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A091590
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Number of terms in the simple continued fraction for the 10^n-th harmonic number, H_n = sum_{k=1 to n} (1/k).
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0
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OFFSET
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0,2
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COMMENTS
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Conjecture: lim n -> infinity, a(n)/10^n -> C = 12*log(2)/Pi^2 = 0.842... - Benoit Cloitre, May 04 2002
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.
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LINKS
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MATHEMATICA
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s = 0; k = 1; Do[ While[s = s + 1/k; k < 10^n, k++ ]; Print[ Length[ ContinuedFraction[s]]]; k++, {n, 0, 6}]
Table[Length[ContinuedFraction[HarmonicNumber[10^n]]], {n, 0, 7}] (* Harvey P. Dale, Aug 24 2015 *)
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CROSSREFS
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KEYWORD
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cofr,hard,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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