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Continued fraction for sqrt(626).
4

%I #18 Feb 16 2024 05:49:34

%S 25,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,

%T 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,

%U 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50

%N Continued fraction for sqrt(626).

%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) = 50 for >= 1.

%F G.f.: 25*(1+x)/(1-x).

%F E.g.f.: 50*exp(x) - 25.

%F a(n) = 25*A040000(n) = 5*A040020(n). (End)

%e 25 + 1/(50 + 1/(50 + 1/(50 + 1/(50 + ...)))) = sqrt(626).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(626)),confrac);

%Y Cf. A042200/A042201 (convergents).

%Y Cf. A040000, A040020.

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_