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A288736
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2-limiting word of the mapping 00->1000, 10->01, starting with 00.
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5
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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
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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
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 (0s and 1s) in the n-th iterate is given by A288732(n), for n >= 0.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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EXAMPLE
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The first three n-th iterates for n == 2 mod 3 are
011000
011000011011011000
011000011011011000011000011011011011011000
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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" -> "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 *)
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CROSSREFS
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Cf. A288729 (0-limiting word), A288737, A288740, A288733 (1-limiting word), A288741 (3-limiting word).
Sequence in context: A125720 A095130 A284789 * A270803 A030301 A316341
Adjacent sequences: A288733 A288734 A288735 * A288737 A288738 A288739
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 16 2017
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STATUS
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approved
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