login
A287320
0-limiting word of the morphism 0->10, 1->22, 2->0
4
0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 1, 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, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0
OFFSET
1,3
COMMENTS
Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 10
2nd: 2210
3rd: 002210
4th: 1010002210
5th: 221022101010002210
The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 mod 3.
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
U = 2.28537528186132044169516884721360670506...,
V = 3.87512979416277882597397059430967806752...,
W = 3.28537528186132044169516884721360670506...
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}.
LINKS
EXAMPLE
3rd iterate: 002210
6th iterate: 002210002210221022101010002210
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 12 (* A287320 *)
Flatten[Position[s, 0]] (* A287321 *)
Flatten[Position[s, 1]] (* A287322 *)
Flatten[Position[s, 2]] (* A287323 *)
SubstitutionSystem[{0->{1, 0}, 1->{2, 2}, 2->{0}}, {2}, {10}][[1]] (* Harvey P. Dale, Aug 17 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 23 2017
STATUS
approved