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Continued fraction for sqrt(130).
1

%I #21 Aug 04 2024 03:06:11

%S 11,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,

%T 2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,2,2,22,

%U 2,2,22,2,2,22,2,2,22,2,2,22

%N Continued fraction for sqrt(130).

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

%F From _Elmo R. Oliveira_, Aug 03 2024: (Start)

%F G.f.: (11 + 2*x + 2*x^2 + 11*x^3)/(1 - x^3).

%F a(n) = a(n-3), n > 3. (End)

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

%t ContinuedFraction[Sqrt[130],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 12 2011*)

%Y Cf. A041236/A041237 (convergents).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_.