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%I #19 Sep 08 2022 08:45:13
%S 0,2,5,7,10,13,16,19,22,26,29,32,36,39,42,46,49,53,57,60,64,67,71,75,
%T 78,82,86,90,93,97,101,105,109,113,116,120,124,128,132,136,140,144,
%U 148,152,156,160,164,168,172,176,180,184,188,192,196,201,205,209,213,217,221
%N Asymptotic form for prime.
%C 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).
%H G. C. Greubel, <a href="/A094065/b094065.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = floor(Re( n*(2 + log(n)/2 - sqrt((2*Pi + i*n)/(Pi*n))) )).
%t Table[Floor[Re[n*(2 +Log[n]/2 -Sqrt[I/Pi+2/n])]], {n, 1, 70}]
%o (PARI) {a(n) = floor( real(n*(2 + log(n)/2 - sqrt((2*Pi + I*n)/(Pi*n))) ))}; \\ _G. C. Greubel_, Mar 18 2019
%o (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
%o (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
%K nonn
%O 1,2
%A _Roger L. Bagula_, May 31 2004
%E Edited by _G. C. Greubel_, Mar 18 2019
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