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).

%I A106636 #11 Jun 07 2025 08:19:50
%S A106636 9,13,16,19,21,24,26,28,31,32,34,36,38,39,41,43,44,46,48,49,51,53,54,
%T A106636 56,57,59,60,61,63,65,66,67,68,71,71,73,74,76,77,78,79,81,82,83,85,86,
%U A106636 88,89,90,91,93,94,96,96,97,99,100,101,103,104,105,106,108,108
%N 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).
%C A106636 Previous name: Pair rational approximations of Zeta zeros as an integer sequence.
%C A106636 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).
%t A106636 a[n_] := Round[Im[ZetaZero[n]]*2/Pi]; Array[a, 70] (* _Amiram Eldar_, Jun 07 2025 *)
%Y A106636 Cf. A002410, A013629, A092783, A106635.
%K A106636 nonn
%O A106636 0,1
%A A106636 _Roger L. Bagula_, May 11 2005
%E A106636 Name edited and data corrected and extended by _Amiram Eldar_, Jun 07 2025