OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0111000
0110111000
01011110111000
0011111011110111000
10001111011111011110111000
01110001110111111011111011110111000
011011100011011111110111111011111011110111000
The 4-limiting word is the limit of the n-th iterates for n == 4 mod 5.
The number of letters (0's and 1's) in the n-th iterate is given by A288243(n), for n >= 0.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first two n-th iterates for n == 3 mod 5:
01011110111000
010111101110001011111111011111110111111011111011110111000
(The lengths of the first 10 such iterates are 10, 45, 127, 279, 534, 947, 1594, 2573, 4018, 6126.)
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[54]] - 48 (* A288864 *)
Flatten[Position[st, 0]] (* A288865 *)
Flatten[Position[st, 1]] (* A288866 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 24 2017
STATUS
approved