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

14, 21, 25, 48, 146, 776, 3764, 7847, 7904, 18048, 90930, 92219, 587741

Offset

1,1

Comments

We consider here the imaginary part of 1/2 + i*y = z, for which Zeta(z) is a zero.

No more terms below the 600000th nontrivial zero of the Riemann zeta function. - Robert G. Wilson v, Sep 30 2015

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

Links

Table of n, a(n) for n=1..13.

Andrew M. Odlyzko, Tables of zeros of the Riemann zeta function.

Andrew M. Odlyzko, On the distribution of spacings between zeros of the zeta function.

Index entries for zeta function.

Formula

a(n) = A002410(A255739(n)).

Example

-------------------------------------------------------------------
                                     Absolute      New
k      Im(rho_k)       A002410(k)   difference   record   n   a(n)
-------------------------------------------------------------------
1    14.134725142    >    14        0.134725142    Yes    1    14
2    21.022039639    >    21        0.022039639    Yes    2    21
3    25.010857580    >    25        0.010857580    Yes    3    25
4    30.424876126    >    30        0.424876126    Not
5    32.935061588    <    33        0.064938412    Not
6    37.586178159    <    38        0.413821841    Not
7    40.918719012    <    41        0.081280988    Not
8    43.327073281    >    43        0.327073281    Not
9    48.005150881    >    48        0.005150881    Yes    4    48
10   49.773832478    <    50        0.226167522    Not
...
where rho_k is the k-th nontrivial zero of Riemann zeta function.
We computed more digits of Im(rho_k), but in the above table only 9 digits after the decimal point appear.

Crossrefs

Cf. A002410, A013629, A092783, A255739.

Sequence in context: A002410 A108606 A129497 * A093994 A114985 A344703

Adjacent sequences: A255739 A255740 A255741 * A255743 A255744 A255745

Keyword

nonn,hard,more

Author

Omar E. Pol, Mar 16 2015

Extensions

a(6)-a(10) from Robert G. Wilson v, Sep 29 2015

a(11)-a(12) from Robert G. Wilson v, Sep 30 2015

a(13) using Odlyzko's tables added by Amiram Eldar, Aug 10 2023

Status

approved