A065453 Decimal expansion of imaginary part of 4th nontrivial zero of Riemann zeta function.

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

Offset: 2

Author

N. J. A. Sloane, Nov 24 2001

Keywords

• nonn
• cons

Comments

See A002410 and A058303 for more information.

Examples

			The zero is at 1/2 + i * 30.42487612585951321031189753058409132...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 2..10000
• 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
• Index entries for zeta function.

Crossrefs

Imaginary part of k-th nontrivial zero of Riemann zeta function: A058303 (k=1), A065434 (k=2), A065452 (k=3), A065453 (k=4: this), A192492 (k=5), A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).

Cf. A002410 (round), A013629 (floor), A092783 (ceiling).

Programs

Mathematica

RealDigits[ Im[ ZetaZero[4]], 10, 99] // First (* Jean-François Alcover, Mar 07 2013 *)

PARI

solve(x=30,31,real(zeta(1/2+x*I))) \\ Charles R Greathouse IV, Mar 10 2016

PARI

lfunzeros(lzeta,[30,31])[1] \\ Charles R Greathouse IV, Mar 10 2016