A231165 -id:A231165 - cp's OEIS frontend

A231157 Number of Gram blocks [g(j), g(j+1)) up to 10^n with 0 <= j < 10^n.

1, 10, 100, 916, 8374, 78694, 755132, 7297808, 71004697

Offset: 0

Arkadiusz Wesolowski, Nov 04 2013

nonn

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.

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

Cf. A114856, A231158-A231165.

A231158 Number of Gram blocks [g(j), g(j+2)) up to 10^n with 0 <= j < 10^n.

Original entry on oeis.org

0, 42, 780, 9445, 100203, 1034545, 10493487

Offset: 2

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157, A231159-A231165.

A231159 Number of Gram blocks [g(j), g(j+3)) up to 10^n with 0 <= j < 10^n.

Original entry on oeis.org

0, 22, 779, 13822, 184107, 2169610

Offset: 3

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157, A231158, A231160-A231165.

A231160 Number of Gram blocks [g(j), g(j+4)) up to 10^n with 0 <= j < 10^n.

Original entry on oeis.org

0, 19, 709, 19115, 340360

Offset: 4

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157-A231159, A231161-A231165.

A231161 Number of Gram blocks [g(j), g(j+5)) up to 10^n with 0 <= j < 10^n.

Original entry on oeis.org

0, 1, 32, 821, 25813

Offset: 4

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157-A231160, A231162-A231165.

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.

Original entry on oeis.org

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

Offset: 2

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157-A231161, A231163-A231165.

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.

Original entry on oeis.org

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

Offset: 0

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157-A231162, A231164, A231165.

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.

Original entry on oeis.org

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

Offset: 2

Arkadiusz Wesolowski, Nov 04 2013

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.

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

Cf. A114856, A231157-A231163, A231165.

cp's OEIS Frontend

A231157 Number of Gram blocks [g(j), g(j+1)) up to 10^n with 0 <= j < 10^n.

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A231158 Number of Gram blocks [g(j), g(j+2)) up to 10^n with 0 <= j < 10^n.

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A231159 Number of Gram blocks [g(j), g(j+3)) up to 10^n with 0 <= j < 10^n.

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A231160 Number of Gram blocks [g(j), g(j+4)) up to 10^n with 0 <= j < 10^n.

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A231161 Number of Gram blocks [g(j), g(j+5)) up to 10^n with 0 <= j < 10^n.

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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.

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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.

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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.

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Author

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Comments

Links

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