Two M ~ 6 well-recorded strike-slip earthquakes struck just 4 km and 48 days apart in Kagoshima prefecture, Japan, in 1997, providing an opportunity to study earthquake interaction. Aftershocks are abundant where the Coulomb stress is calculated to have been increased by the first event, and they abruptly stop where the stress is dropped by the second event. This ability of the main shocks to toggle seismicity on and off argues that static stress changes play a major role in exciting aftershocks, whereas the dynamic Coulomb stresses, which should only promote seismicity, appear to play a secondary role. If true, the net stress changes from a sequence of earthquakes might be expected to govern the subsequent seismicity distribution. However, adding the stress changes from the two Kagoshima events does not fully capture the ensuing seismicity, such as its rate change, temporal decay, or migration away from the ends of the ruptures. We therefore implement a stress transfer model that incorporates rate/state friction, in which seismicity is treated as a sequence of independent nucleation events that are dependent on the fault slip, slip rate, and elapsed time since the last event. The model reproduces the temporal response of seismicity to successive stress changes, including toggling, decay, and aftershock migration. Nevertheless, the match of observed to predicted seismicity is quite imperfect, due perhaps to inadequate knowledge of several model parameters. However, to demonstrate the potential of this approach, we build a probabilistic forecast of larger earthquakes on the expected rate of small aftershocks, taking advantage of the large statistical sample the small shocks afford. Not surprisingly, such probabilities are highly time- and location-dependent: During the first decade after the main shocks, the seismicity rate and the chance of successive large shocks are about an order of magnitude higher than the background rate and are concentrated exclusively in the stress triggering zones.