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Continued fraction for sqrt(822).
2

%I #23 Jan 10 2024 00:29:12

%S 28,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,2,

%T 1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,

%U 2,1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2,28,2,1,56,1,2

%N Continued fraction for sqrt(822).

%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 10 2024: (Start)

%F Multiplicative with a(2^e) = 2, a(3^e) = 28, and a(p^e) = 1 for p >= 5.

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

%p with(numtheory): Digits := 300: convert(evalf(sqrt(822)),confrac);

%t ContinuedFraction[Sqrt[822],100] (* or *) PadRight[{28},100,{56,1,2,28,2,1}] (* _Harvey P. Dale_, Jan 15 2023 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_