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A002945 Continued fraction for cube root of 2.
(Formerly M2220)
9

%I M2220

%S 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,

%T 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,

%U 7,6

%N Continued fraction for cube root of 2.

%D S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harry J. Smith, <a href="/A002945/b002945.txt">Table of n, a(n) for n = 1..20000</a>

%H BCMATH, <a href="http://www.numbertheory.org/php/cfrac_nthroot.html">Continued fraction expansion of the n-th root of a positive rational</a>

%H E. Bombieri and A. J. van der Poorten, <a href="http://www-centre.mpce.mq.edu.au/alfpapers/a113.pdf">Continued fractions of algebraic numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DelianConstant.html">Delian Constant</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%F Bombieri/van der Poorten give a complicated formula.

%e 2^(1/3) = 1.25992104989487316... = 1 + 1/(3 + 1/(1 + 1/(5 + 1/(1 + ...))))

%t ContinuedFraction[Power[2, (3)^-1],70] (* _Harvey P. Dale_, Sep 29 2011 *)

%o (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]

%Y Cf. A002946, A002947, A002948, A002949, A002580 (decimal expansion).

%K cofr,nonn

%O 1,2

%A _N. J. A. Sloane_.

%E BCMATH link from Keith R Matthews (keithmatt(AT)gmail.com), Jun 04 2006

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Last modified July 25 09:40 EDT 2014. Contains 244907 sequences.