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Continued fraction for sqrt(401).
5

%I #19 Feb 15 2024 13:01:59

%S 20,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,

%T 40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,

%U 40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40

%N Continued fraction for sqrt(401).

%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) = 40 for n >= 1.

%F G.f.: 20*(1+x)/(1-x).

%F E.g.f.: 40*exp(x) - 20.

%F a(n) = 20*A040000(n) = 10*A040002(n) = 5*A040012(n). (End)

%e 20 + 1/(40 + 1/(40 + 1/(40 + 1/(40 + ...)))) = sqrt(401).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(401)),confrac);

%Y Cf. A041760/A041761 (convergents).

%Y Cf. A040000, A040002, A040012.

%K nonn,cofr,easy,less

%O 0,1

%A _N. J. A. Sloane_