A040866 - OEIS

%I #20 Jan 17 2024 01:36:30

%S 29,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,

%T 1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,

%U 13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13,1,58,1,13

%N Continued fraction for sqrt(896).

%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) = 13, a(2^e) = 58 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 3/2^(s-2) + 45/2^(2*s)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(896)),confrac);

%t ContinuedFraction[Sqrt[896],100] (* or *) PadRight[{29},100,{58,1,13,1}] (* _Harvey P. Dale_, Mar 14 2014 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_