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Search: id:A091590
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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
1
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| 1, 8, 68, 834, 8356, 84548, 841817, 8425934, 84277586
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Conjecture: lim n -> infinity, a(n)/10^n -> C = 12*ln(2)/Pi^2 = 0.842... - Benoit Cloitre (benoit7848c(AT)orange.fr), 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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Eric Weisstein's World of Mathematics, Harmonic Number
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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}]
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CROSSREFS
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Cf. A055573. n-th harmonic number H(m) = A001008(n)/A002805(n).
Sequence in context: A073555 A113357 A030992 this_sequence A087487 A015575 A124152
Adjacent sequences: A091587 A091588 A091589 this_sequence A091591 A091592 A091593
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KEYWORD
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cofr,hard,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 22 2004
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EXTENSIONS
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Corrected and extended by Eric Weisstein (eric(AT)weisstein.com), Jan 23, 2004
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