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Continued fraction for sqrt(726).
1

%I #20 Jan 10 2024 00:27:13

%S 26,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,

%T 1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,

%U 16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16,1,52,1,16

%N Continued fraction for sqrt(726).

%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 10 2024: (Start)

%F Multiplicative with a(2) = 16, 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-2) + 3/2^s + 9/2^(2*s-2)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(726)),confrac);

%t ContinuedFraction[Sqrt[726],100] (* or *) PadRight[{26},100,{52,1,16,1}] (* _Harvey P. Dale_, Jul 31 2021 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_