We did an in-between thing -- not dropping the nap entirely but more like every other day, and then a couple of days a week, and then once a week, etc.
I think it was right around there (three or so, maybe earlier).
Man I remember when that would drive me crazy. Basically there was no way she was going to sleep at the usual naptime. But then she'd get tired way earlier than her usual bedtime, and if I put her to bed then she'd either have a terrible time falling asleep (and then the actual bedtime would be pushed way back), or she'd fall asleep and then wake up again at like 2 AM. Ugh.
I think what I ended up doing was taking her for a drive on days when I really thought she needed to nap (just by observation), as that would pretty much always knock her out. If I just put her down to sleep, it wasn't happening.
Then gradually let off the naps.
But yeah that transition period wasn't pretty!