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 A040037 Continued fraction for sqrt(44). 3

%I

%S 6,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,

%T 12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,12,1,1,1,2,1,1,1,

%U 12,1,1,1,2,1,1,1,12,1,1,1,2,1

%N Continued fraction for sqrt(44).

%H Harry J. Smith, <a href="/A040037/b040037.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)=(1/56)*{-72*(n mod 8)+5*[(n+1) mod 8]+5*[(n+2) mod 8]+12*[(n+3) mod 8]-2*[(n+4) mod 8]+5*[(n+5) mod 8]+5*[(n+6) mod 8]+82*[(n+7) mod 8]}-6*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava_, Jun 09 2009]

%e 6.633249580710799698229865473... = 6 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + ...)))) [From _Harry J. Smith_, Jun 05 2009]

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

%t ContinuedFraction[Sqrt[44],300] (*From Vladimir Joseph Stephan Orlovsky, Mar 06 2011*)

%t PadRight[{6},80,{12,1,1,1,2,1,1,1}] (* _Harvey P. Dale_, Apr 02 2013 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(44)); for (n=0, 20000, write("b040037.txt", n, " ", x[n+1])); } [From _Harry J. Smith_, Jun 05 2009]

%Y Cf. A010498 Decimal expansion. [From _Harry J. Smith_, Jun 05 2009]

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_.

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