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Search: id:A002945
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| A002945 |
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Continued fraction for cube root of 2.
(Formerly M2220)
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+0
3
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| 1, 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3, 2, 1, 3, 4, 1, 1, 2, 14, 3, 12, 1, 15, 3, 1, 4, 534, 1, 1, 5, 1, 1, 121, 1, 2, 2, 4, 10, 3, 2, 2, 41, 1, 1, 1, 3, 7, 2, 2, 9, 4, 1, 3, 7, 6
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
BCMATH, Continued fraction expansion of the n-th root of a positive rational
E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers
Eric Weisstein's World of Mathematics, Delian Constant
G. Xiao, Contfrac
Index entries for continued fractions for constants
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FORMULA
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Bombieri/van der Poorten give a complicated formula.
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EXAMPLE
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2^(1/3) = 1.25992104989487316... = 1 + 1/(3 + 1/(1 + 1/(5 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
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PROGRAM
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(2^(1/3)); for (n=1, 20000, write("b002945.txt", n, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
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CROSSREFS
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Cf. A002946, A002947, A002948, A002949.
Cf. A002580 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 08 2009]
Sequence in context: A094919 A143069 A010286 this_sequence A093423 A134700 A085407
Adjacent sequences: A002942 A002943 A002944 this_sequence A002946 A002947 A002948
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KEYWORD
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cofr,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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BCMATH link from Keith R Matthews (keithmatt(AT)gmail.com), Jun 04 2006
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