A284386 - OEIS

%I #7 Apr 27 2017 11:36:38

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

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

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

%N Fixed point of the morphism 0->1, 1->1101.

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

%H Clark Kimberling, <a href="/A284386/b284386.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->1101-> 1101110111101->

%t s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 1, 0, 1}}] &, {0}, 13]; (* A284386 *)

%t Flatten[Position[s, 0]];  (* A184483 *)

%t Flatten[Position[s, 1]];  (* A184482 *)

%Y Cf. A184483, A184482.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Mar 26 2017