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
Keywords
Examples
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.
Links
- 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
Programs
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Mathematica
Join[{14}, Table[Round[Im[ZetaZero[n] - ZetaZero[n - 1]]], {n, 2, 100}]] (* Alonso del Arte, Jan 29 2013 *) -
PARI
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
Extensions
Extended by R. J. Mathar, Jul 04 2009
Comments