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 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