A234323 - OEIS

%I #32 Jan 03 2023 14:49:55

%S 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,

%T 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,

%U 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

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

%C It gives the number of zeros for each integer.

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

%H Simon Plouffe, <a href="/A234323/b234323.txt">Table of n, a(n) for n = 1..1000000</a>

%H LMFDB David Platt's <a href="https://www.lmfdb.org/zeros/zeta/">Table of the first 103 billion zeros</a>.

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/OEIS/b234323.txt.gz">Table for a(n) up to 2 billion</a> - note the file is 25 gigabytes uncompressed

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_zeta_function_zeros">Riemann zeta function zeros</a>

%e 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.

%o (PARI) #lfunzeros(lzeta,[n,n+1]) \\ _Charles R Greathouse IV_, Mar 10 2016

%Y Cf. A013629, A002410.

%K nonn

%O 1

%A _Simon Plouffe_, Dec 23 2013