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%I #13 Dec 27 2015 03:58:54
%S 2,8,61,5118,461665855,623226225881980511,
%T 414504377324573765293514801448728784,
%U 236902165576254773155426469727218731977450593637429985699626109166408392
%N Egyptian fraction representation for the cube root of 100.
%C Fractional part of 100^(1/3) = 1/2 + 1/8 + 1/61 + ... Generated with Perl's Math::BigFloat module. Number of digits in terms is as follows: 1, 1, 2, 4, 9, 18, 36, 72, 144, 287, ...
%H G. Deslauriers and S. Dubuc, <a href="http://resolver.sub.uni-goettingen.de/purl?PPN378850199_0051/dmdlog6">Le calcul de la racine cubique selon Héron</a>, Elem. Math. 51 (1996), pp. 28-34.
%H Aoife Hennessy, <a href="http://repository.wit.ie/1693/1/AoifeThesis.pdf">A Study of Riordan Arrays with Applications to Continued Fractions, Orthogonal Polynomials and Lattice Paths</a>, Ph. D. Thesis, Waterford Institute of Technology, Oct. 2011.
%e Cube root of 100 = 4.6415888336127788924100763509194465765513491250112...
%t lst={};k=N[100^(1/3),1000];Do[s=Ceiling[1/k];AppendTo[lst,s];k=k-1/s,{n,12}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 02 2009 *)
%Y Cf. A010670.
%K frac,nonn
%O 1,1
%A Jonathan Wellons (wellons(AT)gmail.com), Aug 23 2007
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