A231164 - OEIS

%I #6 Nov 07 2013 23:13:31

%S 0,42,796,10157,113477,1223692,12864188

%N Number of Gram blocks [g(j), g(j+1)) up to 10^n, 0 <= j < 10^n, which contain exactly two zeros of Z(t), where Z(t) is the Riemann-Siegel Z-function.

%C We call a Gram point g(j) "good" if j is not in A114856, and "bad" otherwise. A "Gram block of length k" is an interval [g(j), g(j+k)) such that g(j) and g(j+k) are good Gram points, g(j+1), ..., g(j+k-1) are bad Gram points, and k >= 1.

%H Richard P. Brent, <a href="http://www.ams.org/journals/mcom/1979-33-148/S0025-5718-1979-0537983-2/">On the Zeros of the Riemann Zeta Function in the Critical Strip</a>, Math. Comp. 33 (1979), pp. 1361-1372.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GramBlock.html">Gram Block</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GramPoint.html">Gram Point</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Riemann-SiegelFunctions.html">Riemann-Siegel Functions</a>

%Y Cf. A114856, A231157-A231163, A231165.

%K nonn,more

%O 2,2

%A _Arkadiusz Wesolowski_, Nov 04 2013