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Continued fraction for sqrt(897).
1

%I #22 Jan 17 2024 01:36:51

%S 29,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,

%T 1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,

%U 18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18,1,58,1,18

%N Continued fraction for sqrt(897).

%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 a(n) = a(n-4) for n > 4 with a(0) = 29, a(1) = a(3) = 1, a(2) = 18, a(4) = 58. - _Wesley Ivan Hurt_, Dec 31 2023

%F From _Amiram Eldar_, Jan 17 2024: (Start)

%F Multiplicative with a(2) = 18, a(2^e) = 58 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 17/2^s + 5/2^(2*s-3)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(897)),confrac);

%t ContinuedFraction[Sqrt[897],80] (* or *) PadRight[{29},80,{58,1,18,1}] (* _Harvey P. Dale_, Oct 14 2013 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_