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A287179
1-limiting word of the morphism 0->10, 1->20, 2->1.
5
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, 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, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 1
OFFSET
1,7
COMMENTS
Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 10
2nd: 2010
3rd: 1102010
4th: 2020101102010
5th: 11011020102020101102010
The 1-limiting word is the limit of the words for which the number of iterations is odd.
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 = 2.246979603717467061050009768008...,
V = 2.801937735804838252472204639014...,
W = 5.048917339522305313522214407023...
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}.
LINKS
EXAMPLE
1st iterate: 10
3rd iterate: 1102010
5th iterate: 110110201020201011020100
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 9] (* A287179 *)
Flatten[Position[s, 0]] (* A287180 *)
Flatten[Position[s, 1]] (* A287181 *)
Flatten[Position[s, 2]] (* A287182 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 22 2017
STATUS
approved