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 A112539 #22 Jan 20 2025 22:50:13
%S A112539 1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,
%T A112539 1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,
%U A112539 1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0
%N A112539 Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.
%e A112539 Triangle begins:
%e A112539 1;
%e A112539 0;
%e A112539 1, 0;
%e A112539 0, 1, 0, 1;
%e A112539 1, 0, 1, 0, 0, 1, 0, 1;
%e A112539 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;
%e A112539 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;
%e A112539 ...
%t A112539 s = {1}; Do[s = Join[s, Mod[s + 1, 2]]; s = Join[s, s], {n, 4}]; s (* _Robert G. Wilson v_, Dec 22 2005 *)
%o A112539 (Python)
%o A112539 s = [1]
%o A112539 for _ in range(4):
%o A112539 s = s + [(x + 1) % 2 for x in s]
%o A112539 s = s + s
%o A112539 print(s) # _Robert C. Lyons_, Jan 19 2025
%o A112539 (PARI)
%o A112539 aiter(x) = my(s=[1]); for(i=1, x, s=concat(s, if(i%2, [1-e|e<-s], s))); s \\ _Ruud H.G. van Tol_, Jan 20 2025
%Y A112539 Cf. A112865 (as +-1), A341389 (complement).
%Y A112539 Cf. A104104, A010060.
%K A112539 easy,nonn
%O A112539 1,1
%A A112539 _Alexandre Losev_, Dec 15 2005
%E A112539 More terms from _Robert G. Wilson v_, Dec 22 2005