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Fixed point of the morphism 0->1, 1->1011.
1

%I #8 Apr 27 2017 11:36:00

%S 1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,

%T 1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,

%U 1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1

%N Fixed point of the morphism 0->1, 1->1011.

%C Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (5+sqrt(13))/2 and s = (-1+sqrt(13))/2, so that 1/r + 1/s = 1. Conjecture: 1 < n*r - u(n) < 3 and -1 < n*s - v(n) < 1 for n >= 1.

%H Clark Kimberling, <a href="/A284368/b284368.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->1011-> 1011110111011->

%t s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 1}}] &, {0}, 10] (* A284368 *)

%t Flatten[Position[s, 0]] (* A184485 *)

%t Flatten[Position[s, 1]] (* A184484 *)

%Y Cf. A184484, A184485.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Mar 26 2017