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A234323 Number of nontrivial zeros of the Riemann Zeta function in the interval 1/2+i[n,n+1). 8
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

It gives the number of zeros for each integer.

The average value is a(n) ~ log(n)/(2*Pi).

LINKS

Simon Plouffe, a(n)from 1 to 1000000

LMFDB David Platt's table of the zeros up to 103 billion Table of the first 103 billion zeros.

Simon Plouffe Table for a(n) up to 2 billion: note the file is 25 gigabytes uncompressed  

Wikipedia, Riemann Zeta function zeros Riemann zeta function zeros

EXAMPLE

First zero is at 14.134, therefore a(14) = 1, the second is at 21.022 therefore a(21) = 1, there are 2 zeros between 111 and 112, a(111) = 2.

PROG

(PARI) #lfunzeros(lzeta, [n, n+1]) \\ Charles R Greathouse IV, Mar 10 2016

CROSSREFS

Cf. A013629, A002410.

Sequence in context: A011728 A297043 A133010 * A162782 A011727 A297042

Adjacent sequences:  A234320 A234321 A234322 * A234324 A234325 A234326

KEYWORD

nonn

AUTHOR

Simon Plouffe, Dec 23 2013

STATUS

approved

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Last modified June 19 23:01 EDT 2019. Contains 324222 sequences. (Running on oeis4.)