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%I #42 Jul 26 2021 22:49:18
%S 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,
%T 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,
%U 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
%N Gaps between the nontrivial zeros of Riemann zeta function, rounded to nearest integers, with a(1)=14.
%C We consider here the imaginary part of 1/2 + iy = z, for which Zeta(z) is a zero.
%C Note that these are not the first differences of A002410 because rounding is done here AFTER computing the differences. - _R. J. Mathar_, Jul 04 2009
%C What is the largest n such that a(n) > 0? - _Charles R Greathouse IV_, Jan 08 2012
%C This doesn't seem feasible to compute, probably more than 10^200. - _Charles R Greathouse IV_, Jan 29 2013
%H T. D. Noe, <a href="/A161914/b161914.txt">Table of n, a(n) for n = 1..1000</a>
%H A. M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/zeta_tables">Tables of zeros of the Riemann zeta function</a>
%H A. M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/arch/zeta.zero.spacing.pdf">On the distribution of spacings between zeros of the zeta function</a>
%H <a href="/index/Z#zeta_function">Index entries for zeta function</a>
%e 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.
%t Join[{14}, Table[Round[Im[ZetaZero[n] - ZetaZero[n - 1]]], {n, 2, 100}]] (* _Alonso del Arte_, Jan 29 2013 *)
%o (PARI) diff(v)=vector(#v-1,i,v[i+1]-v[i])
%o concat(14, round(diff(lfunzeros(lzeta, 100)))) \\ _Charles R Greathouse IV_, Jul 26 2021
%Y Cf. A002410, A162774, A162780-A162782, A208436, A210447, A221974.
%K nonn
%O 1,1
%A _Omar E. Pol_, Jun 26 2009
%E Extended by _R. J. Mathar_, Jul 04 2009
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