A346289 Decimal expansion of the length of first, and largest, gap between nontrivial zeta zeros.

6, 8, 8, 7, 3, 1, 4, 4, 9, 7, 0, 3, 6, 8, 6, 1, 2, 0, 2, 1, 7, 1, 2, 2, 7, 6, 1, 0, 3, 3, 4, 4, 3, 2, 5, 0, 6, 5, 5, 0, 0, 8, 3, 4, 0, 9, 2, 0, 3, 5, 3, 8, 5, 7, 8, 9, 4, 3, 9, 5, 2, 9, 4, 3, 4, 3, 7, 6, 3, 5, 1, 5, 6, 2, 5, 9, 6, 3, 4, 0, 3, 4, 7, 6, 4, 6, 4

Offset

1,1

Comments

Simonič shows that this gap is in fact larger than all other gaps between zeros of the Riemann zeta function, see the proof of Lemma 3.

Links

Table of n, a(n) for n=1..87.

Aleksander Simonič, Lehmer pairs and derivatives of Hardy's Z-function, arXiv:1612.08627 [math.NT], 2016-2017.

Index entries for zeta function.

Formula

Equals A065434 - A058303.

Example

6.8873144970368612021712276103344325065500834092035385789439529434376351562596....

Mathematica

Im[ZetaZero[2] - ZetaZero[1]] // RealDigits[#, 10, 88]& // First (* Peter Luschny, Jul 16 2021 *)

Prog

(PARI) call((x, y)->y-x, lfunzeros(1, 22))

Crossrefs

Cf. A065434, A058303.

Sequence in context: A100221 A157683 A300897 * A049110 A136050 A281112

Adjacent sequences: A346286 A346287 A346288 * A346290 A346291 A346292

Keyword

nonn,cons

Author

Charles R Greathouse IV, Jul 13 2021

Status

approved