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Search: id:A112286
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| A112286 |
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a(n) = numerator of sum of reciprocals of the terms of the continued fraction for H(n) = sum{k=1 to n} 1/k. |
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+0
7
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| 1, 3, 11, 7, 71, 7, 17, 152, 2699, 701, 691, 248, 133, 137, 61933, 809, 20705, 64896, 3587, 17449, 445, 61897, 208, 20663, 1163, 982, 27281, 1871, 2466139, 44339, 21293609, 13417971, 6229, 54238033, 99737, 3585191, 33583, 40756259, 5956441
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Continued Fraction
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EXAMPLE
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1 +1/2 +1/3 +1/4 +1/5 +1/6 = 49/20 = 2 + 1/(2 + 1/(4 + 1/2)).
So a(6) is 7, the numerator of 7/4 = 1/2 + 1/2 + 1/4 + 1/2.
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MATHEMATICA
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f[n_] := Plus @@ (1/# &) /@ ContinuedFraction[Sum[1/k, {k, n}]]; Table[Numerator[f[n]], {n, 40}] (*Chandler* )
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CROSSREFS
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m-th harmonic number H(m) = A001008(m)/A002805(m).
Cf. A055573, A058027, A100398, A110020, A112287.
Sequence in context: A083557 A119324 A006495 this_sequence A126261 A050097 A070613
Adjacent sequences: A112283 A112284 A112285 this_sequence A112287 A112288 A112289
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KEYWORD
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nonn,frac
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AUTHOR
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Leroy Quet Sep 01 2005
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EXTENSIONS
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Extended by Hans Havermann and Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 06 2005
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