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URL: https://oeis.org/A106635

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A106635
a(n) = round(2*Im(z(n))/Pi - 4), where z(n) is the n-th zero of the Riemann zeta function on the critical line (with a positive imaginary part).
1
5, 9, 12, 15, 17, 20, 22, 24, 27, 28, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 53, 55, 56, 57, 59, 61, 62, 63, 64, 67, 67, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87, 89, 90, 92, 92, 93, 95, 96, 97, 99, 100, 101, 102, 104, 104, 106
OFFSET
0,1
COMMENTS
Previous name: Rational approximations of Zeta zeros as an integer sequence.
The average error in the approximation is low (-0.0559729) for the first 30 zeta zeros. The idea is that the imaginary part of the zeta zero is a bad rational approximation of the type: 4/(a(n)+4) to give b(n) = 2*Pi*(a(n)+4)/4.
MATHEMATICA
a[n_] := Round[Im[ZetaZero[n]]*2/Pi - 4]; Array[a, 70] (* Amiram Eldar, Jun 07 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 11 2005
EXTENSIONS
Name edited and data corrected and extended by Amiram Eldar, Jun 07 2025
STATUS
approved