A040752 - OEIS

%I #20 Jan 10 2024 00:27:40

%S 27,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,

%T 1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,

%U 12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12,1,54,1,12

%N Continued fraction for sqrt(780).

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).

%F From _Amiram Eldar_, Jan 10 2024: (Start)

%F Multiplicative with a(2) = 12, a(2^e) = 54 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 11/2^s + 21/2^(2*s-1)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(780)),confrac);

%t ContinuedFraction[Sqrt[780],120] (* or *) PadRight[{27},120,{54,1,12,1}] (* _Harvey P. Dale_, Apr 23 2016 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_