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Continued fraction for fifth root of 4.
(Formerly M2607)
2

%I M2607 #31 Jul 05 2024 11:10:01

%S 1,3,7,1,2,2,1,2,4,56,1,14,2,1,1,3,5,6,2,1,1,2,1,1,8,1,2,2,1,5,1,4,1,

%T 1,3,3,1,1,3,7,4,1,10,1,2,1,8,2,4,1,1,9,2,2,2,1,2,1,1,1,92,1,26,4,31,

%U 1,2,4,1,62,8,5,1,1,1,2,1,1,63,1,2,5,4,2,1

%N Continued fraction for fifth root of 4.

%D H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harry J. Smith, <a href="/A003118/b003118.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 1.319507910772894259374001971... = 1 + 1/(3 + 1/(7 + 1/(1 + 1/(2 + ...)))). - _Harry J. Smith_, May 11 2009

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(4^(1/5)); for (n=1, 20000, write("b003118.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 11 2009

%Y Cf. A005533 (decimal expansion).

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_

%E Offset changed by _Andrew Howroyd_, Jul 05 2024