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%I #16 Aug 24 2015 11:32:19
%S 1,8,68,834,8356,84548,841817,8425934,84277586
%N Number of terms in the simple continued fraction for the 10^n-th harmonic number, H_n = sum_{k=1 to n} (1/k).
%C Conjecture: lim n -> infinity, a(n)/10^n -> C = 12*log(2)/Pi^2 = 0.842... - _Benoit Cloitre_, May 04 2002
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.
%H J. Sondow and E. W. Weisstein, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">MathWorld: Harmonic Number</a>
%t s = 0; k = 1; Do[ While[s = s + 1/k; k < 10^n, k++ ]; Print[ Length[ ContinuedFraction[s]]]; k++, {n, 0, 6}]
%t Table[Length[ContinuedFraction[HarmonicNumber[10^n]]], {n, 0, 7}] (* _Harvey P. Dale_, Aug 24 2015 *)
%Y Cf. A055573. n-th harmonic number H(m) = A001008(n)/A002805(n).
%K cofr,hard,nonn
%O 0,2
%A _Robert G. Wilson v_, Jan 22 2004
%E Corrected and extended by _Eric W. Weisstein_, Jan 23 2004
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