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A010328 Continued fraction for cube root of 100. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 18:50 EDT 2021. Contains 345365 sequences. (Running on oeis4.)