A040378 - OEIS

%I #17 Dec 20 2023 08:05:54

%S 19,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,

%T 1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,

%U 18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18,1,38,1,18

%N Continued fraction for sqrt(398).

%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 20 2023: (Start)

%F Multiplicative with a(2) = 18, a(2^e) = 38 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 17/2^s + 5/2^(2*s-2)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(398)),confrac);

%t ContinuedFraction[Sqrt[398], 100] (* _Amiram Eldar_, Dec 20 2023 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_