4000 watt generator for 30 amp 120v RV?

The factory cable on my travel trailer is 30amp 120v = 3600watt capacity. I'm considering purchasing a 4000w propane generator, but it has two 120v 15amp outlets. I tested my neighbor's 5500 watt generator using one of its 120v 15amp receptacles with my travel trailer (I bought a 15amp to 30amp adapter for $5 at WalMart) - but the AC kept tripping the generator fuse. What is my best option? Find a generator wired for 120v 30amps? Rewire the one I'm going to buy?