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A288861 3-limiting word of the mapping 00->1000, 10->011, starting with 00. 7
0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 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, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0111000
0110111000
01011110111000
0011111011110111000
10001111011111011110111000
01110001110111111011111011110111000
011011100011011111110111111011111011110111000
The 3-limiting word is the limit of the n-th iterates for n == 3 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 == 3 mod 5:
0110111000
011011100011011111110111111011111011110111000
(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[53]] - 48 (* A288861 *)
Flatten[Position[st, 0]] (* A288862 *)
Flatten[Position[st, 1]] (* A288863 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)
CROSSREFS
Cf. A288226 (0-limiting word), A288855 (1-limiting word), A288858 (2-limiting word), A288864 (4-limiting word), A288862, A288863, A288243.
Sequence in context: A163532 A014578 A323153 * A030190 A353471 A157658
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 23 2017
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)