A234323 Number of nontrivial zeros of the Riemann zeta function in the interval 1/2 + i[n,n+1).

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

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, Table of n, a(n) for n = 1..1000000

LMFDB David Platt's 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

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: A297043 A355451 A133010 * A162782 A011727 A297042

Adjacent sequences: A234320 A234321 A234322 * A234324 A234325 A234326

Keyword

nonn

Author

Simon Plouffe, Dec 23 2013

Status

approved