A002946 - OEIS

%I M0408 #44 Jul 04 2024 19:57:43

%S 1,2,3,1,4,1,5,1,1,6,2,5,8,3,3,4,2,6,4,4,1,3,2,3,4,1,4,9,1,8,4,3,1,3,

%T 2,6,1,6,1,3,1,1,1,1,12,3,1,3,1,1,4,1,6,1,5,1,2,1,3,3,11,8,1,139,8,2,

%U 8,5,1,2,2,2,2,3,1,1,2,1,1,1,52,2,46,2,2,3

%N Continued fraction for cube root of 3.

%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="/A002946/b002946.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 3^(1/3) = 1.44224957030740838... = 1 + 1/(2 + 1/(3 + 1/(1 + 1/(4 + ...)))). - _Harry J. Smith_, May 08 2009

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

%t ContinuedFraction[Power[3, (3)^-1],120] (* _Harvey P. Dale_, May 11 2011 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(3^(1/3)); for (n=1, 20000, write("b002946.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 08 2009

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

%Y Cf. A002581 (decimal expansion).

%Y Cf. A002353, A002354 (convergents).

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_

%E Offset changed by _Andrew Howroyd_, Jul 04 2024