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 A100060 a(n)=1 if the n-th second difference of the imaginary parts of the nontrivial zeros of the Riemann zeta function is positive, otherwise a(n)=0. 9
 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differences between zeta function gaps: increases are 1 and decreases are 0. The ratios of the numbers of 0's to the number of 1's in the first 10^n differences are 0/1, 5/5, 50/50, 493/507, 4998/5002, 49949/50049, ... LINKS J. B. Conrey, A. Ghosh, D. Goldston, S. M. Gonek, D. R. Heath-Brown, On the distribution of gaps between zeros of the Zeta-Function, Quart. J. Math. oxford 36 (1985) 43-51. A. M. Odlyzko, On the distribution of spacings between zeros of the Zeta Function, Math. Comp. 48 (177) (1987) 273-308. A. M. Odlyzko, Tables EXAMPLE The first few positive t values of the zeros 1/2+i*t are (14.13..., 21.02..., 25.01..., 30.42..., 32.93..., 37.58..., 40.91..., 43.32...). First differences are (6.88..., 3.98..., 5.41..., 2.51..., 4.65..., 3.33..., 2.40...). Second differences are (-2.89..., 1.42..., -2.90..., 2.14..., -1.31..., -0.92...) which yields (0, 1, 0, 1, 0, 0, ...). MATHEMATICA zz = { (* the list of values in the link *) }; yy = Drop[zz, 1] - Drop[zz, -1]; Join[{1}, Table[ If[ yy[[n + 1]] > yy[[n]], 1, 0], {n, 104}]] (* Or *) zz = { (* the list of values in the link *) }; yy = Drop[zz, 1] - Drop[zz, -1]; xx = Drop[yy, 1] - Drop[yy, -1]; Join[{1}, Table[ If[ xx[[n]] > 0, 1, 0], {n, 104}]] (* Robert G. Wilson v, Jan 14 2005 *) Flatten[{1, (Sign[Differences[Differences[Im[ZetaZero[Range[106]]]]]] + 1)/2}] (* Mats Granvik, Jul 23 2015 *) CROSSREFS Cf. A102522, A102523. Sequence in context: A040053 A267513 A004569 * A328101 A147850 A286046 Adjacent sequences:  A100057 A100058 A100059 * A100061 A100062 A100063 KEYWORD nonn AUTHOR Gary W. Adamson, Oct 31 2004 EXTENSIONS Corrected and extended by Robert G. Wilson v, Jan 13 2005 Edited by M. F. Hasler, Jul 27 2015 STATUS approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)