The first 10 numbers in skew binary are 0, 1, 2, 10, 11, 12, 20, 100, 101, and 102.
The basic pattern is that it's like trinary, but once you get to something ending in some 1s and finally a 2, the two starts to migrate upward, leaving 0s behind it (as in 10112, 10120, 10200, 11000) until the 2 disappears and you keep on going normally. The effect is that instead of digits flipping over all at once, as in 999998, 999999, 1000000, it happens one at a time. Very interesting number system.