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Continued fraction for sqrt(577).
4

%I #19 Feb 15 2024 17:28:26

%S 24,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,

%T 48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,

%U 48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48

%N Continued fraction for sqrt(577).

%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) = 48 for n >= 1.

%F G.f.: 24*(1+x)/(1-x).

%F E.g.f.: 48*exp(x) - 24.

%F a(n) = 24*A040000(n) = 12*A040002(n) = 8*A040006(n). (End)

%e 24 + 1/(48 + 1/(48 + 1/(48 + 1/(48 + ...)))) = sqrt(577).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(577)),confrac);

%Y Cf. A042104/A042105 (convergents).

%Y Cf. A040000, A040002, A040006.

%K nonn,cofr,easy,less

%O 0,1

%A _N. J. A. Sloane_