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Search: id:A084845
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| A084845 |
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Numerators of the continued fraction n+1/(n+1/...) [n times]. |
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+0
4
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| 1, 5, 33, 305, 3640, 53353, 927843, 18674305, 426938895, 10928351501, 309601751184, 9616792908241, 324971855514293, 11868363584907985, 465823816409224245, 19553538801258341377, 874091571490181406680
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The n-th term of the Lucas sequence U(n,-1). The denominator is the (n-1)-th term. Adjacent terms of the sequence U(n,-1) are relatively prime. - T. D. Noe (noe(AT)sspectra.com), Aug 19 2004
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LINKS
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Eric Weisstein's World of Mathematics, Lucas Sequence
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EXAMPLE
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a(4)=305 since 4+1/(4+1/(4+1/4))=305/72
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MAPLE
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with(combinat, fibonacci):seq(fibonacci(i+1, i), i=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
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MATHEMATICA
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myList[n_] := Module[{ex = {n}}, Do[ex = {ex, n}, {n - 1}]; Flatten[ex]] Table[Numerator[FromContinuedFraction[myList[n]]], {n, 1, 20}]
Table[s=n; Do[s=n+1/s, {n-1}]; Numerator[s], {n, 20}] (T. D. Noe)
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CROSSREFS
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A084844 gives Denominators.
Cf. A097690, A097691.
Sequence in context: A129890 A120733 A001828 this_sequence A098460 A087618 A134152
Adjacent sequences: A084842 A084843 A084844 this_sequence A084846 A084847 A084848
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KEYWORD
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frac,nonn
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AUTHOR
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Hollie L. Buchanan II (hb2math(AT)hotmail.com), Jun 08 2003
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