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 A013629 Floor of imaginary parts of nontrivial zeros of Riemann zeta function. 22
 14, 21, 25, 30, 32, 37, 40, 43, 48, 49, 52, 56, 59, 60, 65, 67, 69, 72, 75, 77, 79, 82, 84, 87, 88, 92, 94, 95, 98, 101, 103, 105, 107, 111, 111, 114, 116, 118, 121, 122, 124, 127, 129, 131, 133, 134, 138, 139, 141, 143, 146, 147, 150, 150, 153, 156, 157, 158, 161 (list; graph; refs; listen; history; text; internal format)
 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) = 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 Cf. A002410 (rounded values: main entry), A092783 (ceiling). 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). Sequence in context: A213536 A230095 A133185 * A234802 A162780 A002410 Adjacent sequences:  A013626 A013627 A013628 * A013630 A013631 A013632 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

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Last modified July 18 15:26 EDT 2019. Contains 325143 sequences. (Running on oeis4.)