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%I #21 Feb 13 2024 08:16:26
%S 13,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,
%T 26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,
%U 26,26,26,26,26,26,26,26
%N Continued fraction for sqrt(170).
%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 12 2024: (Start)
%F a(n) = 26 for n >= 1.
%F G.f.: 13*(1+x)/(1-x).
%F E.g.f.: 26*exp(x) - 13.
%F a(n) = 13*A040000(n). (End)
%e 13 + 1/(26 + 1/(26 + 1/(26 + 1/(26 + ...)))) = sqrt(170).
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[170],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 25 2011*)
%Y Cf. A040000, A041312/A041313 (convergents).
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_.
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