A287341 - OEIS

%I #5 May 24 2017 17:25:49

%S 1,1,2,0,2,0,1,1,2,0,2,0,2,0,2,0,0,1,1,0,1,1,2,0,2,0,0,1,1,0,1,1,1,1,

%T 2,0,2,0,1,1,2,0,2,0,2,0,2,0,0,1,1,0,1,1,2,0,2,0,0,1,1,0,1,1,2,0,2,0,

%U 0,1,1,0,1,1,2,0,2,0,0,1,1,0,1,1,0,1

%N 1-limiting word of the morphism 0->11, 1->20, 2->0.

%C Starting with 0, the first 5 iterations of the morphism yield words shown here:

%C 1st:  11

%C 2nd:  2020

%C 3rd:  011011

%C 4th:  112020112020

%C 5th:  20200110112020011011

%C The 1-limiting word is the limit of the words for which the number of iterations congruent to 1 mod 3.

%C Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively.  Then 1/U + 1/V + 1/W = 1, where

%C U = 2.7692923542386314152404094643350334926...,

%C V = 2.4498438945029551040577327454145475624...,

%C W = 4.3344900716222708116779374775820643087...

%C If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,5,6,10}, and w(n) - w(n-1) is in {2,4,8,10,16}.

%H Clark Kimberling, <a href="/A287341/b287341.txt">Table of n, a(n) for n = 1..10000</a>

%e 3rd iterate: 011011

%e 6th iterate: 011011112020112020011011112020112020

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 10] (* A287341 *)

%t Flatten[Position[s, 0]] (* A287342 *)

%t Flatten[Position[s, 1]] (* A287343 *)

%t Flatten[Position[s, 2]] (* A287344 *)

%Y Cf. A287337 (0-limiting word), A287342, A287343, A287344, A287345 (2-limiting word).

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, May 24 2017