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A094065
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Asymptotic form for prime.
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1
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0, 2, 5, 7, 10, 13, 16, 19, 22, 26, 29, 32, 36, 39, 42, 46, 49, 53, 57, 60, 64, 67, 71, 75, 78, 82, 86, 90, 93, 97, 101, 105, 109, 113, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 201, 205, 209, 213, 217, 221
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OFFSET
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1,2
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COMMENTS
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This sequence results from a solution to a particular Laplacian of a linear perturbation associated with a Gaussian Dirichlet L-function used in a zeta zeros quantum Hamiltonian. The associated wave equation is: Psi(n, s) = (1+i)*exp(k_2 + k_1*s - s^2/(4*n)), where k_1 = (-4 + log(n))/4 and k_2 = n*log(n).
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LINKS
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FORMULA
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a(n) = floor(Re( n*(2 + log(n)/2 - sqrt((2*Pi + i*n)/(Pi*n))) )).
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MATHEMATICA
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Table[Floor[Re[n*(2 +Log[n]/2 -Sqrt[I/Pi+2/n])]], {n, 1, 70}]
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PROG
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(PARI) {a(n) = floor( real(n*(2 + log(n)/2 - sqrt((2*Pi + I*n)/(Pi*n))) ))}; \\ G. C. Greubel, Mar 18 2019
(Magma) C<i> := ComplexField(); [Floor(Re( n*(2 + Log(n)/2 - Sqrt((2*Pi(C) + i*n)/(Pi(C)*n))) )): n in [1..70]]; // G. C. Greubel, Mar 18 2019
(Sage) [floor( (n*(2 + log(n)/2 - sqrt((2*pi + i*n)/(pi*n)))).real()) for n in (1..70)] # G. C. Greubel, Mar 18 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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