A040205 - OEIS

%I #18 Nov 29 2023 05:20:28

%S 14,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,

%T 4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,

%U 28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1,28,1,4,1

%N Continued fraction for sqrt(220).

%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_, Nov 29 2023: (Start)

%F Multiplicative with a(2) = 4, a(2^e) = 28 for e >= 2, and a(p^e) = 1 for an odd prime p.

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

%p with(numtheory): Digits := 300: convert(evalf(sqrt(220)),confrac);

%t ContinuedFraction[Sqrt[220], 100] (* _Amiram Eldar_, Nov 29 2023 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_