A214673 Floor of the moduli of the zeros of the complex Lucas function.
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 109, 111, 113, 115, 117, 119, 121, 123, 125
Offset: 0
Keywords
References
- Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", John Wiley and Sons, 2001.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
Programs
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Magma
R:= RealField(100); [Floor((2*n+1)*Pi(R)/Sqrt(Pi(R)^2 + (2*Log((1+Sqrt(5))/2))^2)) : n in [0..100]]; // G. C. Greubel, Mar 09 2024
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Mathematica
Table[Floor[(2*n+1)*Pi/Sqrt[Pi^2+(2*Log[GoldenRatio])^2]], {n,0,100}] (* G. C. Greubel, Mar 09 2024 *)
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SageMath
[floor((2*n+1)*pi/sqrt(pi^2 +4*(log(golden_ratio))^2)) for n in range(101)] # G. C. Greubel, Mar 09 2024
Formula
a(n) = floor((2*n+1)*tau/2), n>=0, with tau/2 = rho(0) = 2*Pi / sqrt(Pi^2 + (2*log(phi))^2).
Comments