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A275579 Nearest integer to imaginary part of Riemann zeta zeros divided by 2*Pi. 6
2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence never increases by more than 1. The first differences are given by A275737 starting: 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, ...
LINKS
Guilherme França, André LeClair, Statistical and other properties of Riemann zeros based on an explicit equation for the n-th zero on the critical line, arXiv:1307.8395 [math.NT], 2013-2014, page 13, formula (25).
FORMULA
a(n) = round(im(zetazero(n))/(2*Pi)) = round(A002410(n)/(2*Pi)).
a(n) ~ (n - 11/8)/LambertW(exp(1)^(-1)*(n - 11/8)) (This is the Franca LeClair asymptotic at page 13, formula (25).)
MATHEMATICA
Table[Round[Im[ZetaZero[n]]/(2*Pi)], {n, 1, 60}]
CROSSREFS
Sequence in context: A064067 A202306 A373178 * A198292 A020892 A196165
KEYWORD
nonn
AUTHOR
Mats Granvik, Aug 02 2016
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)