A040696 - OEIS

%I #25 Jan 03 2024 02:57:05

%S 26,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,

%T 7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,

%U 52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1,52,1,7,1

%N Continued fraction for sqrt(723).

%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 03 2024: (Start)

%F Multiplicative with a(2) = 7, a(2^e) = 52 for e >= 2, and a(p^e) = 1 for an odd prime p.

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

%p with(numtheory): Digits := 300: convert(evalf(sqrt(723)),confrac);

%t ContinuedFraction[Sqrt[723],120] (* _Harvey P. Dale_, Jun 02 2011 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_