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%I #20 Sep 08 2022 04:52:27
%S 0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,
%T 1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,
%U 0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1
%N Fixed point of the morphism 0->010, 1->100.
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F a(3k-2)=a(k), a(3k-1)=1-a(k), a(3k)=0 for k>=1, a(0)=0.
%F Conjecture: a(n) = 2n - 1 - A285347(n).
%F This conjecture is correct, and proved in A285347. - _Michel Dekking_, Sep 07 2022
%e 0->010->010100010->
%t t = Nest[Flatten[# /. {0->{0,1,0}, 1->{1,0,0}}] &, {0}, 5] (*A189668*)
%t f[n_] := t[[n]]
%t Flatten[Position[t, 0]] (*A189669*)
%t Flatten[Position[t, 1]] (*A189670*)
%t s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
%t Table[s[n], {n, 1, 120}] (*A189671*)
%Y Cf. A189628, A189669, A189670, A189671, A285347.
%K nonn
%O 1
%A _Clark Kimberling_, Apr 25 2011
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