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A040420 Continued fraction for sqrt(442).

%I A040420 #21 Nov 28 2024 12:02:08
%S A040420 21,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,
%T A040420 42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,
%U A040420 42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42
%N A040420 Continued fraction for sqrt(442).
%H A040420 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040420 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040420 From _Elmo R. Oliveira_, Feb 15 2024: (Start)
%F A040420 a(n) = 42 for n >= 1.
%F A040420 G.f.: 21*(1+x)/(1-x).
%F A040420 E.g.f.: 42*exp(x) - 21.
%F A040420 a(n) = 21*A040000(n) = 7*A040006(n) = 3*A040042(n). (End)
%e A040420 21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).
%p A040420 with(numtheory): Digits := 300: convert(evalf(sqrt(442)),confrac);
%t A040420 Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[442],120]] (* or *) PadRight[{21},120,{42}] (* _Harvey P. Dale_, Nov 28 2024 *)
%Y A040420 Cf. A041840/A041841 (convergents).
%Y A040420 Cf. A040000, A040006, A040042.
%K A040420 nonn,cofr,easy,less
%O A040420 0,1
%A A040420 _N. J. A. Sloane_