%I #18 Mar 11 2023 08:43:28
%S 3,1,1,3,9,11,17,23,29,35,41,47,53,59,69,75,81,91,97,103,113,123,
%T 129,135,145,155,161,171,181,187,197,207,217,223,237,247,253,263,273,
%U 283,293,307,313,323,329,343,353,359,373,383,393,403,417,423,437,451,457,467,481,491,501,511,525,535,545,559,569
%N Numbers of the lines Im zeta(sigma + i t)=0 that escape to the right.
%C This sequence contains important information about the graphics of the lines Re zeta(s)=0 and Im zeta(s)=0, where zeta(s) is the Riemann zeta function. Only the first two terms are negative. It is an increasing sequence. The values of this sequence alternatively are congruent to 1 or 3 (mod 4).
%D J. van de Lune, Some observations concerning the zerocurves of the Real and imaginary parts of Riemann's zeta function, Afdeling Zuivere Wiskunde [Department of Pure Mathematics], 201. Mathematisch Centrum, Amsterdam, 1983. i+25 pp
%D A. Speiser, Geometrisches zur Riemannschen Zetafunktion, Math. Ann., Vol. 110 (1935), pp. 514521
%D Albert A. Utzinger, Die reellen Züge der Riemann'schen Zetafunktionen, Zürich Univ. Phil. Dissertation, Leemann, 1934.
%H J. AriasdeReyna, <a href="https://arxiv.org/abs/math/0309433">XRay of Riemann zetafunction</a>, arXiv:math/0309433 [math.NT] (2003), 42 p.
%e a(4)=3 because the line number 3, that pass for the second nontrivial zero of the zeta function, is the fourth parallel line that goes to infinity to the right of the splane.
%Y Cf. A088750.
%K hard,sign
%O 1,1
%A _Juan AriasdeReyna_, Oct 14 2003
