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A002945
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Continued fraction for cube root of 2.
(Formerly M2220)
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9
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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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
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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 + ...))))
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MATHEMATICA
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ContinuedFraction[Power[2, (3)^-1], 70] (* From Harvey P. Dale, Sep 29 2011 *)
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PROG
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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, May 08 2009]
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CROSSREFS
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Cf. A002946, A002947, A002948, A002949, A002580 (decimal expansion).
Sequence in context: A010286 A176801 A187367 * A171232 A093423 A134700
Adjacent sequences: A002942 A002943 A002944 * 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.
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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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STATUS
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approved
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