A040451 - OEIS

%I #19 Dec 26 2023 06:39:21

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

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

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

%N Continued fraction for sqrt(473).

%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) = 2, a(2^e) = 42 for e >= 2, and a(p^e) = 1 for an odd prime p.

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

%p with(numtheory): Digits := 300: convert(evalf(sqrt(473)),confrac);

%t ContinuedFraction[Sqrt[473],120] (* or *) PadRight[{21},120,{42,1,2,1}] (* _Harvey P. Dale_, May 15 2021 *)

%K nonn,cofr,easy,less,mult

%O 0,1

%A _N. J. A. Sloane_