A132574 Egyptian fraction representation for the cube root of 100.

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

Offset

1,1

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, ...

Links

Table of n, a(n) for n=1..8.

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.

Example

Cube root of 100 = 4.6415888336127788924100763509194465765513491250112...

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 *)

Crossrefs

Cf. A010670.

Sequence in context: A327078 A332779 A116976 * A086903 A161566 A192516

Adjacent sequences: A132571 A132572 A132573 * A132575 A132576 A132577

Keyword

frac,nonn

Author

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

Status

approved