A106635 -id:A106635 - cp's OEIS frontend

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).

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

Roger L. Bagula, May 11 2005

nonn

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).

Cf. A002410, A013629, A092783, A106635.

a[n_] := Round[Im[ZetaZero[n]]*2/Pi]; Array[a, 70] (* Amiram Eldar, Jun 07 2025 *)

Name edited and data corrected and extended by Amiram Eldar, Jun 07 2025

cp's OEIS Frontend

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).

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