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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. 10
14, 21, 25, 48, 146, 776, 3764, 7847, 7904, 18048, 90930, 92219, 587741 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A002410 A108606 A129497 * A093994 A114985 A344703
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

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)