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Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.
3

%I #22 Jan 20 2025 22:50:13

%S 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 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 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 Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.

%e Triangle begins:

%e 1;

%e 0;

%e 1, 0;

%e 0, 1, 0, 1;

%e 1, 0, 1, 0, 0, 1, 0, 1;

%e 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;

%e 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 ...

%t 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 (Python)

%o s = [1]

%o for _ in range(4):

%o s = s + [(x + 1) % 2 for x in s]

%o s = s + s

%o print(s) # _Robert C. Lyons_, Jan 19 2025

%o (PARI)

%o 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 Cf. A112865 (as +-1), A341389 (complement).

%Y Cf. A104104, A010060.

%K easy,nonn,changed

%O 1,1

%A _Alexandre Losev_, Dec 15 2005

%E More terms from _Robert G. Wilson v_, Dec 22 2005