Yamaha has a 4500 inverter generator I believe.
As for will a certain generator run YOUR A/C, it's really a YMMV because it depends on a number of things.
What A/C unit, how old, how efficient and does it have a hard start?
What generator, how old, what temp, what altitude, well taken care of and new gas?
What else is running at the time? Is the converter off, the fridge set to gas, water heater too?
One poster here claims to have tested the surge abilities of a pair of EU 2000's, a EU3000is and a Champ 3100 inverter. According to him the Champ has the most surge capacity of them all.
The professor of the 3000w generator thread picked up one of the early 3100's and had no issue running his 15.000 BTU A/C.
So you will never really know unless you try. Here you can rent various generators to see if they will cut it. I know it takes more than the popular inverter solutions at altitude so the solar A/C keeps us from having to listen to the 3500/4000.
Were I to buy again I would chose the newer 3800 Champ.