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Continued fraction for cube root of 5.
(Formerly M0300)
3

%I M0300 #40 Jul 04 2024 19:58:32

%S 1,1,2,2,4,3,3,1,5,1,1,4,10,17,1,14,1,1,3052,1,1,1,1,1,1,2,2,1,3,2,1,

%T 13,5,1,1,1,13,2,41,1,4,12,1,5,2,7,1,1,3,33,2,1,1,1,1,1,1,3,2,2,1,15,

%U 12,8,10,48,1,2,1,1,3,4,1,474,1,13,2,4,1,1,49

%N Continued fraction for cube root of 5.

%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="/A002948/b002948.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 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>

%e 5^(1/3) = 1.70997594667669698... = 1 + 1/(1 + 1/(2 + 1/(2 + 1/(4 + ...)))). - _Harry J. Smith_, May 08 2009

%p with(numtheory): cfrac(5^(1/3),80,'quotients'); # _Muniru A Asiru_, Nov 02 2018

%t ContinuedFraction[5^(1/3), 100] (* _G. C. Greubel_, Nov 02 2018 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/3)); for (n=1, 20000, write("b002948.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 08 2009

%o (Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(5^(1/3)); // _G. C. Greubel_, Nov 02 2018

%Y Cf. A005481 (decimal expansion).

%Y Cf. A002357, A002358 (convergents).

%K nonn,cofr

%O 0,3

%A _N. J. A. Sloane_

%E Offset changed by _Andrew Howroyd_, Jul 04 2024