|
%I #19 Feb 15 2024 13:01:33
%S 21,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,
%T 42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,
%U 42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42
%N Continued fraction for sqrt(442).
%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 15 2024: (Start)
%F a(n) = 42 for n >= 1.
%F G.f.: 21*(1+x)/(1-x).
%F E.g.f.: 42*exp(x) - 21.
%F a(n) = 21*A040000(n) = 7*A040006(n) = 3*A040042(n). (End)
%e 21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).
%p with(numtheory): Digits := 300: convert(evalf(sqrt(442)),confrac);
%Y Cf. A041840/A041841 (convergents).
%Y Cf. A040000, A040006, A040042.
%K nonn,cofr,easy,less
%O 0,1
%A _N. J. A. Sloane_
|
