

A287234


0limiting 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
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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 0limiting 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(n1) is in {1,2,3}, v(n)  v(n1) is in {2,3,4}, and w(n)  w(n1) 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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



