IMHO: When you need generator power, there's nothing more worthless than the money spent on an underpowered generator for the job you need accomplished. Staying overnight at Cracker Barrel, Flying J, Rest Stop, dry camping, etc: is fine, we do it all the time and I've got to be comfortable when we do it. Our 5'er has a built in 6500W run generator with a 7500W surge capacity. During warm/hot temperatures, who wants to lay in bed and sweat because your 2400w generator can't handle the air conditioner compressor start up surge? To effectively run a 13,500 BTU RV air conditioner requires a minimum 3000W run power generator that has a 3500W start up surge capacity. A generator with any less capacity and you run the possibility of damage to your under powered generator, your air conditioner, your power panel, and your sanity after spending a night dry camping at Cracker Barrel with the windows open and a hot RV bedroom.
There will be others that will argue a 2400W generator will do the job of operating a 13,500BTU RV air conditioner. I however subscribe to the principle that it costs only a skosh more to go 1st Class. If yer gonna do something, do it right or leave it alone. Good luck.
Happy camping!!! See y'all down the road!!!:)