cp's OEIS Frontend

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).

%I A106635 #10 Jun 07 2025 08:19:59
%S A106635 5,9,12,15,17,20,22,24,27,28,30,32,34,35,37,39,40,42,44,45,47,49,50,
%T A106635 52,53,55,56,57,59,61,62,63,64,67,67,69,70,72,73,74,75,77,78,79,81,82,
%U A106635 84,85,86,87,89,90,92,92,93,95,96,97,99,100,101,102,104,104,106
%N 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).
%C A106635 Previous name: Rational approximations of Zeta zeros as an integer sequence.
%C A106635 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.
%t A106635 a[n_] := Round[Im[ZetaZero[n]]*2/Pi - 4]; Array[a, 70] (* _Amiram Eldar_, Jun 07 2025 *)
%Y A106635 Cf. A002410, A013629, A092783, A106636.
%K A106635 nonn
%O A106635 0,1
%A A106635 _Roger L. Bagula_, May 11 2005
%E A106635 Name edited and data corrected and extended by _Amiram Eldar_, Jun 07 2025