A013629 -id:A013629 - cp's OEIS frontend

A002410 Nearest integer to imaginary part of n-th zero of Riemann zeta function.

14, 21, 25, 30, 33, 38, 41, 43, 48, 50, 53, 56, 59, 61, 65, 67, 70, 72, 76, 77, 79, 83, 85, 87, 89, 92, 95, 96, 99, 101, 104, 105, 107, 111, 112, 114, 116, 119, 121, 123, 124, 128, 130, 131, 133, 135, 138, 140, 141, 143, 146, 147, 150, 151, 153, 156, 158, 159, 161

Offset: 1

N. J. A. Sloane

"All these zeros of the form s + it have real part s = 1/2 and are simple. Thus the Riemann hypothesis is true at least for t < 3330657430697." - Wedeniwski
From Daniel Forgues, Jul 24 2009: (Start)
All nontrivial zeros on the critical line, of the form 1/2 + i*t, have an associated conjugate nontrivial zero of the form 1/2 - i*t.
Any nontrivial zeros off the critical line, if ever found, would come in pairs (1/2 +- delta) + i*t, 0 < delta < 1/2. Each of these pairs, again if ever found, would then have their associated conjugate pair (1/2 +- delta) - i*t, 0 < delta < 1/2. (End)
The sequence is not strictly increasing. - Joerg Arndt, Jan 17 2015
The fraction of numbers n such that a(n) = a(n-1) has density 1. There are only finitely many numbers n with a(n) > a(n-1) + 1, see A208436. - Charles R Greathouse IV, Mar 07 2018
Conjecture: Noninteger rationals of the form m/2^bigomega(m) that can be used to approximate this sequence, i.e. a(n) ~~ 2*Pi*A374074(n)/2^bigomega(A374074(n)) - n/2 +- (...), where '~~' means 'close to'. - Friedjof Tellkamp, Jul 04 2024

			The imaginary parts of the first 4 zeros are 14.134725... (A058303), 21.0220396... (A065434), 25.01085758... (A065452), 30.424876... (A065453).

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W. F. Galway, Computations related to the Riemann Hypothesis
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Mats Granvik, Illustration of Andre LeClair's approximation of the initial terms
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Mats Granvik, Plots from the Mathematica programs comparing limiting ratios vs Newton-Raphson method for finding Riemann zeta zeros.
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E. Klarreich, Prime Time
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N. Levinson, At Least One-Third of Zeros of Riemann's Zeta-Function are on sigma=1/2, Proc Natl Acad Sci U S A. 1974 Apr; 71(4): 1013-1015.
P. Li, On Montgomery's Pair Correlation Conjecture to the Zeros of the Riemann Zeta Function
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J. van de Lune & H. J. J. te Riele, Rigorous High Speed Separation Of Zeros Of Riemann's Zeta Function, II
J. van de Lune & H. J. J. te Riele, Rigorous High Speed Separation Of Zeros of Riemann's Zeta Function, III
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J. C. Perez-Moure, Evidences that the Riemann Hypothesis is true
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H. J. J. te Riele, Some historical and other notes about the Mertens conjecture and its recent disproof
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Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros
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A. Zaccagnini, Primes in almost all short intervals and the distribution of the zeros of the Riemann zeta-function
Index entries for zeta function

Cf. A013629 (floor), A092783 (ceiling), A057641, A057640, A058209, A058210, A120401, A122526, A072080, A124288 ("unstable" zeta zeros), A124289 ("unstable twins"), A236212, A177885, A374074 (approximation).

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

Table[Round[Im[ZetaZero[n]]], {n, 59}] (* Jean-François Alcover, May 02 2011 *)

apply(round,lfunzeros(lzeta,100)) \\ Charles R Greathouse IV, Mar 10 2016

def A002410_list(n):
    Z = lcalc.zeros(n)
    return [round(z) for z in Z]
A002410_list(59) # Peter Luschny, May 02 2014

a(n) ~ (2*Pi*e) * e^(W0(n/e)), where W0 is the principal branch of Lambert's W function. - Charles R Greathouse IV, Sep 14 2012, corrected by Hal M. Switkay, Oct 04 2021

a(n) ~ 2*Pi*(n - 11/8)/ProductLog((n - 11/8)/exp(1)). This is the asymptotic by Guilherme França and André LeClair. - Mats Granvik, Mar 10 2015; corrected May 16 2016

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004

A058303 Decimal expansion of the imaginary part of the first nontrivial zero of the Riemann zeta function.

Original entry on oeis.org

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

Offset: 2

Robert G. Wilson v, Dec 08 2000

"The Riemann Hypothesis, considered by many to be the most important unsolved problem of mathematics, is the assertion that all of zeta's nontrivial zeros line up with the first two all of which lie on the line 1/2 + sqrt(-1)*t, which is called the critical line. It is known that the hypothesis is obeyed for the first billion and a half zeros." (Wagon)

We can compute 105 digits of this zeta zero as the numerical integral: gamma = Integral_{t=0..gamma+15} (1/2)*(1 - sign((RiemannSiegelTheta(t) + Im(log(zeta(1/2 + i*t))))/Pi - n + 3/2)) where n=1 and where the initial value of gamma = 1. The upper integration limit is arbitrary as long as it is greater than the zeta zero computed recursively. The recursive formula fails at zeta zeros with indices n equal to sequence A153815. - Mats Granvik, Feb 15 2017

			14.1347251417346937904572519835624702707842571156992...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.15.3, p. 138.
S. Wagon, "Mathematica In Action," W. H. Freeman and Company, NY, 1991, page 361.

Iain Fox, Table of n, a(n) for n = 2..20000
P. J. Forrester and A. Mays, Finite size corrections in random matrix theory and Odlyzko's data set for the Riemann zeros, arXiv preprint arXiv:1506.06531 [math-ph], 2015.
P. J. Forrester and A. Mays, Finite size corrections in random matrix theory and Odlyzko's data set for the Riemann zeros, Proceedings of the Royal Society A, Vol: 471, Issue: 2182, 2015.
Fredrik Johansson, The first nontrivial zero to over 300000 decimal digits.
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.
Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.
Eric Weisstein's World of Mathematics, Xi-Function.
Index entries for zeta function.

Imaginary part of k-th nontrivial zero of Riemann zeta function: A058303 (k=1: this), A065434 (k=2), 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); A057641, A057640, A058209, A058210.

Digits:= 150; Re(fsolve(Zeta(1/2+I*t)=0, t=14.13)); # Iaroslav V. Blagouchine, Jun 24 2016

FindRoot[ Zeta[1/2 + I*t], {t, 14 + {-.3, +.3}}, AccuracyGoal -> 100, WorkingPrecision -> 120]
RealDigits[N[Im[ZetaZero[1]], 100]][[1]] (* Charles R Greathouse IV, Apr 09 2012 *)
(* The following numerical integral takes about 9 minutes to compute *)Clear[n, t, gamma]; gamma = 1; numberofzetazeros = 1; Quiet[Do[gamma = N[NIntegrate[(1/2)*(1 - Sign[(RiemannSiegelTheta[t] + Im[Log[Zeta[I*t + 1/2]]])/Pi - n + 3/2]), {t, 0, gamma + 15}, PrecisionGoal -> 110, MaxRecursion -> 350, WorkingPrecision -> 120], 105]; Print[gamma], {n, 1, numberofzetazeros}]]; RealDigits[gamma][[1]] (* Mats Granvik, Feb 15 2017 *)

solve(x=14,15,imag(zeta(1/2+x*I))) \\ Charles R Greathouse IV, Feb 26 2012

lfunzeros(1,15)[1] \\ Charles R Greathouse IV, Mar 07 2018

zeta(1/2 + i*14.1347251417346937904572519836...) = 0.

A065434 Decimal expansion of imaginary part of 2nd nontrivial zero of Riemann zeta function.

Original entry on oeis.org

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

Offset: 2

N. J. A. Sloane, Nov 24 2001

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

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

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.

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).

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

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

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

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

A065452 Decimal expansion of imaginary part of 3rd nontrivial zero of Riemann zeta function.

Original entry on oeis.org

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

Offset: 2

N. J. A. Sloane, Nov 24 2001

See A002410 and A058303 for more information.

			The zero is at 1/2 + i * 25.01085758014568876321379099256282181865954967...

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

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.

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

Cf. A002410 (these values rounded to nearest integer), A013629 (floor), A092783 (ceiling).

ZetaZero[3] // Im // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Mar 05 2013 *)

solve(x=25,25.1,real(zeta(1/2+x*I))) \\ Charles R Greathouse IV, Jun 30 2011

lfunzeros(1,[25,26])[1] \\ or: lfunzeros(1,26)[3]. - M. F. Hasler, Nov 23 2018

Minor edits by M. F. Hasler, Nov 23 2018

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

Original entry on oeis.org

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

N. J. A. Sloane, Nov 24 2001

See A002410 and A058303 for more information.

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

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.

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).

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

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

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

A092783 Ceiling of imaginary parts of zeros of Riemann zeta function.

Original entry on oeis.org

15, 22, 26, 31, 33, 38, 41, 44, 49, 50, 53, 57, 60, 61, 66, 68, 70, 73, 76, 78, 80, 83, 85, 88, 89, 93, 95, 96, 99, 102, 104, 106, 108, 112, 112, 115, 117, 119, 122, 123, 125, 128, 130, 132, 134, 135, 139, 140, 142, 144, 147, 148, 151, 151, 154, 157, 158, 159, 162, 164, 166, 168, 170, 170, 174

Offset: 1

Jorge Coveiro, Apr 14 2004

nonn

OEIS index entries for sequences related to the zeta function.

Cf. A002410: nearest integer to imaginary part of n-th zero of Riemann zeta function (main entry).
Cf. A013629: floor of imaginary parts of zeros of Riemann zeta function.
Imaginary part of k-th nontrivial zero of Riemann zeta function: A058303 (k=1), A065434 (k=2), A065452 (k=3), A065453 (k=4), A192492 (k=5), A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).

Table[Ceiling[Im[ZetaZero[n]]], {n, 1, 65}] (* Jean-François Alcover, Feb 25 2019 *)

apply(ceil, lfunzeros(1,[1,180])) \\ M. F. Hasler, Nov 23 2018

def A092783_list(n):
    Z = lcalc.zeros(n)
    return [ceil(z) for z in Z]
A092783_list(50) # Peter Luschny, May 02 2014

a(n) = 1+A013629(n). - Robert G. Wilson v, Jan 27 2015

More terms, link and cross-references from M. F. Hasler, Nov 23 2018

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

Original entry on oeis.org

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

Alonso del Arte, Jul 02 2011

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

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

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

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).

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

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

lfunzeros(lzeta,[32,33])[1] \\ Charles R Greathouse IV, Mar 10 2016

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

A305741 Decimal expansion of imaginary part of 6th nontrivial zero of Riemann zeta function.

Original entry on oeis.org

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

Offset: 2

Seiichi Manyama, Jun 23 2018

			The zero is at 1/2 + i * 37.58617815882567125721776348070533282140559735083...

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

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

Cf. A002410 (rounded values: main entry), A013629 (floor), A092783 (ceiling).

RealDigits[Im[ZetaZero[6]], 10, 120][[1]] (* Vaclav Kotesovec, Jun 23 2018 *)

lfunzeros(1,[37,38])[1] \\ M. F. Hasler, Nov 23 2018

A305742 Decimal expansion of imaginary part of 7th nontrivial zero of Riemann zeta function.

Original entry on oeis.org

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

Offset: 2

Seiichi Manyama, Jun 23 2018

			The zero is at 1/2 + i * 40.918719012147495187398126914633254395726165962777...

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

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

Cf. A002410 (rounded values: main entry), A013629 (floor), A092783 (ceiling).

RealDigits[Im[ZetaZero[7]], 10, 120][[1]] (* Vaclav Kotesovec, Jun 23 2018 *)

lfunzeros(1,[40,41])[1] \\ M. F. Hasler, Nov 23 2018

A305743 Decimal expansion of imaginary part of 8th nontrivial zero of Riemann zeta function.

Original entry on oeis.org

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

Offset: 2

Seiichi Manyama, Jun 23 2018

			The zero is at 1/2 + I*43.3270732809149995194961221654068... - _M. F. Hasler_, Nov 21 2018

Andrew M. Odlyzko, Tables of zeros of the Riemann zeta function
OEIS index entries for sequences related to the zeta function.

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

Cf. A002410 (rounded values: main entry), A013629 (floor), A092783 (ceiling).

RealDigits[Im[ZetaZero[8]], 10, 120][[1]] (* Vaclav Kotesovec, Jun 23 2018 *)

solve(X=43,44,imag(zeta(0.5+X*I))) \\ M. F. Hasler, Nov 21 2018

lfunzeros(1,[43,44])[1] \\ M. F. Hasler, Nov 23 2018

cp's OEIS Frontend

A002410 Nearest integer to imaginary part of n-th zero of Riemann zeta function.

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A058303 Decimal expansion of the imaginary part of the first nontrivial zero of the Riemann zeta function.

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A065434 Decimal expansion of imaginary part of 2nd nontrivial zero of Riemann zeta function.

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A065452 Decimal expansion of imaginary part of 3rd nontrivial zero of Riemann zeta function.

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

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A092783 Ceiling of imaginary parts of zeros of Riemann zeta function.

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