A040497 - OEIS

%I #23 Nov 08 2024 13:13:12

%S 22,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,4,

%T 1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,

%U 4,1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4,11,4,1,44,1,4

%N Continued fraction for sqrt(520).

%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_, Dec 26 2023: (Start)

%F Multiplicative with a(2^e) = 4, a(3^e) = 11, and a(p^e) = 1 for an odd prime p >= 5.

%F Dirichlet g.f.: zeta(s) * (1 + 3/2^s) * (1 + 10/3^s). (End)

%F Sum_{k=1..n} a(k) ~ 65*n/6. - _Vaclav Kotesovec_, Nov 08 2024

%p with(numtheory): Digits := 300: convert(evalf(sqrt(520)),confrac);

%t ContinuedFraction[Sqrt[520], 100] (* _Amiram Eldar_, Dec 26 2023 *)

%t PadRight[{22},120,{44,1,4,11,4,1}] (* _Harvey P. Dale_, Nov 08 2024 *)

%K nonn,cofr,easy,less,mult

%O 0,1

%A _N. J. A. Sloane_