A192492 Decimal expansion of imaginary part of 5th nontrivial zero of Riemann zeta function.

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

Offset

2,1

Comments

The real part of the 5th nontrivial zero is of course 1/2 (A020761; the Riemann hypothesis is here assumed to be true).

Links

Table of n, a(n) for n=2..97.

Andrew M. Odlyzko, The first 100 (non trivial) zeros of the Riemann Zeta function, to over 1000 decimal digits each, AT&T Labs - Research.

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

Example

The zero is at 1/2 + i * 32.9350615877391896906623689640749...

Mathematica

(* ZetaZero was introduced in Version 6.0 *) RealDigits[ZetaZero[5], 10, 100][[1]]

Prog

(PARI) solve(y=32, 33, real(zeta(1/2+y*I))) \\ Charles R Greathouse IV, Mar 10 2016
(PARI) lfunzeros(lzeta, [32, 33])[1] \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Cf. A002410: nearest integer to imaginary part of n-th zero of Riemann zeta function (main entry); also A013629 (floor) and A092783 (ceiling).

The imaginary parts of the first 4 zeros are 14.134725... (A058303), 21.0220396... (A065434), 25.01085758... (A065452), 30.424876... (A065453). Others are A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).

The real parts of the trivial zeros are given by A005843 multiplied by -1 (and ignoring the initial 0 of that sequence).

Sequence in context: A228936 A169862 A245884 * A351444 A104005 A224578

Adjacent sequences: A192489 A192490 A192491 * A192493 A192494 A192495

Keyword

nonn,cons

Author

Alonso del Arte, Jul 02 2011

Extensions

Example and cross-references edited by M. F. Hasler, Nov 23 2018

Status

approved