I've been through this, albeit, with a fifth wheel. You'll get all kind of responses, and they'll be all over the place, but each person and camper is different.
From my research, I thought I had a very good chance of running the 13,500 btu air conditioner in my old trailer with a Yamaha 2400 inverter. It worked.
We just got a New Jayco this spring with a 15,000 btu air conditioner. The generator wouldn't start it. So yesterday, I bought and installed a Supco, SPP6, hard start capacitor and now I can run it. It took me pulling the shroud off (4 screws), that control cover off (2 screws), plugging in 2 wires, and a couple zip ties. It ran it with 90 degree heat and nothing else switched off (even fridge on electric). Although, like everything else forum related, a capacitor doesn't seem to work for everyone.
I would think that you "might" get a 2000 watt to run it (I've seen reports of 13,500 run by them) a 2400 watt would more likely be enough and anything over 3000 watts would almost positively work.
As said before, inverter generators are worth the money in their quietness. I love how quiet my Yamaha is and I can run it in a campgrounds with out feeling bad disturbing the peace. But I didn't want to have two light generators to deal with, or one really heavy one to deal with. I feel that mine is right in the middle.
2016 Jayco Eagle HT 29.5BHDS (ordered 12/30/15, delivered 3/8/16)
2015 F-350 crew cab, short bed, 6.7L PSD, Pullrite Superglide 3300 hitch