OFFSET
1,1
REFERENCES
H. M. Edwards, Riemann's Zeta Function, Academic Press, NY, 1974, p. 96.
C. B. Haselgrove and J. C. P. Miller, Tables of the Riemann Zeta Function. Royal Society Mathematical Tables, Vol. 6, Cambridge Univ. Press, 1960, p. 58.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ 2*Pi*n/log n. - Charles R Greathouse IV, Jun 30 2011
a(n) ~ (2*Pi*e) * e^(W0(n/e)), where W0 is the principal branch of Lambert's W function. - Hal M. Switkay, Oct 04 2021
a(n) = A092783(n) - 1. - M. F. Hasler, Nov 23 2018
EXAMPLE
The imaginary parts of the first 4 zeros are 14.134725... (A058303), 21.0220396... (A065434), 25.01085758... (A065452), 30.424876... (A065453). Therefore the sequence starts: 14, 21, 25, 30, ..., as does A002410 (rounded values; main entry). But the 5th, 6th and 7th values are 32.935... (A192492), 37.586... (A305741), 40.9187... (A305742), whence a(n) = A002410(n)-1 and A002410 = A092783 (ceiling) for these. - M. F. Hasler, Nov 23 2018
MATHEMATICA
Table[Floor[Im[ZetaZero[n]]], {n, 60}] (* Alonso del Arte, Feb 07 2011 *)
PROG
(Sage)
def A013629_list(n):
Z = lcalc.zeros(n)
return [floor(z) for z in Z]
A013629_list(50) # Peter Luschny, May 02 2014
(PARI) lfunzeros(lzeta, 100)\1 \\ Charles R Greathouse IV, Mar 10 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
John Morrison (John.Morrison(AT)armltd.co.uk)
EXTENSIONS
Edited by Daniel Forgues, Jun 30 2011
Definition corrected by Jonathan Sondow, Sep 18 2011
STATUS
approved