If A 13,500 AC pulls more than 25 amps to start it has problems. I used a 2000 Honda for 2 years before I got my new genny, it would start 1 AC o-k but nothing else.
It is not uncommon for a RV A/C to pull 3 times it's normal running amps during start up.
The normal would be 13/14 running amps, so that would be over 40 amps at start but briefly..
At worse, over a long period of time you could damage either the A/C or the genset if the gen is only rated at 3000w.