OFFSET
1,4
COMMENTS
Starting with 0, the first 4 iterations of the morphism yield words shown here:
1st: 10
2nd: 2110
3rd: 0212110
4th: 100210212110
The 1-limiting word is the limit of the words for which the number of iterations is congruent to 1 mod 3.
Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. 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 = 3.079595623491438786010417...,
V = 2.324717957244746025960908...,
W = U + 1 = 4.079595623491438786010417....
If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,3,4}, and w(n) - w(n-1) is in {2,3,4,5,7}.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The 1st, 4th, and 7th iterates are
10, 100210212110, 10021021211002121102110100210212110211010021211010021100210212110.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 21 2017
STATUS
approved