This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A255739 #33 Aug 10 2023 02:22:51
%S A255739 1,2,3,9,51,473,3233,7657,7722,20002,124170,126137,977155
%N A255739 Indices of nontrivial zeros of Riemann zeta function whose imaginary part sets a record for the absolute minimal difference from an integer.
%C A255739 We consider here the imaginary part of 1/2 + iy = z, for which Zeta(z) is a zero.
%C A255739 No more terms below 600000. - _Robert G. Wilson v_, Sep 30 2015
%C A255739 Is there an Im(rho_k) that is also a 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
%C A255739 No more terms below 2001052. - _Amiram Eldar_, Aug 10 2023
%H A255739 Andrew M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/zeta_tables">Tables of zeros of the Riemann zeta function</a>.
%H A255739 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 A255739 <a href="/index/Z#zeta_function">Index entries for zeta function</a>.
%F A255739 A255742(n) = A002410(a(n)).
%e A255739 -------------------------------------------------------------------
%e A255739 Absolute New
%e A255739 k Im(rho_k) A002410(k) difference record n a(n)
%e A255739 -------------------------------------------------------------------
%e A255739 1 14.134725142 > 14 0.134725142 Yes 1 1
%e A255739 2 21.022039639 > 21 0.022039639 Yes 2 2
%e A255739 3 25.010857580 > 25 0.010857580 Yes 3 3
%e A255739 4 30.424876126 > 30 0.424876126 Not
%e A255739 5 32.935061588 < 33 0.064938412 Not
%e A255739 6 37.586178159 < 38 0.413821841 Not
%e A255739 7 40.918719012 < 41 0.081280988 Not
%e A255739 8 43.327073281 > 43 0.327073281 Not
%e A255739 9 48.005150881 > 48 0.005150881 Yes 4 9
%e A255739 10 49.773832478 < 50 0.226167522 Not
%e A255739 ...
%e A255739 where rho_k is the k-th nontrivial zero of Riemann zeta function.
%e A255739 We computed more digits of Im(rho_k), but in the above table only 9 digits beyond the decimal point appear.
%t A255739 mn = Infinity; k = 1; lst = {}; While[k < 2501, a = N[ Abs[ Im[ ZetaZero[
%t A255739 k]] - Round[ Im[ ZetaZero[ k]] ]], 32]; If[a < mn, AppendTo[lst, k];
%t A255739 Print[k]; mn = a]; k++]; lst (* _Robert G. Wilson v_, Sep 29 2015 *)
%Y A255739 Cf. A002410, A255742.
%K A255739 nonn,hard,more
%O A255739 1,2
%A A255739 _Omar E. Pol_, Mar 17 2015
%E A255739 a(6)-a(10) from _Robert G. Wilson v_, Sep 29 2015
%E A255739 a(11)-a(12) from _Robert G. Wilson v_, Sep 30 2015
%E A255739 a(13) using Odlyzko's tables added by _Amiram Eldar_, Aug 10 2023