A221974 -id:A221974 - cp's OEIS frontend

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

Omar E. Pol, Jun 26 2009

nonn

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

			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.

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

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

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

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

Extended by R. J. Mathar, Jul 04 2009

cp's OEIS Frontend

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

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