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URL: https://oeis.org/A106636

⇱ A106636 - OEIS


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A106636
a(n) = round(2*Im(z(n))/Pi), where z(n) is the n-th zero of the Riemann zeta function on the critical line (with a positive imaginary part).
1
9, 13, 16, 19, 21, 24, 26, 28, 31, 32, 34, 36, 38, 39, 41, 43, 44, 46, 48, 49, 51, 53, 54, 56, 57, 59, 60, 61, 63, 65, 66, 67, 68, 71, 71, 73, 74, 76, 77, 78, 79, 81, 82, 83, 85, 86, 88, 89, 90, 91, 93, 94, 96, 96, 97, 99, 100, 101, 103, 104, 105, 106, 108, 108
OFFSET
0,1
COMMENTS
Previous name: Pair 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. Pair rational is (this sequence) : a(n)/(a(n)+4).
MATHEMATICA
a[n_] := Round[Im[ZetaZero[n]]*2/Pi]; 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