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Continued fraction for sqrt(677).
5

%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_