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A002949 Continued fraction for cube root of 6.

%I A002949 M3202 #49 Jul 05 2024 10:07:21
%S A002949 1,1,4,2,7,3,508,1,5,5,1,1,1,2,1,1,24,1,1,1,3,3,30,4,10,158,6,1,1,2,
%T A002949 12,1,10,1,1,3,2,1,1,89,1,1,2,1,1,1,3,1,2,1,7,1,2,18,1,17,2,2,10,14,3,
%U A002949 1,2,1,2,1,5,1,1,2,26,1,4,65,1,1,1,27,1,2,1,4
%N A002949 Continued fraction for cube root of 6.
%D A002949 H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
%D A002949 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002949 Harry J. Smith, <a href="/A002949/b002949.txt">Table of n, a(n) for n = 0..19999</a>
%H A002949 Herman P. Robinson, <a href="/A003116/a003116.pdf">Letter to N. J. A. Sloane, Nov 13 1973</a>.
%H A002949 J. Shallit & N. J. A. Sloane, <a href="/A002949/a002949.pdf">Correspondence 1974-1975</a>
%H A002949 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A002949 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A002949 6^(1/3) = 1.81712059283213965... = 1 + 1/(1 + 1/(4 + 1/(2 + 1/(7 + ...)))). - _Harry J. Smith_, May 08 2009
%p A002949 with(numtheory):
%p A002949 cfrac(6^(1/3),100,'quotients'); # _Muniru A Asiru_, Nov 02 2018
%t A002949 ContinuedFraction[6^(1/3), 100] (* _G. C. Greubel_, Nov 02 2018 *)
%o A002949 (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(6^(1/3)); for (n=1, 20000, write("b002949.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 08 2009
%o A002949 (Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(6^(1/3)); // _G. C. Greubel_, Nov 02 2018
%Y A002949 Cf. A005486 (decimal expansion).
%Y A002949 Cf. A002359, A002360 (convergents).
%K A002949 nonn,cofr
%O A002949 0,3
%A A002949 _N. J. A. Sloane_
%E A002949 Offset changed by _Andrew Howroyd_, Jul 05 2024