%I #10 Apr 27 2017 11:36:58
%S 1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,
%T 0,0,1,1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,
%U 0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1
%N Fixed point of the morphism 0->1, 1->1100.
%C Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (3+sqrt(3))/2 and s = sqrt(3), so that 1/r + 1/s = 1. Conjecture: -3 < n*r - u(n) < 4 and -2 < n*s - v(n) < 4 for n >= 1.
%H Clark Kimberling, <a href="/A284505/b284505.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 0-> 1-> 1100-> 1100110011-> ...
%t s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 1, 0, 0}}] &, {0}, 16]; (* A284505 *)
%t Flatten[Position[s, 0]]; (* A284506 *)
%t Flatten[Position[s, 1]]; (* A284507 *)
%Y Cf. A284506, A284507.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Apr 04 2017