Search: a288991 -id:a288991
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1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 53, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n)/n -> 1.28... and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.
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LINKS
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MATHEMATICA
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z = 10; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A288991 *)
Flatten[Position[st, 0]] (* A288992 *)
Flatten[Position[st, 1]] (* A288993 *)
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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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3, 10, 14, 18, 21, 25, 28, 32, 35, 42, 49, 52, 56, 59, 66, 70, 74, 77, 81, 85, 92, 95, 99, 102, 109, 113, 117, 120, 124, 127, 131, 134, 141, 148, 155, 159, 163, 166, 173, 180, 183, 187, 191, 198, 205, 212, 215, 219, 222, 229, 236, 239, 243, 247, 254, 258
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n)/n -> 4.56... and if m denotes this number, then -1 < m - a(n)/n < 2 for n >= 1.
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LINKS
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MATHEMATICA
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z = 10; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A288991 *)
Flatten[Position[st, 0]] (* A288992 *)
Flatten[Position[st, 1]] (* A288993 *)
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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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A289000
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Length of n-th iterate of the mapping 00->0010, 01->001, 10->001, starting with 00.
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+10
3
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2, 4, 7, 12, 20, 34, 58, 99, 169, 288, 491, 837, 1428, 2437, 4159, 7099, 12118, 20686, 35312, 60280, 102903, 175665, 299877, 511920, 873900, 1491838, 2546724, 4347527, 7421690, 12669614, 21628381, 36921953, 63029713, 107598447, 183682035, 313564844, 535288668
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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MATHEMATICA
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z = 20; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
Table[StringLength[w[n]], {n, 0, 20}] (* A289000 *)
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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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EXTENSIONS
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STATUS
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approved
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A288996
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Length of n-th iterate of the mapping 00->0010, 01->001, 10->000, starting with 00.
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+10
2
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2, 4, 7, 12, 22, 39, 68, 121, 213, 379, 676, 1206, 2155, 3832, 6823, 12156, 21658, 38584, 68716, 122402, 218016, 388317, 691583, 1231599, 2193224, 3905575, 6954709, 12384775, 22053977, 39271946, 69933281, 124534373, 221766354, 394914918, 703253649, 1252338238
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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z = 20; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
Table[StringLength[w[n]], {n, 0, 20}] (* A288996 *)
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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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EXTENSIONS
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STATUS
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approved
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