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A288220 1-limiting word of the mapping 00->1000, 10->010, starting with 00. 5
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0101000
00100101000
100001000100101000
01010000010100001000100101000
00100101000100001001010000010100001000100101000
The 1-limiting word is the limit of the n-th iterates for n == 1 mod 3.
The number of letters (0's and 1's) in the n-th iterate is given by A288219(n), for n >= 0.
LINKS
EXAMPLE
The first two n-th iterates for n == 1 mod 3:
1000
100001000100101000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[22]] - 48 (* A288220 *)
Flatten[Position[st, 0]] (* A288221 *)
Flatten[Position[st, 1]] (* A288222 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288219 *)
CROSSREFS
Cf. A288216 (0-limiting word), A288221, A288222, A288219, A288223 (2-limiting word).
Sequence in context: A354819 A322075 A369255 * A173856 A288926 A027356
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 19 2017
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)