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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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9
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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
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OFFSET
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1,2
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COMMENTS
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Is anything known about the asymptotics of this sequence?
Should be asymptotic to D*n^(3/2) with D=0.4.... - Benoit Cloitre, Dec 23 2003
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LINKS
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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, Sep 17 2005 *)
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PROG
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(PARI) a(n) = vecsum(contfrac(sum(k=1, n, 1/k))); \\ Michel Marcus, Mar 23 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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