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A094065 Asymptotic form for prime. 5
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 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A057347 A067008 A189757 * A073593 A241510 A088947

Adjacent sequences:  A094062 A094063 A094064 * A094066 A094067 A094068

KEYWORD

nonn

AUTHOR

Roger L. Bagula, May 31 2004

EXTENSIONS

Edited by G. C. Greubel, Mar 18 2019

STATUS

approved

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Last modified August 17 11:06 EDT 2019. Contains 326057 sequences. (Running on oeis4.)