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A288665
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0-limiting word of the mapping 00->0110, 10->000, starting with 00.
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6
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0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1
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OFFSET
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1
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COMMENTS
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Iterates of the mapping, starting with 00:
00
0110
01000
00000110
0110011001000
010000100000000110
00000110000001100110011001000
01100110010000110011001000010000100000000110
The 0-limiting word is the limit of the n-th iterates for n == 0 mod 3.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).
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LINKS
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EXAMPLE
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The first three n-th iterates for n == 0 mod 3 are
00
00000110
00000110000001100110011001000
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MATHEMATICA
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s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[9]] - 48 (* A288665 *)
Flatten[Position[st, 0]] (* A288666 *)
Flatten[Position[st, 1]] (* A288667 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A288668 conjectured *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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