A189718 - OEIS

%I #23 Mar 05 2016 04:18:10

%S 0,1,1,1,0,0,1,0,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1,0,

%T 1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,1,1,0,

%U 0,1,0,0,0,1,1,1,0,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,1,0,0,0,1

%N Fixed point of the morphism 0->011, 1->100.

%C This is a kind of "Thue-Morse-Morse" construction (cf. A010060)! Start with A_0 = 0, then extend by setting B_k = complement of A_k and A_{k+1} = A_k B_k B_k. Sequence is limit of A_k as k -> infinity. Thus A_0 = 0; A_1 = 0,1,1; A_2 = 0,1,1,1,0,0,1,0,0; A_3 = 0,1,1,1,0,0,1,0,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1,0,1,1; - _N. J. A. Sloane_, Mar 04 2016

%H Chai Wah Wu, <a href="/A189718/b189718.txt">Table of n, a(n) for n = 0..19682</a>

%F a(3k-2)=a(k), a(3k-1)=1-a(k), a(3k)=1-a(k) for k>=1, a(0)=0.

%e 0->011->011100100->

%t t = Nest[Flatten[# /. {0->{0,1,1}, 1->{1,0,0}}] &, {0}, 5] (*A189718*)

%t f[n_] := t[[n]]

%t Flatten[Position[t, 0]] (*A189719*)

%t Flatten[Position[t, 1]] (*A189720*)

%t s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;

%t Table[s[n], {n, 1, 120}] (*A189721*)

%o (Python)

%o A189718_list = [0]

%o for _ in range(9):

%o     A189718_list += [1-d for d in A189718_list]*2 # _Chai Wah Wu_, Mar 04 2016

%Y Cf. A010060, A189628, A189719, A189720, A189721, A269723.

%K nonn

%O 0

%A _Clark Kimberling_, Apr 26 2011

%E Offset 0 to match A010060 and A269723 by _Chai Wah Wu_, Mar 04 2016