There's Threes (https://itunes.apple.com/us/app/threes!/id779157948?mt=8) which is similar but not the same (since it requires a 1 and a 2 to generate a 3, which makes it slightly more troublesome. I prefer powers of 2, too, they appeal my inner nerd.
Some important differences:
* the first step is explicitly 1 + 2 = 3 (which you mentioned), 1+1 and 2+2 do NOT add
* You move all tiles a single space at once, rather than 'to the edge'. Note tiles only merge when they push together, so an edge or other cards restricting their movement. This is a side effect design decision of single space moving. I do not know if two pairs will merge, e.g. will 3 + 3 + 6 + 6 leave 6 + 12? I suspect it will, but I haven't seen it.
* Numbers 1 and 2 both spawn, and there is a 'next number' indicator, although placement still appears random. (A 3 spawned in the tutorial, but I think that was a special case)
Overall this leads to a very different feel to the game.
Yeah, after Threes, 2048 felt a little easier, though. Enjoy Threes, I already thing it was well worth it: real moment killer without being excessively mindless