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Continued fraction for cube root of 4.
(Formerly M0200)
3

%I M0200 #40 Jul 04 2024 19:58:10

%S 1,1,1,2,2,1,3,2,3,1,3,1,30,1,4,1,2,9,6,4,1,1,2,7,2,3,2,1,6,1,1,1,25,

%T 1,7,7,1,1,1,1,266,1,3,2,1,3,60,1,5,1,8,5,6,1,4,20,1,4,1,1,14,1,4,4,1,

%U 1,1,1,7,3,1,1,2,1,3,1,4,4,1,1,1,3,1,34,8,2,10,6,3,1,2,31,1,1,1,4,3,44,1,45

%N Continued fraction for cube root of 4.

%D H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.

%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="/A002947/b002947.txt">Table of n, a(n) for n = 0..19999</a>

%H S. Lang and H. Trotter, <a href="http://dx.doi.org/10.1515/crll.1972.255.112">Continued fractions for some algebraic numbers</a>, J. Reine Angew. Math. 255 (1972), 112-134.

%H S. Lang and H. Trotter, <a href="/A002945/a002945.pdf">Continued fractions for some algebraic numbers</a>, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]

%H Herman P. Robinson, <a href="/A003116/a003116.pdf">Letter to N. J. A. Sloane, Nov 13 1973</a>.

%H Gang 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>

%e 4^(1/3) = 1.58740105196819947... = 1 + 1/(1 + 1/(1 + 1/(2 + 1/(2 + ...)))). - _Harry J. Smith_, May 08 2009

%t ContinuedFraction[4^(1/3), 80] (* _Alonso del Arte_, Jul 24 2015 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(4^(1/3)); for (n=1, 20000, write("b002947.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 08 2009

%o (Magma) [ContinuedFraction(4^(1/3))]; // _Vincenzo Librandi_, Aug 02 2015

%Y Cf. A005480 (decimal expansion). - _Harry J. Smith_, May 08 2009

%Y Cf. A002355, A002356 (convergents).

%K nonn,cofr,easy

%O 0,4

%A _N. J. A. Sloane_

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003

%E Offset changed by _Andrew Howroyd_, Jul 04 2024