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Continued fraction for sqrt(435).
3

%I #23 Dec 20 2023 08:05:24

%S 20,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,

%T 5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,

%U 40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1

%N Continued fraction for sqrt(435).

%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_, Dec 20 2023: (Start)

%F Multiplicative with a(2) = 5, a(2^e) = 40 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-2) + 35/2^(2*s)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(435)),confrac);

%t A040414[0]:=20; A040414[n_]:=Part[{1,5,1,40},1+Mod[n+3,4]]; (* _Enrique Pérez Herrero_, Aug 26 2010 *)

%t ContinuedFraction[Sqrt[435], 100] (* _Amiram Eldar_, Dec 20 2023 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_