2400 is marginal, at best if the ac is in good shape. It may trip the break and will not start the ac compressor fast enough, especially if any other big current draw is on (fridges, water heater) and obviously microwave is always a no-no.
3000w+ is the only safe choice for the system because the average 13,500 btu ac will draw 3000-3600w on startup. Granted, it's only for a second, but we all know how fast electricity works... a second is a long time.
2013 Winnebago 2301BH-Red
2012 Ram 2500 Megacab HO CTD