%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_