A189718 Fixed point of the morphism 0->011, 1->100.

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

Links

Chai Wah Wu, Table of n, a(n) for n = 0..19682

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

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

Sequence in context: A288858 A356313 A309218 * A054638 A074322 A284935

Adjacent sequences: A189715 A189716 A189717 * A189719 A189720 A189721

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