A040504 - OEIS

%I #17 Dec 26 2023 06:39:46

%S 22,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,

%T 1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,

%U 21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21,1,44,1,21

%N Continued fraction for sqrt(527).

%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 26 2023: (Start)

%F Multiplicative with a(2) = 21, a(2^e) = 44 for e >= 2, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 5/2^(s-2) + 23/2^(2*s)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(527)),confrac);

%t ContinuedFraction[Sqrt[527], 100] (* _Amiram Eldar_, Dec 26 2023 *)

%K nonn,cofr,easy,less,mult

%O 0,1

%A _N. J. A. Sloane_