A287179 - OEIS

%I #5 May 23 2017 14:31:38

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

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

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

%N 1-limiting word of the morphism 0->10, 1->20, 2->1.

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

%C 1st:  10

%C 2nd:  2010

%C 3rd:  1102010

%C 4th:  2020101102010

%C 5th:  11011020102020101102010

%C The 1-limiting word is the limit of the words for which the number of iterations is odd.

%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 = 2.246979603717467061050009768008...,

%C V = 2.801937735804838252472204639014...,

%C W = 5.048917339522305313522214407023...

%C If n >=2, then u(n) - u(n-1) is in {2,3}, v(n) - v(n-1) is in {1,2,4,6}, and w(n) - w(n-1) is in {2,4,7,10}.

%H Clark Kimberling, <a href="/A287179/b287179.txt">Table of n, a(n) for n = 1..10000</a>

%e 1st iterate: 10

%e 3rd iterate: 1102010

%e 5th iterate: 110110201020201011020100

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 9] (* A287179 *)

%t Flatten[Position[s, 0]] (* A287180 *)

%t Flatten[Position[s, 1]] (* A287181 *)

%t Flatten[Position[s, 2]] (* A287182 *)

%Y Cf. A287121, A287180, A287181, A287182.

%K nonn,easy

%O 1,7

%A _Clark Kimberling_, May 22 2017