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Search: id:A097083
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| A097083 |
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Values of k such that there is exactly one permutation p of (1,2,3,...,k) such that i+p(i) is a Fibonacci number for 1<=i<=k. |
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+0
5
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| 1, 2, 3, 5, 9, 15, 24, 39, 64, 104, 168, 272, 441, 714, 1155, 1869, 3025, 4895, 7920, 12815, 20736, 33552, 54288, 87840
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers k such that A097082(k) = 1. If f is a fibonacci number, and k < f <= 2k, then a permutation for f-k-1 may be extended to a permutation for k, with p(i) = f-i for f-k < i <= k. This explains the sparseness of this sequence. - David Wasserman (dwasserm(AT)earthlink.net), Dec 19 2007
If the formula is correct, the bisections give A059840 and A064831. - David Wasserman (dwasserm(AT)earthlink.net), Dec 19 2007
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FORMULA
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It appears that {a(n)} satisfies a(1)=1, a(2)=2, and, for n>2, a(n)=F(n+2)-a(n-2)-1, where {F(k)} is the sequence of Fibonacci numbers.
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CROSSREFS
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Cf. A073364.
Sequence in context: A085897 A067798 A074693 this_sequence A003476 A017989 A017990
Adjacent sequences: A097080 A097081 A097082 this_sequence A097084 A097085 A097086
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KEYWORD
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nonn,more
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jul 23 2004
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EXTENSIONS
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a(9) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 29 2004
More terms from David Wasserman (dwasserm(AT)earthlink.net), Dec 19 2007
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