I'm not quite sure what I'm doing, but this is the most fun version I've played so far. I'm not sure what I'm doing because I can't keep track of the order the colors appear in.
There's an ordered palette of colors below that matches to the 2^N values from the original. Plus you get used to it after a couple minutes =).
I did manage to get 2048 the first time through, but I made several mistakes thinking I'd be able to merge a couple of purples that weren't really the same. It's less of a problem when they're right next to each other, but when you're thinking ahead, it's easy to get a little lost on the spectrum.