A040372 - OEIS

%I #20 Jun 30 2026 16:21:02

%S 19,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,

%T 3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,

%U 38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1,38,1,3,1

%N Continued fraction for sqrt(392).

%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) = 3, a(2^e) = 38 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 35/2^(2*s)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(392)),confrac);

%t ContinuedFraction[Sqrt[392],120] (* _Harvey P. Dale_, Nov 21 2019 *)

%t (* Alternative: *)

%t PadRight[{19},120,{38,1,3,1}] (* _Harvey P. Dale_, Nov 21 2019 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_