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Search: id:A132917
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| A132917 |
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Order set of the first 300 infinite truncated Fibonacci Words where a(n) is the number of terms (ones and zeros) truncated from the left hand side of the word. |
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3
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| 233, 89, 178, 34, 267, 123, 212, 68, 157, 13, 246, 102, 191, 47, 280, 136, 225, 81, 170, 26, 259, 115, 204, 60, 293, 149, 5, 238, 94, 183, 39, 272, 128, 217, 73, 162, 18, 251, 107, 196, 52, 285, 141, 230, 86, 175, 31, 264, 120, 209, 65, 298, 154, 10, 243, 99, 188
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The sequence can also be built up from left to right directly (with out having to make insertions) as follows: a(0) equals greatest odd Fibonacci number less than n, i.e., [a(0) = F(2m)] The rule for a(n+1) is according to the following (first listed takes priority): a(n+1) = a(n) + F(2m) if less than or equal to n a(n+1) = a(n) - F(2m-1) if greater than 0 a(n+1) = a(n) + F(2m-2) Continue until all n terms have been included in the sequence.
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LINKS
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Kenneth J Ramsey (Ramsey2879(AT)msn.com), Sep 05 2007, Table of n, a(n) for n = 0..299
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FORMULA
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The sequence is generated starting with {2,1} and the numbers 3,4,5,..n are inserted in order into the sequence using the following rules: If n is an even Fibonacci number, it is inserted after the last term If n is an odd Fibonacci number, it is inserted before the first term If n is not a fibonacci number, it is inserted between the adjacent terms, n - GF(even) and n-GF(odd) where GF(odd) and GF(even) are respectfully the greatest odd and even Fibonacci numbers less than n.
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EXAMPLE
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4 appears between 2 and 1 in the sequence because the greatest odd Fibonacci number less than 4 is 2 and the greatest even Fibonacci number less than 4 is 3
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CROSSREFS
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Cf. A132828.
Adjacent sequences: A132914 A132915 A132916 this_sequence A132918 A132919 A132920
Sequence in context: A050423 A126818 A064715 this_sequence A126979 A127340 A105981
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KEYWORD
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nonn,uned
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AUTHOR
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Kenneth J Ramsey (Ramsey2879(AT)msn.com), Sep 05 2007
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