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%I #50 Aug 10 2023 02:23:11
%S 14,21,25,48,146,776,3764,7847,7904,18048,90930,92219,587741
%N Integers setting a record for the absolute minimal difference from the imaginary part of a nontrivial zero of the Riemann zeta function.
%C We consider here the imaginary part of 1/2 + i*y = z, for which Zeta(z) is a zero.
%C No more terms below the 600000th nontrivial zero of the Riemann zeta function. - _Robert G. Wilson v_, Sep 30 2015
%C Is there an Im(rho_k) that is also an positive integer? Is there a minimum gap between an Im(rho_k) and a positive integer? At present it is not known whether this sequence is finite or infinite. - _Omar E. Pol_, Oct 13 2015
%H Andrew M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/zeta_tables">Tables of zeros of the Riemann zeta function</a>.
%H Andrew 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>.
%F a(n) = A002410(A255739(n)).
%e -------------------------------------------------------------------
%e Absolute New
%e k Im(rho_k) A002410(k) difference record n a(n)
%e -------------------------------------------------------------------
%e 1 14.134725142 > 14 0.134725142 Yes 1 14
%e 2 21.022039639 > 21 0.022039639 Yes 2 21
%e 3 25.010857580 > 25 0.010857580 Yes 3 25
%e 4 30.424876126 > 30 0.424876126 Not
%e 5 32.935061588 < 33 0.064938412 Not
%e 6 37.586178159 < 38 0.413821841 Not
%e 7 40.918719012 < 41 0.081280988 Not
%e 8 43.327073281 > 43 0.327073281 Not
%e 9 48.005150881 > 48 0.005150881 Yes 4 48
%e 10 49.773832478 < 50 0.226167522 Not
%e ...
%e where rho_k is the k-th nontrivial zero of Riemann zeta function.
%e We computed more digits of Im(rho_k), but in the above table only 9 digits after the decimal point appear.
%Y Cf. A002410, A013629, A092783, A255739.
%K nonn,hard,more
%O 1,1
%A _Omar E. Pol_, Mar 16 2015
%E a(6)-a(10) from _Robert G. Wilson v_, Sep 29 2015
%E a(11)-a(12) from _Robert G. Wilson v_, Sep 30 2015
%E a(13) using Odlyzko's tables added by _Amiram Eldar_, Aug 10 2023
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