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%I #8 Apr 27 2017 11:35:40
%S 1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,
%T 1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,
%U 1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1
%N Fixed point of the morphism 0->1, 1->101010.
%C Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (9+sqrt(21))/6 and s = (-1+sqrt(21))/2, so that 1/r + 1/s = 1. Conjecture: -2 < n*r - u(n) < 2 and -1 < n*s - v(n) < 2 for n >= 1.
%H Clark Kimberling, <a href="/A284364/b284364.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e 1->101010-> 101010110101011010101->
%t s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0, 1, 0}}] &, {0}, 10] (* A284364 *)
%t Flatten[Position[s, 0]] (* A284365 *)
%t Flatten[Position[s, 1]] (* A284366 *)
%Y Cf. A284365, A284366.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Mar 26 2017
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