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A093999 An asymptotic prime formula derived from a vibrational Hilbert space model for the zeta zeros. 0
2, 3, 5, 13, 43, 53, 61, 79, 83, 127, 131, 139, 157, 223, 251, 313, 337, 347, 367, 397, 463, 479, 499, 541, 547, 557, 643, 659, 769, 797, 853, 859, 887, 991, 1031, 1049, 1201, 1213, 1231, 1237, 1249, 1279, 1291, 1297, 1303, 1321, 1327, 1381, 1399, 1583, 1601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This formula was derived in Mathematica in a Laplacian Hilbert space model using zeta zero like functions to give a spectrum. This specific approach to the Riemann conjecture was suggested by Hilbert himself. Equations for the model are: Phi[n_,s_]=Exp[ -s^2/(4*n)]/n^(s/2)+I*(Exp[ -s^2/(4*n)]/n^(s/2)) H*Phi = \(d\_\(s, s\)\[Phi] + V\[Phi] = E0[n] \[Phi]\)\ \)\) E0[n_]=hbar*(1/2+I*b[n]) Solve[V==0,b[n]] Solve[Im[b[n]]==0,s]

LINKS

Table of n, a(n) for n=1..51.

FORMULA

If Floor[Abs[n*log(n)-Sqrt(n*(n+2*Pi)/Pi)]] is prime then Floor[Abs[n*log(n)-Sqrt(n*(n+2*Pi)/Pi)]]

MATHEMATICA

s=-n*log(n)+Sqrt[n*(n+2*Pi)/Pi)] a=Delete[Union[Table[If[PrimeQ[Floor[ -s]]==True, Abs[Floor[ -s]], 0], {n, 1, 500}]], 1]

CROSSREFS

Sequence in context: A238814 A000756 A192241 * A042445 A332060 A048634

Adjacent sequences:  A093996 A093997 A093998 * A094000 A094001 A094002

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, May 24 2004

STATUS

approved

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Last modified September 20 23:04 EDT 2021. Contains 347596 sequences. (Running on oeis4.)