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A287530
1-limiting word of the mapping 00->1000, 10->001, starting with 00.
4
1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0011000
100010011000
0011000001010011000
1000100110001000001001010011000
0011000001010011000001100010000010001001010011000
The 1-limiting word is the limit of the n-th iterates for odd n.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A287525(n), for n >= 0.
LINKS
EXAMPLE
The first three n-th iterates for even n:
1000
100010011000
1000100110001000001001010011000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[23]] - 48 (* A287530 *)
Flatten[Position[st, 0]] (* A287531 *)
Flatten[Position[st, 1]] (* A287551 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)
CROSSREFS
Cf. A287382 (0-limiting word), A287531, A287551, A287525.
Sequence in context: A102243 A173859 A202108 * A104108 A267056 A089024
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 18 2017
STATUS
approved