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%I #27 Feb 12 2024 20:23:44
%S 11,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,
%T 22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,
%U 22,22,22,22,22,22,22,22
%N Continued fraction for sqrt(122).
%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 11 2024: (Start)
%F a(n) = 22 for n >= 1.
%F G.f.: 11*(1+x)/(1-x).
%F E.g.f.: 22*exp(x) - 11.
%F a(n) = 11*A040000(n). (End)
%e 11 + 1/(22 + 1/(22 + 1/(22 + 1/(22 + ...)))) = sqrt(122).
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[122],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 12 2011*)
%Y Cf. A040000, A041220/A041221 (convergents).
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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