OFFSET
1,7
COMMENTS
Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 10
2nd: 2210
3rd: 002210
4th: 1010002210
5th: 221022101010002210
The 1-limiting word is the limit of the words for which the number of iterations is 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 = 2.28537528186132044169516884721360670506...,
V = 3.87512979416277882597397059430967806752...,
W = 3.28537528186132044169516884721360670506...
If n >=2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
1st iterate: 10
4th iterate: 1010002210
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 23 2017
EXTENSIONS
Definition corrected by Georg Fischer, May 27 2021
STATUS
approved