|
%I #9 Apr 27 2017 11:34:52
%S 1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,
%T 0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,0,
%U 1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1
%N Fixed point of the morphism 0 -> 1, 1 -> 1010.
%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: -1 < n*r - u(n) < 2 and -1 < n*s - v(n) < 2 for n >= 1.
%H Clark Kimberling, <a href="/A283963/b283963.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 -> 1010 -> 1010110101 -> 1010110101101010101101011010 ->
%t s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0}}] &, {0}, 10] (* A283963 *)
%t Flatten[Position[s, 0]] (* A283964 *)
%t Flatten[Position[s, 1]] (* A283965 *)
%Y Cf. A283964, A283965.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Mar 25 2017
|
