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Continued fraction for sqrt(901).
4

%I #25 Feb 16 2024 11:27:30

%S 30,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,

%T 60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,

%U 60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60

%N Continued fraction for sqrt(901).

%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 a(n) = 30*A040000(n). - _Stefano Spezia_, May 14 2023

%F From _Elmo R. Oliveira_, Feb 16 2024: (Start)

%F a(n) = 60 for n >= 1.

%F G.f.: 30*(1+x)/(1-x).

%F E.g.f.: 60*exp(x) - 30. (End)

%e 30 + 1/(60 + 1/(60 + 1/(60 + 1/(60 + ...)))) = sqrt(901).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(901)),confrac);

%t Block[{$MaxExtraPrecision=1000},ContinuedFraction[Sqrt[901],100]] (* or *) PadRight[{30},100,60] (* _Harvey P. Dale_, Sep 01 2014 *)

%Y Cf. A040000, A042740/A042741 (convergents).

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_