As others stated, minimum 3000 watts to run a 13.5K AC. Hopefully someone will chime in that has a 15K AC that 3000 watts is enough.
I have a Champion 3500/4000 watt generator. We bought that to power things out the house when the electric goes out. My wife had some medical issues during a pregnancy, power went out and she couldn't power her medical equipment. Had to go to a hotel for 2 days... spending hundreds of dollars. Immediately after that, we bought the Champion for about $300 from Tractor Supply. Other neighbors have loud contractor style gensets, so we weren't worried about the noise.
For camping... ESPECIALLY around others... get the quietest one you can afford. They will all be loud and annoying, but the quieter they are the less likely someone will destroy it in the middle of the night!
I love my Champion, its well made and starts easy every time. If they made the invertor style at the time I bought mine, I might have bought that instead.