%I #18 Feb 16 2024 05:49:50
%S 26,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,
%T 52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,
%U 52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52,52
%N Continued fraction for sqrt(677).
%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) = 52 for n >= 1.
%F G.f.: 26*(1+x)/(1-x).
%F E.g.f.: 52*exp(x) - 26.
%F a(n) = 26*A040000(n) = 13*A040002(n) = 2*A040156(n). (End)
%e 26 + 1/(52 + 1/(52 + 1/(52 + 1/(52 + ...)))) = sqrt(677).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(677)),confrac);
%Y Cf. A042300/A042301 (convergents).
%Y Cf. A040000, A040002, A040156.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_