This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381577 #9 Feb 28 2025 13:49:23 %S A381577 0,1,2,2,1,0,2,1,0,0,1,2,2,1,0,0,1,2,0,1,2,2,1,0,2,1,0,0,1,2,0,1,2,2, %T A381577 1,0,0,1,2,2,1,0,2,1,0,0,1,2,2,1,0,0,1,2,0,1,2,2,1,0,0,1,2,2,1,0,2,1, %U A381577 0,0,1,2,0,1,2,2,1,0,2,1,0,0,1,2,2,1,0 %N A381577 Unique sequence of 0's, 1's, and 2's such that for any terms x and y with x < y, the subsequence of x's and y's becomes the Thue-Morse sequence after substitution x -> 0, y -> 1. %F A381577 In the Thue-Morse sequence, substitute 0 -> 012, 1 -> 210 once. %o A381577 (Python) %o A381577 def A381577(n): return ((2,1,0) if (n//3).bit_count()&1 else (0,1,2))[n%3] # _Chai Wah Wu_, Feb 28 2025 %Y A381577 Cf. the Thue-Morse sequence A010060 and its other ternary generalizations: A053838, A287150. %K A381577 nonn,easy %O A381577 0,3 %A A381577 _Andrey Zabolotskiy_, Feb 28 2025