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A287234 0-limiting word of the morphism 0->01, 1->20, 2->1, with initial term 1. 5
1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 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, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
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 0-limiting word is the limit of the words for which the number of iterations is even.
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
2nd iterate: 101
4th iterate: 1010120101
6th iterate: 101012010101201012001201010120101
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 0}, 2 -> 1}] &, {1}, 10] (* A287234 *)
Flatten[Position[s, 0]] (* A287235 *)
Flatten[Position[s, 1]] (* A287236 *)
Flatten[Position[s, 2]] (* A287237 *)
CROSSREFS
Cf. A287002 (initial 0 instead of 1), A287235, A287236, A287237, A287240 (1-limiting word).
Sequence in context: A364389 A116927 A137276 * A309938 A140581 A137277
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 23 2017
STATUS
approved

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Last modified June 18 20:38 EDT 2024. Contains 373487 sequences. (Running on oeis4.)