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Continued fraction for sqrt(842).
4

%I #18 Feb 16 2024 11:27:05

%S 29,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,

%T 58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,

%U 58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58

%N Continued fraction for sqrt(842).

%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 16 2024: (Start)

%F a(n) = 58 for n >= 1.

%F G.f.: 29*(1+x)/(1-x).

%F E.g.f.: 58*exp(x) - 29.

%F a(n) = 29*A040000(n). (End)

%e 29 + 1/(58 + 1/(58 + 1/(58 + 1/(58 + ...)))) = sqrt(842).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(842)),confrac);

%Y Cf. A040000, A042624/A042625 (convergents).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_