A231163 - OEIS

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A231163

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

1, 10, 100, 916, 8390, 79427, 769179, 7507820, 73771910

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OFFSET

0,2

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=0..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-A231162, A231164, A231165.

Sequence in context: A224007 A136876 A231157 * A136858 A334612 A125948

Adjacent sequences: A231160 A231161 A231162 * A231164 A231165 A231166

KEYWORD

nonn,more

AUTHOR

Arkadiusz Wesolowski, Nov 04 2013

STATUS

approved