OFFSET
1,2
COMMENTS
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).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
FORMULA
a(n) = floor(Re( n*(2 + log(n)/2 - sqrt((2*Pi + i*n)/(Pi*n))) )).
MATHEMATICA
Table[Floor[Re[n*(2 +Log[n]/2 -Sqrt[I/Pi+2/n])]], {n, 1, 70}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 31 2004
EXTENSIONS
Edited by G. C. Greubel, Mar 18 2019
STATUS
approved