A231165 - OEIS

A231165

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

0, 6, 86, 1289, 14932, 166570

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,2

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=3..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-A231164.

Sequence in context: A230782 A318042 A155654 * A091881 A004701 A177570

Adjacent sequences: A231162 A231163 A231164 * A231166 A231167 A231168

KEYWORD

nonn,more

AUTHOR

Arkadiusz Wesolowski, Nov 04 2013

STATUS

approved