A040593 - OEIS

%I #21 Jan 03 2024 03:01:24

%S 24,1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,

%T 1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6,

%U 8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6,8,6,1,48,1,6

%N Continued fraction for sqrt(618).

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F From _Amiram Eldar_, Jan 03 2024: (Start)

%F Multiplicative with a(2^e) = 6, a(3^e) = 8, and a(p^e) = 1 for prime p >= 5.

%F Dirichlet g.f.: zeta(s) * (1 + 5/2^s) * (1 + 7/3^s). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(618)),confrac);

%t ContinuedFraction[Sqrt[618],100] (* or *) PadRight[{24},100,{48,1,6,8,6,1}] (* _Harvey P. Dale_, May 31 2021 *)

%K nonn,cofr,easy,mult,less

%O 0,1

%A _N. J. A. Sloane_