A161914 Gaps between the nontrivial zeros of Riemann zeta function, rounded to nearest integers, with a(1)=14.

14, 7, 4, 5, 3, 5, 3, 2, 5, 2, 3, 3, 3, 1, 4, 2, 2, 3, 4, 1, 2, 4, 2, 3, 1, 4, 2, 1, 3, 2, 2, 2, 2, 4, 1, 2, 2, 3, 3, 2, 1, 3, 2, 2, 2, 1, 3, 2, 1, 2, 3, 1, 3, 1, 2, 3, 1, 1, 2, 2, 3, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 1, 3, 1, 2, 1, 3, 2, 2, 2, 1, 2, 3, 2, 1, 3, 1, 2, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1

Offset

1,1

Comments

We consider here the imaginary part of 1/2 + iy = z, for which Zeta(z) is a zero.

Note that these are not the first differences of A002410 because rounding is done here AFTER computing the differences. - R. J. Mathar, Jul 04 2009

What is the largest n such that a(n) > 0? - Charles R Greathouse IV, Jan 08 2012

This doesn't seem feasible to compute, probably more than 10^200. - Charles R Greathouse IV, Jan 29 2013

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

A. M. Odlyzko, Tables of zeros of the Riemann zeta function

A. M. Odlyzko, On the distribution of spacings between zeros of the zeta function

Index entries for zeta function

Example

The absolute difference between the first nontrivial zero (14.134725...) and the second nontrivial zero (21.022039...) is equal to 6.887314... which rounded to nearest integer is equal to 7, then a(2) = 7.

Mathematica

Join[{14}, Table[Round[Im[ZetaZero[n] - ZetaZero[n - 1]]], {n, 2, 100}]] (* Alonso del Arte, Jan 29 2013 *)

Prog

(PARI) diff(v)=vector(#v-1, i, v[i+1]-v[i])
concat(14, round(diff(lfunzeros(lzeta, 100)))) \\ Charles R Greathouse IV, Jul 26 2021

Crossrefs

Cf. A002410, A162774, A162780-A162782, A208436, A210447, A221974.

Sequence in context: A048932 A329022 A033334 * A162774 A254873 A004479

Adjacent sequences: A161911 A161912 A161913 * A161915 A161916 A161917

Keyword

nonn

Author

Omar E. Pol, Jun 26 2009

Extensions

Extended by R. J. Mathar, Jul 04 2009

Status

approved