A010670 -id:A010670 - cp's OEIS frontend

A132574 Egyptian fraction representation for the cube root of 100.

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

Offset: 1

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

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, ...

			Cube root of 100 = 4.6415888336127788924100763509194465765513491250112...

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.

Cf. A010670.

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 *)

A010328 Continued fraction for cube root of 100.

Original entry on oeis.org

4, 1, 1, 1, 3, 1, 3, 4, 4, 1, 1, 3, 1, 16, 1, 1, 1, 5, 8, 5, 1, 1, 1, 6, 4, 3, 1, 1, 1, 23, 1, 5, 3, 12, 2, 1, 1, 3, 1, 1, 1, 99, 1, 1, 8, 6, 2, 3, 1, 1, 2, 1, 3, 1, 2, 6, 2, 1, 1, 1, 3, 2, 8, 1, 1, 3, 4, 3, 1, 1, 2, 7, 38, 1, 2, 1, 1, 1, 6, 6

Offset: 0

N. J. A. Sloane

Heron (or Hero) of Alexandria calculated this constant as 4 + 9/14 or (4; 1, 1, 1, 4) in the first century AD, see Deslauriers & Dubuc or Metrica book III section 20. - Charles R Greathouse IV, Jan 16 2012

			100^(1/3) = 4.641588833612778... = 4 + 1/(1 + 1/(1 + 1/(1 + 1/(3 + ...)))). - _Harry J. Smith_, May 08 2009

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Deslauriers and S. Dubuc, Le calcul de la racine cubique selon Héron, Elem. Math. 51 (1996), pp. 28-34.
G. Xiao, Contfrac

Cf. A010670 = Decimal expansion.

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(100^(1/3)); for (n=1, 20001, write("b010328.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

cp's OEIS Frontend

A132574 Egyptian fraction representation for the cube root of 100.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica