This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091590 #21 Feb 16 2025 08:32:52
%S A091590 1,8,68,834,8356,84548,841817,8425934,84277586
%N A091590 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 A091590 Conjecture: lim n -> infinity, a(n)/10^n -> C = 12*log(2)/Pi^2 = 0.842... - _Benoit Cloitre_, May 04 2002
%D A091590 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.
%H A091590 J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">MathWorld: Harmonic Number</a>
%F A091590 a(n) = A055573(10^n). - _Andrew Howroyd_, Aug 10 2024
%t A091590 s = 0; k = 1; Do[ While[s = s + 1/k; k < 10^n, k++ ]; Print[ Length[ ContinuedFraction[s]]]; k++, {n, 0, 6}]
%t A091590 Table[Length[ContinuedFraction[HarmonicNumber[10^n]]], {n, 0, 7}] (* _Harvey P. Dale_, Aug 24 2015 *)
%Y A091590 Cf. A055573. n-th harmonic number H(m) = A001008(n)/A002805(n).
%K A091590 hard,nonn
%O A091590 0,2
%A A091590 _Robert G. Wilson v_, Jan 22 2004
%E A091590 Corrected and extended by _Eric W. Weisstein_, Jan 23 2004