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A288736
2-limiting word of the mapping 00->1000, 10->01, starting with 00.
5
0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
011000
01011000
0011011000
10001011011000
011000011011011000
0101100001011011011000
00110110000011011011011000
1000101101100010001011011011011000
The 2-limiting word is the limit of the n-th iterates for n == 2 mod 4. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288732(n), for n >= 0.
LINKS
EXAMPLE
The first three n-th iterates for n == 2 mod 3 are
011000
011000011011011000
011000011011011000011000011011011011011000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[22]] - 48 (* A288736 *)
Flatten[Position[st, 0]] (* A288737 *)
Flatten[Position[st, 1]] (* A288740 *)
CROSSREFS
Cf. A288729 (0-limiting word), A288737, A288740, A288733 (1-limiting word), A288741 (3-limiting word).
Sequence in context: A125720 A095130 A284789 * A270803 A030301 A316341
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 16 2017
STATUS
approved