A287331 - OEIS

%I #9 May 27 2021 17:17:36

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

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

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

%N 1-limiting word of the morphism 0->10, 1->22, 2->0, starting with 0.

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

%C 1st:  10

%C 2nd:  2210

%C 3rd:  002210

%C 4th:  1010002210

%C 5th:  221022101010002210

%C The 1-limiting word is the limit of the words for which the number of iterations is 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 = 2.28537528186132044169516884721360670506...,

%C V = 3.87512979416277882597397059430967806752...,

%C W = 3.28537528186132044169516884721360670506...

%C If n >=2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.

%H Clark Kimberling, <a href="/A287331/b287331.txt">Table of n, a(n) for n = 1..10000</a>

%e 1st iterate: 10

%e 4th iterate: 1010002210

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 10] (* A287331 *)

%t Flatten[Position[s, 0]] (* A287332 *)

%t Flatten[Position[s, 1]] (* A287333 *)

%t Flatten[Position[s, 2]] (* A287334 *)

%Y Cf. A287175, A287332, A287333, A287334.

%K nonn,easy

%O 1,7

%A _Clark Kimberling_, May 23 2017

%E Definition corrected by _Georg Fischer_, May 27 2021