I think it was around 270 (Drowzee). I got it up to around 100 to make everything really easy to catch, then mostly ran back and forth in and out of buildings without actually encountering anything. Every so often, I would get bored enough to encounter and catch another Drowzee. So in total, I spent about 20 hours on the combo before getting frustrated and quitting (without any shinies, I might add). I do have way too much candy, though.
I haven't been able to bring myself to actively combo anything else yet, sadly.