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Search: id:A058027
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| A058027 |
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Sum of terms of continued fraction for n-th harmonic number, 1 +1/2 +1/3+.. +1/n. |
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+0
8
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| 1, 3, 7, 14, 15, 10, 16, 19, 26, 35, 72, 41, 38, 79, 83, 42, 59, 143, 68, 61, 70, 51, 50, 78, 74, 82, 130, 113, 111, 315, 235, 1190, 211, 407, 112, 122, 142, 246, 693, 133, 138, 162, 1904, 243, 170, 539, 363, 210, 197, 518, 275, 502, 527, 316, 1729, 224, 228, 909
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Is anything known about the asymptotics of this sequence?
Comment from Benoit Cloitre, Dec 23, 2003: Should be asymptotic to D*n^(3/2) D=0.4....
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LINKS
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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 = 11/6 = 1 + 1/(1 + 1/5). So sum of terms of continued fraction is 1 + 1 + 5 = 7.
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MATHEMATICA
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Table[Plus @@ ContinuedFraction[HarmonicNumber[n]], {n, 60}] - Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 17 2005
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CROSSREFS
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m-th harmonic number H(m) = A001008(m)/A002805(m).
Cf. A055573, A100398, A110020, A112286, A112287.
Sequence in context: A135623 A089305 A112618 this_sequence A128661 A009461 A001843
Adjacent sequences: A058024 A058025 A058026 this_sequence A058028 A058029 A058030
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Nov 15 2000
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