A231980 Imaginary part of first nontrivial Riemann zeta zero divided by Pi.

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

Offset

1,1

Comments

The pattern of nines and triple twos appear in the following numbers when adding one half and dividing with sqrt(5):

0.9999222720896... = sqrt(Im(ZetaZero(1))/Pi + 1/2)/sqrt(5).

4.4992227511047... = Im(ZetaZero(1))/Pi.

5.4922296657516... = Im(ZetaZero(2))/Pi - sqrt(Im(ZetaZero(2))/Pi+1/2)/sqrt(5).

2.4992229102932... = Re( lim_{s->1/ZetaZero(2)} zeta(s)*(1 - 1/6^(s-1)) ). - Mats Granvik, Mar 03 2016

Links

Table of n, a(n) for n=1..105.

Formula

Equals Im(ZetaZero(1))/Pi.

Example

4.4992227511047348484865414231801573901....

Mathematica

RealDigits[N[Im[ZetaZero[1]]/Pi, 105]][[1]]

Prog

(PARI) solve(y=14, 15, imag(zeta(1/2+y*I)))/Pi \\ Charles R Greathouse IV, Mar 10 2016
(PARI) lfunzeros(lzeta, [14, 15])[1]/Pi \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Cf. A058303, A000796.

Sequence in context: A005441 A362294 A198497 * A175051 A011364 A016713

Adjacent sequences: A231977 A231978 A231979 * A231981 A231982 A231983

Keyword

nonn,cons

Author

Mats Granvik, Nov 16 2013

Status

approved