A093999 An asymptotic prime formula derived from a vibrational Hilbert space model for the zeta zeros.

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

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