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Continued fraction for fifth root of 5.
(Formerly M0059)
4

%I M0059 #48 Jul 05 2024 11:10:12

%S 1,2,1,1,1,2,1,2,8,1,25,1,5,1,22,1,8,1,1,9,1,1,4,1,2,1,2,1,2,2,1,1,1,

%T 1,2,1,6,2,46,1,12,1,32,1,2,3,2,3,55,1,12,3,8,1,1,11,1,4,1,1,1,2,1,1,

%U 7,1,1,4,3,3,3218,1,3,1,2,2,3,1,1,2,11,1,7,57,2,2,2,2,1,1,67,1,2,3,1,1,13,3

%N Continued fraction for fifth root of 5.

%C Fifth root of 5 = 5^(1/5). - _Harry J. Smith_, May 10 2009

%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="/A002951/b002951.txt">Table of n, a(n) for n = 0..19999</a>

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

%H J. Shallit & N. J. A. Sloane, <a href="/A002949/a002949.pdf">Correspondence 1974-1975</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 1.379729661461214832390063464... = 1 + 1/(2 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, May 10 2009

%p with(numtheory): cfrac(5^(1/5),100,'quotients'); # _Muniru A Asiru_, Nov 02 2018

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

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/5)); for (n=1, 20000, write("b002951.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 10 2009

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

%Y Cf. A005534 (decimal expansion).

%Y Cf. A002363, A002364 (convergents).

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_

%E More terms copied from Smith's b-file by _Hagen von Eitzen_, Jul 20 2009

%E Offset changed by _Andrew Howroyd_, Jul 05 2024