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%I #30 Feb 12 2024 20:23:11
%S 10,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,
%T 20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,
%U 20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20
%N Continued fraction for sqrt(101).
%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) = 20 for n >= 1.
%F G.f.: 10*(1+x)/(1-x).
%F E.g.f.: 20*exp(x) - 10.
%F a(n) = 10*A040000(n) = 5*A040002(n) = 2*A040020(n). (End)
%e 10 + 1/(20 + 1/(20 + 1/(20 + 1/(20 + ...)))) = sqrt(101).
%p Digits := 200: convert(evalf(sqrt(101)),confrac,150,'cvgts'):
%t ContinuedFraction[Sqrt[101],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 10 2011*)
%t PadRight[{10},100,{20}] (* _Harvey P. Dale_, Apr 22 2022 *)
%Y Cf. A248803 (decimal expansion), A041180/A041181 (convergents).
%Y Cf. A040000, A040002, A040020.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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