According to the best guess chart, 3 would be the bare minimum. You really should try to keep it closer to 5 or 6. That way you would have a bit of a buffer zone in case something tries to get started, as it seems to be trying to do. When you shock your pool, are you keeping it at shock level until you can go overnight without losing more than 1ppm? If not, then the algae tends to come right back, because you haven't killed all of it.