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 A214657 Floor of the moduli of the zeros of the complex Fibonacci function. 1
 0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 108, 110, 112, 114, 116, 118, 120, 122, 124 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For the complex Fibonacci function F(z) and its zeros see the T. Koshy reference given in A214315. There the formula for the real and imaginary parts of the zeros is also given.   F: C -> C, z -> F(z) with F(z) := (exp(log(phi)*z) - exp(I*Pi*z)*exp(-log(phi)*z))/(2*phi-1), with phi := (1+sqrt(5))/2 and the imaginary unit I. The zeros in the complex plane lie on a straight line with angle Phi = -arctan(2*log(phi)/Pi). They are equally spaced with distance tau defined below. Phi is approximately -0.2972713044, corresponding to about -17.03 degrees. The moduli are |z_0(k)| = tau*k, with tau:= 2*Pi/sqrt(Pi^2 + (2*log(phi))^2), which is approximately 1.912278633. a(n) = floor(tau*n) is a Beatty sequence with the complementary sequence b(n) := floor(sigma*n), with sigma:= tau/(tau-1), approximately 2.096156332. LINKS FORMULA a(n) = floor(tau*n), n>=0, with tau = |z_0(1)|given in the comment section. EXAMPLE The complementary Beatty sequences a(n) and  b(n) start: n:     0 1 2 3 4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 ... a(n):  0 1 3 5 7  9 11 13 15 17 19 21 22 24 26 28 30 32 34 ... b(n): (0)2 4 6 8 10 12 14 16 18 20 23 25 27 29 31 33 35 37 ... CROSSREFS Cf. A214315, A214656. Sequence in context: A251238 A059547 A064719 * A137803 A059533 A189397 Adjacent sequences:  A214654 A214655 A214656 * A214658 A214659 A214660 KEYWORD nonn AUTHOR Wolfdieter Lang, Jul 25 2012 STATUS approved

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Last modified September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)