Every finite subsequence of your sequence is also a subsequence of the Thue-Morse sequence and vice versa. So in a sense, each is a shifted version of the other; it’s just that they’re shifted infinitely much in a way that’s difficult to define.
Every finite subsequence of your sequence is also a subsequence of the Thue-Morse sequence and vice versa. So in a sense, each is a shifted version of the other; it’s just that they’re shifted infinitely much in a way that’s difficult to define.