Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Dec 20 2023 08:05:24
%S 20,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,
%T 5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,
%U 40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1,40,1,5,1
%N Continued fraction for sqrt(435).
%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 20 2023: (Start)
%F Multiplicative with a(2) = 5, a(2^e) = 40 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-2) + 35/2^(2*s)). (End)
%p with(numtheory): Digits := 300: convert(evalf(sqrt(435)),confrac);
%t A040414[0]:=20; A040414[n_]:=Part[{1,5,1,40},1+Mod[n+3,4]]; (* _Enrique Pérez Herrero_, Aug 26 2010 *)
%t ContinuedFraction[Sqrt[435], 100] (* _Amiram Eldar_, Dec 20 2023 *)
%K nonn,cofr,easy,mult
%O 0,1
%A _N. J. A. Sloane_