A040406 - OEIS

%I #18 Dec 20 2023 08:05:34

%S 20,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,

%T 1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,

%U 40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1,40,1,1,1

%N Continued fraction for sqrt(427).

%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) = 1, a(2^e) = 40 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 39/2^(2*s)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(427)),confrac);

%t ContinuedFraction[Sqrt[427],90] (* or *) PadRight[{20},90,{40,1,1,1}] (* _Harvey P. Dale_, Mar 18 2013 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_