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Continued fraction for sqrt(730).
4

%I #18 Feb 16 2024 05:50:02

%S 27,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,

%T 54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,

%U 54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54,54

%N Continued fraction for sqrt(730).

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

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F From _Elmo R. Oliveira_, Feb 15 2024: (Start)

%F a(n) = 54 for n >= 1.

%F G.f.: 27*(1+x)/(1-x).

%F E.g.f.: 54*exp(x) - 27.

%F a(n) = 27*A040000(n) = 9*A040006(n) = 3*A040072(n). (End)

%e 27 + 1/(54 + 1/(54 + 1/(54 + 1/(54 + ...)))) = sqrt(730).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(730)),confrac);

%Y Cf. A042404/A042405 (convergents).

%Y Cf. A040000, A040006, A040072.

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_