A231164 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.

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

Offset

2,2

Comments

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.

Links

Table of n, a(n) for n=2..8.

Richard P. Brent, On the Zeros of the Riemann Zeta Function in the Critical Strip, Math. Comp. 33 (1979), pp. 1361-1372.

Eric Weisstein's World of Mathematics, Gram Block

Eric Weisstein's World of Mathematics, Gram Point

Eric Weisstein's World of Mathematics, Riemann-Siegel Functions

Crossrefs

Cf. A114856, A231157-A231163, A231165.

Sequence in context: A231158 A030197 A225980 * A020933 A241923 A231162

Adjacent sequences: A231161 A231162 A231163 * A231165 A231166 A231167

Keyword

nonn,more

Author

Arkadiusz Wesolowski, Nov 04 2013

Status

approved