A040506 - OEIS

%I #21 Jul 14 2024 13:24:47

%S 23,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,

%T 46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,

%U 46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46

%N Continued fraction for sqrt(530).

%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) = 46 for n >= 1.

%F G.f.: 23*(1+x)/(1-x).

%F E.g.f.: 46*exp(x) - 23.

%F a(n) = 23*A040000(n). (End)

%e 23 + 1/(46 + 1/(46 + 1/(46 + 1/(46 + ...)))) = sqrt(530).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(530)),confrac);

%t Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[530],100]] (* or *) PadRight[{23},100,{46}] (* _Harvey P. Dale_, Jul 14 2024 *)

%Y Cf. A040000, A042012/A042013 (convergents).

%K nonn,cofr,easy,less

%O 0,1

%A _N. J. A. Sloane_