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A214671 Floor of the real parts of the zeros of the complex Lucas function on the right half plane. 2
0, 2, 4, 6, 8, 10, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 30, 31, 33, 35, 37, 39, 41, 42, 44, 46, 48, 50, 52, 53, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 74, 75, 77, 79, 81, 83, 85, 86, 88, 90, 92, 94, 95, 97, 99, 101, 103, 105, 106, 108, 110, 112, 114, 116, 117, 119 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For the complex Lucas function and its zeros see the Koshy reference. This function is L: C -> C, z -> L(z), with

  L(z) = exp(log(phi)*z) + exp(I*Pi*z)*exp(-log(phi)*z),

  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.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

a(n) = floor((k+1/2)*alpha), with alpha/2 = x_0(0) defined in the comment section.

CROSSREFS

Cf. A214672 (floor of imaginary parts), A214673 (moduli),  A214315 (Fibonacci case).

Sequence in context: A067030 A072427 A050420 * A291171 A185449 A096922

Adjacent sequences:  A214668 A214669 A214670 * A214672 A214673 A214674

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Jul 25 2012

STATUS

approved

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Last modified June 18 14:52 EDT 2019. Contains 324213 sequences. (Running on oeis4.)