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Search: id:A084844
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| A084844 |
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Denominators of the continued fraction n+1/(n+1/...) [n times]. |
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+0
4
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| 1, 2, 10, 72, 701, 8658, 129949, 2298912, 46866034, 1082120050, 27916772489, 795910114440, 24851643870041, 843458630403298, 30918112619119426, 1217359297034666112, 51240457936070359069, 2296067756927144738850
(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-1)-th term of the Lucas sequence U(n,-1). The numerator is the n-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)=72 since 4+1/(4+1/(4+1/4))=305/72
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MAPLE
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a:=proc(n) if n=1 then 2 else fibonacci(n, n) fi end: seq(a(n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT))yahoo.com), Jan 03 2007
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MATHEMATICA
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myList[n_] := Module[{ex = {n}}, Do[ex = {ex, n}, {n - 1}]; Flatten[ex]] Table[Denominator[FromContinuedFraction[myList[n]]], {n, 1, 20}]
Table[s=n; Do[s=n+1/s, {n-1}]; Denominator[s], {n, 20}] (T. D. Noe)
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CROSSREFS
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A084845 gives Numerators.
Cf. A097690, A097691.
Sequence in context: A060842 A111554 A052555 this_sequence A144011 A088189 A001395
Adjacent sequences: A084841 A084842 A084843 this_sequence A084845 A084846 A084847
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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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