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

0,1

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).

Links

Table of n, a(n) for n=0..63.

Mathematica

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

Crossrefs

Cf. A002410, A013629, A092783, A106635.

Sequence in context: A065977 A294999 A153051 * A186427 A050109 A294357

Adjacent sequences: A106633 A106634 A106635 * A106637 A106638 A106639

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