%N Floor of the real parts of the zeros of the complex Lucas function on the right half plane.
%C For the complex Lucas function and its zeros see the Koshy reference. This function is L: C -> C, z -> L(z), with
%C L(z) = exp(log(phi)*z) + exp(I*Pi*z)*exp(-log(phi)*z),
%C with the complex unit I and the golden section phi:=(1+sqrt(5))/2. The complex zeros are z_0(k) = x_0(k) + y_0(k)*I, with x_0(k) = (k+1/2)*alpha and y_0(k) = (k+1/2)*a, where alpha and a appear in the Fibonacci case as alpha = 2*(Pi^2)/(Pi^2 + (2*log(phi))^2) and a = 4*Pi*log(phi)/(Pi^2 + (2*log(phi))^2). The x_0 and y_0 values are shifted compared to the zeros of the Fibonacci case by alpha/2, respectively a/2. Approximately alpha/2 = 0.9142023915 and a/2 = 0.2800649542.
%F a(n) = floor((k+1/2)*alpha), with alpha/2 = x_0(0) defined in the comment section.
%Y Cf. A214672 (floor of imaginary parts), A214673 (moduli), A214315 (Fibonacci case).
%A _Wolfdieter Lang_, Jul 25 2012