A132574 Egyptian fraction representation for the cube root of 100.

2, 8, 61, 5118, 461665855, 623226225881980511, 414504377324573765293514801448728784, 236902165576254773155426469727218731977450593637429985699626109166408392

Offset: 1

Author

Jonathan Wellons (wellons(AT)gmail.com), Aug 23 2007

Keywords

• frac
• nonn

Comments

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, ...

Examples

			Cube root of 100 = 4.6415888336127788924100763509194465765513491250112...
		

Links

• G. Deslauriers and S. Dubuc, Le calcul de la racine cubique selon Héron, Elem. Math. 51 (1996), pp. 28-34.
• Aoife Hennessy, A Study of Riordan Arrays with Applications to Continued Fractions, Orthogonal Polynomials and Lattice Paths, Ph. D. Thesis, Waterford Institute of Technology, Oct. 2011.

Crossrefs

Cf. A010670.

Programs

Mathematica

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 *)