A040865 - OEIS

%I #20 Jan 17 2024 01:36:15

%S 29,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,

%T 1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,

%U 10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10,1,58,1,10

%N Continued fraction for sqrt(895).

%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_, Jan 17 2024: (Start)

%F Multiplicative with a(2) = 10, a(2^e) = 58 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 9/2^s + 3/2^(2*s-4)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(895)),confrac);

%t ContinuedFraction[Sqrt[895],120] (* or *) PadRight[{29},120,{58,1,10,1}] (* _Harvey P. Dale_, Dec 29 2015 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_