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A255742 Integers setting a record for the absolute minimal difference from the imaginary part of a nontrivial zero of the Riemann zeta function.

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%I A255742 #50 Aug 10 2023 02:23:11
%S A255742 14,21,25,48,146,776,3764,7847,7904,18048,90930,92219,587741
%N A255742 Integers setting a record for the absolute minimal difference from the imaginary part of a nontrivial zero of the Riemann zeta function.
%C A255742 We consider here the imaginary part of 1/2 + i*y = z, for which Zeta(z) is a zero.
%C A255742 No more terms below the 600000th nontrivial zero of the Riemann zeta function. - _Robert G. Wilson v_, Sep 30 2015
%C A255742 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 A255742 Andrew M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/zeta_tables">Tables of zeros of the Riemann zeta function</a>.
%H A255742 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 A255742 <a href="/index/Z#zeta_function">Index entries for zeta function</a>.
%F A255742 a(n) = A002410(A255739(n)).
%e A255742 -------------------------------------------------------------------
%e A255742                                      Absolute      New
%e A255742 k      Im(rho_k)       A002410(k)   difference   record   n   a(n)
%e A255742 -------------------------------------------------------------------
%e A255742 1    14.134725142    >    14        0.134725142    Yes    1    14
%e A255742 2    21.022039639    >    21        0.022039639    Yes    2    21
%e A255742 3    25.010857580    >    25        0.010857580    Yes    3    25
%e A255742 4    30.424876126    >    30        0.424876126    Not
%e A255742 5    32.935061588    <    33        0.064938412    Not
%e A255742 6    37.586178159    <    38        0.413821841    Not
%e A255742 7    40.918719012    <    41        0.081280988    Not
%e A255742 8    43.327073281    >    43        0.327073281    Not
%e A255742 9    48.005150881    >    48        0.005150881    Yes    4    48
%e A255742 10   49.773832478    <    50        0.226167522    Not
%e A255742 ...
%e A255742 where rho_k is the k-th nontrivial zero of Riemann zeta function.
%e A255742 We computed more digits of Im(rho_k), but in the above table only 9 digits after the decimal point appear.
%Y A255742 Cf. A002410, A013629, A092783, A255739.
%K A255742 nonn,hard,more
%O A255742 1,1
%A A255742 _Omar E. Pol_, Mar 16 2015
%E A255742 a(6)-a(10) from _Robert G. Wilson v_, Sep 29 2015
%E A255742 a(11)-a(12) from _Robert G. Wilson v_, Sep 30 2015
%E A255742 a(13) using Odlyzko's tables added by _Amiram Eldar_, Aug 10 2023