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A288226
0-limiting word of the mapping 00->1000, 10->011, starting with 00.
9
0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0111000
0110111000
01011110111000
0011111011110111000
10001111011111011110111000
01110001110111111011111011110111000
011011100011011111110111111011111011110111000
The 0-limiting word is the limit of the n-th iterates for n == 0 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
EXAMPLE
The first two n-th iterates for n == 0 mod 5: 00 and 0011111011110111000. (The lengths of the first 10 such iterates are 2, 19, 71, 178, 366, 676, 1172, 1939, 3086, 4770.)
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[50]] - 48 (* A288226 *)
Flatten[Position[st, 0]] (* A288227 *)
Flatten[Position[st, 1]] (* A288228 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)
CROSSREFS
Cf. A288855 (1-limiting word), A288858 (2-limiting word), A288861 (3-limiting word), A288864 (4-limiting word), A288227, A288228, A288243.
Sequence in context: A228487 A295306 A295303 * A373253 A377988 A104121
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 22 2017
STATUS
approved