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A287240
1-limiting word of the morphism 0->01, 1->20, 2->1, with initial term 1.
5
2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0
OFFSET
1,1
COMMENTS
Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 20
2nd: 101
3rd: 200120
4th: 1010120101
5th: 2001200120101200120
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 {1,2,3}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,5,7}.
LINKS
EXAMPLE
1st iterate: 20
3rd iterate: 200120
5th iterate: 2001200120101200120
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 0}, 2 -> 1}] &, {1}, 11] (* A287240 *)
Flatten[Position[s, 0]] (* A287241 *)
Flatten[Position[s, 1]] (* A287242 *)
Flatten[Position[s, 2]] (* A287243 *)
CROSSREFS
Cf. A287002 (initial 0 instead of 2), A287234 (0-limiting word), A287241, A287242, A287243.
Sequence in context: A325189 A357637 A130731 * A025875 A026840 A357648
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2017
STATUS
approved