A040411 - OEIS

%I #18 Dec 20 2023 08:05:41

%S 20,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,

%T 40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,

%U 40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1,40,1,3,1,1,1,3,1

%N Continued fraction for sqrt(432).

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).

%F From _Amiram Eldar_, Dec 20 2023: (Start)

%F Multiplicative with a(2) = 3, a(4) = 1, a(2^e) = 40 for e >= 3, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) - 1/2^(2*s-1) + 39/2^(3*s)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(432)),confrac);

%t ContinuedFraction[Sqrt[432],120] (* or *) PadRight[{20},120,{40,1,3,1,1,1,3,1}] (* _Harvey P. Dale_, May 22 2016 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_