A038113 Lexicographically first strictly increasing base 4 autovarious sequence: a(n) = number of distinct a(k) mod 4^n (written in base 4).

1, 2, 11, 12, 21, 101, 1001, 1002, 1011, 10001, 10002, 10011, 10012, 10021, 10101, 11001, 11002, 100001, 100002, 100011, 100012, 100021, 100101, 101001, 101002, 101011, 110001, 110002, 110011, 110012, 110021, 110101, 111001, 111002, 200001