OFFSET
1,1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0111000
0110111000
01011110111000
0011111011110111000
10001111011111011110111000
01110001110111111011111011110111000
011011100011011111110111111011111011110111000
The 1-limiting word is the limit of the n-th iterates for n == 1 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 == 1 mod 5: 1000 and 10001111011111011110111000. (The lengths of the first 10 such iterates are 4, 26, 87, 208, 417, 759, 1302, 2136, 3376, 5192.)
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[51]] - 48 (* A288855 *)
Flatten[Position[st, 0]] (* A288856 *)
Flatten[Position[st, 1]] (* A288857 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 22 2017
STATUS
approved