

A287121


0limiting word of the morphism 0>10, 1>20, 2>1.


5



2, 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, 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, 2, 0, 2, 0, 1, 0
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OFFSET

1,1


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 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 {2,3}, v(n)  v(n1) is in {1,2,4,6}, and w(n)  w(n1) is in {2,4,7,10}.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

2nd iterate: 2010
4th iterate: 2020101102010
6th iterate: 202010202010110201011011020102020101102010


MATHEMATICA

s = Nest[Flatten[# /. {0 > {1, 0}, 1 > {2, 0}, 2 > 1}] &, {0}, 10] (* A287121 *)
Flatten[Position[s, 0]] (* A287122 *)
Flatten[Position[s, 1]] (* A287123 *)
Flatten[Position[s, 2]] (* A287124 *)


CROSSREFS

Cf. A287122, A287123, A287124, A287129.
Sequence in context: A039973 A035171 A088700 * A035446 A126211 A095414
Adjacent sequences: A287118 A287119 A287120 * A287122 A287123 A287124


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, May 22 2017


STATUS

approved



