OFFSET
1,4
COMMENTS
Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 11
2nd: 2121
3rd: 021021
4th: 1102111021
5th: 212111021212111021
The 1-limiting word is the limit of the words for which the number of iterations congruent to 1 mod 3.
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 = 5.5707505637226408833903376944272134...,
V = 1.9375648970813894129869852971548390...,
W = 3.2853752818613204416951688472136067...
If n >=2, then u(n) - u(n-1) is in {3,5,9}, v(n) - v(n-1) is in {1,2,3}, and w(n) - w(n-1) is in {2,3,5}.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
4th iterate: 1102111021
7th iterate: 11021110210210212121110211102111021021021212111021
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2017
STATUS
approved