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Continued fraction for sqrt(290).
4

%I #18 Feb 15 2024 08:46:05

%S 17,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,

%T 34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,

%U 34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34

%N Continued fraction for sqrt(290).

%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 14 2024: (Start)

%F a(n) = 34 for n >= 1.

%F G.f.: 17*(1+x)/(1-x).

%F E.g.f.: 34*exp(x) - 17.

%F a(n) = 17*A040000(n). (End)

%e 17 + 1/(34 + 1/(34 + 1/(34 + 1/(34 + ...)))) = sqrt(290).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(290)),confrac);

%Y Cf. A040000, A041544/A041545 (convergents).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_