A010328 Continued fraction for cube root of 100.

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

0,1

Comments

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

Links

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

Example

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

Prog

(PARI) { 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

Crossrefs

Cf. A010670 = Decimal expansion.

Sequence in context: A134835 A321592 A031278 * A332847 A245501 A247026

Adjacent sequences: A010325 A010326 A010327 * A010329 A010330 A010331

Keyword

nonn,cofr

Author

N. J. A. Sloane

Status

approved