A010209 - OEIS

%I #27 Nov 22 2023 08:31:43

%S 12,1,1,1,5,1,1,1,24,1,1,1,5,1,1,1,24,1,1,1,5,1,1,1,24,1,1,1,5,1,1,1,

%T 24,1,1,1,5,1,1,1,24,1,1,1,5,1,1,1,24,1,1,1,5,1,1,1,24,1,1,1,5,1,1,1,

%U 24,1,1,1,5,1,1,1,24,1,1,1,5

%N Continued fraction for sqrt(160).

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.

%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_, Nov 22 2023: (Start)

%F Multiplicative with a(2) = 1, a(4) = 5, a(2^e) = 24 for e >= 3, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 1/4^(s-1) + 19/8^s). (End)

%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

%t ContinuedFraction[Sqrt[160],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 23 2011 *)

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_