cp's OEIS Frontend

A236212 Floor of the value of Riemann's xi function at n.

%I A236212 #5 Feb 16 2025 08:33:21
%S A236212 0,0,0,0,0,0,1,1,2,3,5,8,13,21,36,63,113,206,386,736,1433,2849,5773,
%T A236212 11919,25059,53613,116658,258032,579856,1323273,3065246,7204159,
%U A236212 17172291,41498712,101635485,252180415,633710357,1612310803,4151993262,10819115820
%N A236212 Floor of the value of Riemann's xi function at n.
%C A236212 On the interval [1, infinity), the xi function takes real values and is (strictly) increasing, so a(n) <= a(n+1) for n >= 1.
%C A236212 Same as floor of the value of the xi function at 1-n, because of the functional equation xi(1-s) = x(s).
%H A236212 J. Sondow and C. Dumitrescu, <a href="http://arxiv.org/abs/1005.1104">A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis</a>, Period. Math. Hungar. 60 (2010), 37-40.
%H A236212 E. Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Xi-Function.html">Xi Function</a>
%H A236212 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_Xi_function">Riemann Xi function</a>
%H A236212 <a href="/index/Z#zeta_function">Index entries for zeta function</a>
%F A236212 a(n) = [xi(n)] for n > 0.
%e A236212 xi(1) = 1/2, so a(1) = [0.5] = 0.
%e A236212 xi(8) = (4*Pi^4)/225 = 1.7317…, so a(8) = [1.7] = 1.
%t A236212 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}]
%Y A236212 Cf. A002410.
%K A236212 nonn
%O A236212 1,9
%A A236212 _Jonathan Sondow_, Jan 25 2014