A112539 Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.

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, 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, 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

Offset: 1

Author

Alexandre Losev, Dec 15 2005

Keywords

• easy
• nonn

Examples

			Triangle begins:
  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, 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;
  ...
		

Crossrefs

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

Cf. A104104, A010060.

Programs

Mathematica

s = {1}; Do[s = Join[s, Mod[s + 1, 2]]; s = Join[s, s], {n, 4}]; s (* Robert G. Wilson v, Dec 22 2005 *)

PARI

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

Python

s = [1]
for _ in range(4):
    s = s + [(x + 1) % 2 for x in s]
    s = s + s
print(s) # Robert C. Lyons, Jan 19 2025

Extensions

More terms from Robert G. Wilson v, Dec 22 2005