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A002946
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Continued fraction for cube root of 3.
(Formerly M0408)
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3
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1, 2, 3, 1, 4, 1, 5, 1, 1, 6, 2, 5, 8, 3, 3, 4, 2, 6, 4, 4, 1, 3, 2, 3, 4, 1, 4, 9, 1, 8, 4, 3, 1, 3, 2, 6, 1, 6, 1, 3, 1, 1, 1, 1, 12, 3, 1, 3, 1, 1, 4, 1, 6, 1, 5, 1, 2, 1, 3, 3, 11, 8, 1, 139, 8, 2, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
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EXAMPLE
| 3^(1/3) = 1.44224957030740838... = 1 + 1/(2 + 1/(3 + 1/(1 + 1/(4 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
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MATHEMATICA
| ContinuedFraction[Power[3, (3)^-1], 120] (* From Harvey P. Dale, May 11 2011 *)
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(3^(1/3)); for (n=1, 20000, write("b002946.txt", n, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
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CROSSREFS
| Cf. A002581 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
Sequence in context: A089555 A098554 A109201 * A205790 A035426 A065516
Adjacent sequences: A002943 A002944 A002945 * A002947 A002948 A002949
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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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