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A161914 Gaps between the nontrivial zeros of Riemann zeta function, rounded to nearest integers, with a(1)=14. 9


%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 *)

%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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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)