

A088749


Numbers of the lines Im zeta(sigma + i t)=0 that escape to the right.


2



3, 1, 1, 3, 9, 11, 17, 23, 29, 35, 41, 47, 53, 59, 69, 75, 81, 91, 97, 103, 113, 123, 129, 135, 145, 155, 161, 171, 181, 187, 197, 207, 217, 223, 237, 247, 253, 263, 273, 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
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OFFSET

1,1


COMMENTS

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 zetafunction of Riemann. Only the two first terms are negative. It is an increasing sequence. The values of this sequence alternatively are congruent with 1 or 3 mod 4.


REFERENCES

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
A. Speiser, Geometrisches zur Riemannschen Zetafunktion, Math. Ann., Vol. 110 (1934), pp. 514521
A. Utzinger, Über die reellen Zuege der Riemannschen Zetafunktion, Dissertation, Zurich, (1934)


LINKS

Table of n, a(n) for n=1..67.
J. AriasdeReyna, XRay of Riemann zetafunction


EXAMPLE

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.


CROSSREFS

Cf. A088750.
Sequence in context: A011085 A199922 A112508 * A024737 A024958 A014516
Adjacent sequences: A088746 A088747 A088748 * A088750 A088751 A088752


KEYWORD

hard,sign


AUTHOR

Juan AriasdeReyna, Oct 14 2003


STATUS

approved



