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Continued fraction for sqrt(27).
12

%I #29 Dec 27 2023 00:10:58

%S 5,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,

%T 10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,5,10,

%U 5,10,5,10,5,10,5,10,5,10,5

%N Continued fraction for sqrt(27).

%H Harry J. Smith, <a href="/A040021/b040021.txt">Table of n, a(n) for n = 0..20000</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>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1).

%e 5.1961524227066318805823390... = 5 + 1/(5 + 1/(10 + 1/(5 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009

%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

%t ContinuedFraction[Sqrt[27],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%t PadRight[{5},120,{10,5}] (* _Harvey P. Dale_, Jul 19 2015 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(27)); for (n=0, 20000, write("b040021.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 04 2009

%o (Magma) ContinuedFraction(Sqrt(27)); // _G. C. Greubel_, Feb 16 2018

%Y Cf. A010482 Decimal expansion. - _Harry J. Smith_, Jun 04 2009

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_