OFFSET
1,2
COMMENTS
Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 11
2nd: 0202
3rd: 110110
4th: 020211020211
5th: 11011002021101100202
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 = 2.7692923542386314152404094643350334926...,
V = 2.4498438945029551040577327454145475624...,
W = 4.3344900716222708116779374775820643087...
If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,5,6,10}, and w(n) - w(n-1) is in {2,4,8,10,16}.
This 0-limiting word and the 1-limiting word A287267 are both fixed points of the irreducible and aperiodic morphism 0->0202, 1->110, 2->11. Therefore they have the same frequencies f0, f1 and f2 of their letters. This implies that the algebraic expressions given for U, V and W in A287267 do also apply to U, V and W above. - Michel Dekking, Oct 09 2019
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..33855
EXAMPLE
2nd iterate: 0202
4th iterate: 020211020211
6th iterate: 020211020211110110020211020211110110
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2017
STATUS
approved