OFFSET
1,2
COMMENTS
No more records up to n = 103800788359.
d(17003807756) = 4.3018209763411.
Successive records occur when gaps between two successive zeros are large.
Recent record of normalized delta computed by Hiary at 2011 occurs for n=436677148707320393224019748290912 where d(n) = 5.77979.
Conjectural next term: 77528045597.
Indices of zeros for successive minimal records of the normalized delta see A328656.
LINKS
Artur Jasinski, Table of n, a(n) for n = 1..41
Ghaith Ayesh Hiary, Fast methods to compute the Riemann zeta function, Ann. of Math. (2) 174 (2011), no. 2, 891-946. MR 2831110 (2012g:11154).
David Platt, Results computation of the largest relative gaps between successive zeta zeros, 2020.
EXAMPLE
n | a(n) | d(n)
---+---------+---------
1 | 1 | 0.88871
2 | 3 | 1.19034
3 | 5 | 1.22634
4 | 8 | 1.43763
5 | 14 | 1.54672
6 | 25 | 1.55244
7 | 33 | 1.74300
8 | 64 | 1.83656
9 | 126 | 1.95400
10 | 213 | 1.95626
11 | 256 | 1.99205
12 | 379 | 2.20138
13 | 1704 | 2.20198
14 | 1935 | 2.45843
15 | 2292 | 2.46772
16 | 8571 | 2.48347
17 | 10942 | 2.50594
18 | 12347 | 2.50648
19 | 13298 | 2.52517
20 | 15323 | 2.67728
21 | 36719 | 2.76188
22 | 46589 | 2.80523
23 | 103715 | 2.83121
24 | 185013 | 3.11058
25 | 880694 | 3.21426
26 | 1493008 | 3.30347
MATHEMATICA
prec = 30; max = 0; aa = {}; Do[kk = N[Im[(ZetaZero[n + 1] - ZetaZero[n])], prec] (Log[N[Im[ZetaZero[n]], prec]/(2 Pi)]/(2 Pi));
If[kk > max, max = kk; AppendTo[aa, n]], {n, 1, 2000000}]; aa
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 20 2019
EXTENSIONS
a(27)-a(41) computed by David Platt, Jan 03 2020
STATUS
approved