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 A040042 Continued fraction for sqrt(50) = 5*sqrt(2). 2

%I

%S 7,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,

%T 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,

%U 14,14,14,14,14,14,14,14,14

%N Continued fraction for sqrt(50) = 5*sqrt(2).

%H Harry J. Smith, <a href="/A040042/b040042.txt">Table of n, a(n) for n=0,...,20000</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%F a(n)=14-7*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava_, Jun 09 2009]

%e 7.07106781186547524400844... = 7 + 1/(14 + 1/(14 + 1/(14 + 1/(14 + ...)))) [From _Harry J. Smith_, Jun 01 2009]

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

%t ContinuedFraction[Sqrt[50],300] (*From Vladimir Joseph Stephan Orlovsky, Mar 07 2011*)

%o (PARI) { allocatemem(932245000); default(realprecision, 47000); x=contfrac(sqrt(50)); for (n=0, 20000, write("b040042.txt", n, " ", x[n+1])); } [From _Harry J. Smith_, Jun 01 2009]

%Y Cf. A010503.

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_.

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