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A040011 Continued fraction for sqrt(15). 4

%I

%S 3,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,

%T 6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,

%U 6,1,6,1,6,1,6,1,6,1,6,1,6

%N Continued fraction for sqrt(15).

%H Harry J. Smith, <a href="/A040011/b040011.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).

%F a(n) = (1/2)(7 + 5*(-1)^n) - 3*(binomial(2*n,n) mod 2), with n>=0. - _Paolo P. Lava_, Jun 11 2009

%e 3.872983346207416885179265399... = 3 + 1/(1 + 1/(6 + 1/(1 + 1/(6 + ...)))). - _Harry J. Smith_, Jun 03 2009

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

%t ContinuedFraction[Sqrt[15],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)

%t PadRight[{3},120,{6,1}] (* _Harvey P. Dale_, Apr 14 2020 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(15)); for (n=0, 20000, write("b040011.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009

%Y Cf. A010472 Decimal expansion. - _Harry J. Smith_, Jun 03 2009

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_

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Last modified April 14 18:15 EDT 2021. Contains 342951 sequences. (Running on oeis4.)