login
Continued fraction for sqrt(321).
1

%I #18 Dec 10 2023 01:49:46

%S 17,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,

%T 1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,

%U 10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10,1,34,1,10

%N Continued fraction for sqrt(321).

%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 10 2023: (Start)

%F Multiplicative with a(2) = 10, a(2^e) = 34 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 9/2^s + 3/2^(2*s-3)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(321)),confrac);

%t ContinuedFraction[Sqrt[321],100] (* or *) PadRight[{17},100,{34,1,10,1}] (* _Harvey P. Dale_, Feb 28 2022 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_