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A010328
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Continued fraction for cube root of 100.
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2
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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; internal format)
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OFFSET
| 0,1
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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]
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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
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EXAMPLE
| 100^(1/3) = 4.641588833612778... = 4 + 1/(1 + 1/(1 + 1/(1 + 1/(3 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(100^(1/3)); for (n=1, 20001, write("b010328.txt", n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
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CROSSREFS
| Cf. A010670 = Decimal expansion.
Sequence in context: A010327 A134835 A031278 * A193512 A173675 A085731
Adjacent sequences: A010325 A010326 A010327 * A010329 A010330 A010331
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KEYWORD
| nonn,cofr
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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