A040446 - OEIS

%I #19 Dec 26 2023 06:39:16

%S 21,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,

%T 42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,

%U 42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1,42,1,1,1,2,1,1,1

%N Continued fraction for sqrt(468).

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).

%F From _Amiram Eldar_, Dec 26 2023: (Start)

%F Multiplicative with a(2) = 1, a(4) = 2, a(2^e) = 42 for e >= 3, and a(p^e) = 1 for an odd prime p.

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

%p with(numtheory): Digits := 300: convert(evalf(sqrt(468)),confrac);

%t ContinuedFraction[Sqrt[468],100] (* or *) PadRight[{21},100,{42,1,1,1,2,1,1,1}] (* _Harvey P. Dale_, Feb 28 2015 *)

%K nonn,cofr,easy,less,mult

%O 0,1

%A _N. J. A. Sloane_