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A189718
Fixed point of the morphism 0->011, 1->100.
9
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, 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, 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
OFFSET
0
COMMENTS
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
FORMULA
a(3k-2)=a(k), a(3k-1)=1-a(k), a(3k)=1-a(k) for k>=1, a(0)=0.
EXAMPLE
0->011->011100100->
MATHEMATICA
t = Nest[Flatten[# /. {0->{0, 1, 1}, 1->{1, 0, 0}}] &, {0}, 5] (*A189718*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189719*)
Flatten[Position[t, 1]] (*A189720*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189721*)
PROG
(Python)
A189718_list = [0]
for _ in range(9):
A189718_list += [1-d for d in A189718_list]*2 # Chai Wah Wu, Mar 04 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 26 2011
EXTENSIONS
Offset 0 to match A010060 and A269723 by Chai Wah Wu, Mar 04 2016
STATUS
approved