodic.