A040544 - OEIS

%I #18 Dec 27 2023 00:47:16

%S 23,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,

%T 4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,

%U 46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1,46,1,4,1

%N Continued fraction for sqrt(568).

%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_, Dec 27 2023: (Start)

%F Multiplicative with a(2) = 4, a(2^e) = 46 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 3/2^s + 21/2^(2*s-1)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(568)),confrac);

%t ContinuedFraction[Sqrt[568],120] (* or *) PadRight[{23},120,{46,1,4,1}] (* _Harvey P. Dale_, Dec 05 2014 *)

%K nonn,cofr,easy,less,mult

%O 0,1

%A _N. J. A. Sloane_