OFFSET
1,9
COMMENTS
On the interval [1, infinity), the xi function takes real values and is (strictly) increasing, so a(n) <= a(n+1) for n >= 1.
Same as floor of the value of the xi function at 1-n, because of the functional equation xi(1-s) = x(s).
LINKS
J. Sondow and C. Dumitrescu, A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis, Period. Math. Hungar. 60 (2010), 37-40.
E. Weisstein's MathWorld, Xi Function
Wikipedia, Riemann Xi function
FORMULA
a(n) = [xi(n)] for n > 0.
EXAMPLE
xi(1) = 1/2, so a(1) = [0.5] = 0.
xi(8) = (4*Pi^4)/225 = 1.7317…, so a(8) = [1.7] = 1.
MATHEMATICA
xi[ s_] := If[ s == 1, 1/2, (s/2)*(s - 1)*Pi^(-s/2)*Gamma[ s/2]*Zeta[ s]]; Table[ Floor[ xi[ n]], {n, 40}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Jan 25 2014
STATUS
approved