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A234323 Number of nontrivial zeros of the Riemann Zeta function in the interval 1/2+i[n,n+1). 8

%I

%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">a(n)from 1 to 1000000</a>

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

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

%H Wikipedia, <a href="http://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

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Last modified September 18 16:22 EDT 2020. Contains 337170 sequences. (Running on oeis4.)