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A214671 Floor of the real parts of the zeros of the complex Lucas function on the right half plane. 2

%I

%S 0,2,4,6,8,10,11,13,15,17,19,21,22,24,26,28,30,31,33,35,37,39,41,42,

%T 44,46,48,50,52,53,55,57,59,61,63,64,66,68,70,72,74,75,77,79,81,83,85,

%U 86,88,90,92,94,95,97,99,101,103,105,106,108,110,112,114,116,117,119

%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).

%K nonn

%O 0,2

%A _Wolfdieter Lang_, Jul 25 2012

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Last modified October 23 12:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)