cp's OEIS Frontend

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

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