A065434 - OEIS

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A065434

Decimal expansion of imaginary part of 2nd nontrivial zero of Riemann zeta function.

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

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OFFSET

2,1

REFERENCES

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.15.3, p. 138.

LINKS

Table of n, a(n) for n=2..100.

Enrico Bombieri, Problems of the Millennium: the Riemann Hypothesis, Clay Mathematics Institute.

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.

EXAMPLE

The zero is at 1/2 + i*21.0220396387715549926284795938969...

MAPLE

Digits:= 150; Re(fsolve(Zeta(1/2+I*t)=0, t=21)); # Iaroslav V. Blagouchine, Jun 25 2016

MATHEMATICA

ZetaZero[2] // Im // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Mar 05 2013 *)

PROG

(PARI) solve(x=21, 22, real(zeta(1/2+x*I))) \\ Charles R Greathouse IV, Jun 30 2011

(PARI) lfunzeros(1, [21, 22])[1] \\ M. F. Hasler, Nov 23 2018

CROSSREFS

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

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

Sequence in context: A256626 A135211 A029294 * A045832 A287528 A328312

Adjacent sequences: A065431 A065432 A065433 * A065435 A065436 A065437

KEYWORD

nonn,cons,changed

AUTHOR

N. J. A. Sloane, Nov 24 2001

STATUS

approved