A231162 Number of Gram blocks [g(j), g(j+1)) up to 10^n, 0 <= j < 10^n, which do not contain any zeros of Z(t), where Z(t) is the Riemann-Siegel Z-function.

0, 42, 808, 10330, 116055, 1253556, 13197331

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-A231161, A231163-A231165.

Sequence in context: A231164 A020933 A241923 * A290364 A030020 A090969

Adjacent sequences: A231159 A231160 A231161 * A231163 A231164 A231165

Keyword

nonn,more

Author

Arkadiusz Wesolowski, Nov 04 2013

Status

approved