Yes your generator will run the 13.5K A/C. I have twin Hondas (close to a true 30A output) run in parallel for my 15K A/C and it runs perfect. One day just for grins and giggles however, I wanted to try my small Powermate genny in the driveway. It like yours only produces 20A. So, I plugged in the trailer and ran the A/C without any problems. I will say though like others mentioned, I did NOT have anything else turned on while the A/C was running.
Also, I added a "hard start" capacitor to my A/C a few years ago, so I don't know if that was the sole reason why the A/C started right up and the 4000W genny didn't bog down.
Thought I'd share this for some of you that may not already know this. ... I figured it could go in the "general" section because it covers a few things.
Few years ago, I was looking to dump the factory GM piece o junk OEM tires, with a All Terain (AT) tire. I needed an AT that would be a compromise for both light off roading AND towing. A strictly classed "mud tire" with a really aggressive tread would be overkill for the streets and a "street tire" tread just wouldn't cut it for light to moderate off roading. I also needed a "E" load rating, vs the weaker "D" rating simply because I tow and load the truck up waaaaay too heavy (don't we all?) when going out in the boonies.
I've had BFG's before on smaller trucks, but BFG at the time didn't make an AT tire in my size 285/R17 with the stronger "E" rating. So, I bought another brand that although were classified as "AT," they just didn't have good traction in the dirt. The tread pattern was too "gentle" for a lack of better terms. However, the "E" load rating of those tires was the more important factor for me. As far as other brands went at the time, they were all the same.
Fast forward today... I'm shopping for new tires again and the tire dealer told me that BFG FINALLY LISTENED to customer demand and now make most of their AT tires for larger sized wheels with an E rating!!!!! YES!!!! BFG has made an E loading AT tire in the past, but it's always been for just a select few sizes of tire. So today, I bought a set in my size. He told me that BFG went to a E rating just a little over a year ago and it was one of the company's biggest customer requests. I feel that BFG pretty much makes the best general use AT tires around for "general" all around use of most camper/truck owners. They have the best tread pattern out there that doesn't go overboard, like a mud tire, when a mud tire performs terribly for general street use.
On a side note, the E rating has 10 ply sidewalls, vs the D's 8-ply sidewalls. The "D" rating sidewalls start to wobble when loaded heavy and up to speed. (Not good.). So, if you're looking for a great AT tire to use for hauling heavy loads and towing, BFG is finally on track again.
Just thought I'd pass the info on.
I have an 2004 2500hd and have had no problems. I too was freaked out with all the posts. It's hard to explain but the ones that failed did not have a plate that mine has. You have the square reciever which is welded under a couple of vertical plates. Between the plates there should be another plate kinda filling the void. I think if you do not have that plate you could have a problem
I welded a piece of c-channel to my brother's '06. Not because his hitch was failing, but because he didn't want it to fail "eventually." I'm not positive, but I believe the '04 and 05's had a slightly different design than the '06. I know it looked different from my '08.
Just checked my hitch on my '08 Silverado HD. Looks good and I tow both "heavy" and "far." I'm also glad that my dual or "previous" profession in my youth was a professionally trained weldor and metal fabricator for a government vendor. I've made numerous trailers and custom hitch receivers in my younger days. I maintain my skills with my own metal shop here at the house, as metal work is no longer a "job" for me, but a serious hobby.
I've seen countless upon countless and absolutely HORRIBLE hitch and hitch receiver "welds" (if you can even call them "welds.") Another problem I've seen is the actual safety chain connection to the trailer tongue itself! My own trailer had the weakest looking weld bead connection that would have absolutely failed in the event the hitch ball failed. Thankfully, I customized the safety chain anchor point and welded a serious upgrade to my trailer.
Check your weld joints on those hitch receivers people. Any signs of cracks along the weld joint and your hitch is a goner.