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 A074903 #51 Feb 16 2025 08:32:47
%S A074903 1,3,5,1,1,3,1,5,7,4,4,9,1,6,5,9,0,0,1,7,9,3,8,6,8,0,0,5,2,5,6,5,2,1,
%T A074903 0,6,8,3,6,0,6,5,1,5,0,8,7,4,2,7,0,1,6,8,7,3,4,5,1,4,7,2,1,1,0,1,3,7,
%U A074903 4,2,2,7,7,1,1,9,5,5,0,1,7,1,2,8,6,9,1,3,0,7,5,1,5,9,7,8,0,2,3,9
%N A074903 Decimal expansion of the mean number of iterations in comparing two numbers via their continued fractions.
%C A074903 Another description: Decimal expansion of the mean number of comparisons (moment sum of index 2) in the basic continued fraction sign algorithm ("BCF-sign").
%C A074903 Still another description: Decimal expansion of expected number of iterations of Gaussian reduction of a 2-dimensional lattice.
%D A074903 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 161.
%D A074903 Philippe Flajolet and Brigitte Vallée, Continued fraction algorithms and constants, in "Constructive, Experimental, and Nonlinear Analysis", Michel Théra Editor, CMS Conference Proceedings, Canadian Mathematical Society Volume 27 (2000), p. 67.
%H A074903 H. Daude, P. Flajolet, and B. Vallee, <a href="http://algo.inria.fr/flajolet/Publications/RR2798.ps.gz">An average-case analysis of the Gaussian algorithm for lattice reduction</a>, INRIA, 1996. [<a href="https://www.semanticscholar.org/paper/An-Average-Case-Analysis-of-the-Gaussian-Algorithm-Daud%C3%A9-Flajolet/5783d4bfc398819b106c216bfea14347dd58550b">alternative link</a>]
%H A074903 Philippe Flajolet, <a href="http://algo.inria.fr/seminars/sem99-00/flajolet.pdf">Continued Fractions, Comparison Algorithms and Fine Structure Constants</a>.
%H A074903 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.
%H A074903 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ValleeConstant.html">Vallée Constant</a>.
%F A074903 Equals (-60/Pi^4)*(24*Li_4(1/2) - Pi^2*log(2)^2 + 21*zeta(3)*log(2) + log(2)^4) + 17, with Li_4 the tetralogarithm function. - _Jean-François Alcover_, Apr 23 2015
%e A074903 1.351131574491659001793868005256521068360651508742701687345147211...
%e A074903 (Only the first 31 digits are the same as those given by Flajolet & Vallée. - _Jean-François Alcover_, Apr 23 2015)
%t A074903 17 - 60/Pi^4 (24*PolyLog[4, 1/2] - Pi^2*Log[2]^2 + 21*Zeta[3]*Log[2] + Log[2]^4) // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Mar 19 2013, after _Steven Finch_ *)
%o A074903 (PARI) 17 - 60*(24*polylog(4, 1/2) - Pi^2*log(2)^2 + 21*zeta(3)*log(2) + log(2)^4)/Pi^4 \\ _Charles R Greathouse IV_, Aug 27 2014
%Y A074903 Cf. A099218.
%K A074903 nonn,cons
%O A074903 1,2
%A A074903 _N. J. A. Sloane_, Sep 15 2002
%E A074903 Corrected and extended by _Jean-François Alcover_, Mar 19 2013
%E A074903 Entry revised by _N. J. A. Sloane_, Apr 24 2015 to include information from two other entries (submitted respectively by _Eric W. Weisstein_, Aug 05 2008 and _Jean-François Alcover_, Apr 23 2015) that formerly described this same constant.