A287360 - OEIS

%I #9 Dec 04 2022 18:23:13

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

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

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

%N 0-limiting word of the morphism 0->11, 1->21, 2->0.

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

%C 1st:  11

%C 2nd:  2121

%C 3rd:  021021

%C 4th:  1102111021

%C 5th:  212111021212111021

%C The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 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 = 5.5707505637226408833903376944272134...,

%C V = 1.9375648970813894129869852971548390...,

%C W = 3.2853752818613204416951688472136067...

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

%H Clark Kimberling, <a href="/A287360/b287360.txt">Table of n, a(n) for n = 1..10000</a>

%e 3rd iterate: 021021

%e 6th iterate: 021021212111021021021212111021

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 12] (* A287360 *)

%t Flatten[Position[s, 0]] (* A287361 *)

%t Flatten[Position[s, 1]] (* A287362 *)

%t Flatten[Position[s, 2]] (* A287363 *)

%t SubstitutionSystem[{0->{1,1},1->{2,1},2->{0}},{0},{9}][[1]] (* _Harvey P. Dale_, Dec 04 2022 *)

%Y Cf. A287361, A287362, A287363, A287364 (1-limiting word);, A287368 (2-limiting word).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 24 2017