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Continued fraction for sqrt(21).
4

%I #37 Dec 27 2023 00:24:01

%S 4,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,

%T 1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,1,2,1,1,8,1,

%U 1,2,1,1,8,1,1,2,1,1,8,1,1

%N Continued fraction for sqrt(21).

%H Harry J. Smith, <a href="/A010125/b010125.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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F a(n) = gcd(Fibonacci(n), Fibonacci(n-6)), n > 0. - _Gary Detlefs_, Dec 29 2010

%e 4.582575694955840006588047193... = 4 + 1/(1 + 1/(1 + 1/(2 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 03 2009

%t ContinuedFraction[Sqrt[21],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%t PadRight[{4},120,{8,1,1,2,1,1}] (* _Harvey P. Dale_, May 16 2020 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(21)); for (n=0, 20000, write("b010125.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009

%Y Cf. A041032/A041033 (convergents), A010477 (decimal expansion).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_