It's not about the running current, but rather the starting current. It takes upwards of 5 times the running current to start the compressor.
Most Ammeters are too slow to measure this. I purchased a Fluke meter, with an "In-Rush" feature.
Here's the actual startup current for my 13,500 BTU A/C unit:
Here's the running current once started:
Here's the tricky part, the generator manufacturers don't give you all the specs. But neither do the folks that make the products that plug into the generators.
My generator is 2400 Watts. 2400W for how long? 2000 Watts continuous. Hayes Equipment put a load on the generator, and reported it can handle a 3000W load for 10 seconds. How much can it handle for the split second needed to spin a motor? FWIW, the 2400W, 2800W, and 3000W Yamaha generators all use the same sized motor.
From my testing, my generator can handle a 50A load, but not a 53.8A load (my air compressor rated at 15A):
So it's already very near its limit. In that split second, the RPMs bump on the generator, the A/C EASILY starts, and the RPMs settle down to about 2/3 throttle. But when trying to start the air compressor, the compressor slowly rolls over, the generator grunts for 10 seconds, then finally indicates "overload".
My website is one of the very few that has actual testing of the Yamaha EF2400iS (I make nothing for this!). I've talked to literally thousands of people on this topic. Many I've talked with have tried unsuccessfully to run a 15K A/C unit with generators. Zero have had success with a 3KW or smaller generator.