cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A123505 Lengths of bit runs in A123504.

Original entry on oeis.org

1, 2, 1, 2, 2, 2, 3, 3, 5, 6, 7, 8, 11, 14, 17, 21, 26, 34, 41, 51, 65, 80, 101, 125, 157, 196, 245, 305, 381, 477, 595, 743, 927, 1159, 1448, 1807, 2258, 2819, 3521, 4397, 5492, 6859, 8565, 10698, 13361, 16685, 20839, 26026, 32503, 40593, 50697, 63315, 79074
Offset: 2

Views

Author

Gary W. Adamson, Oct 01 2006

Keywords

Comments

A123507 records the bit runs of A123506 and uses the second zero in an analogous operation.
Record the numbers of consecutive bit runs of A123504, see example.

Examples

			A123504 = 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1...; therefore the numbers of bit runs are 1, 2, 1, 2, 2, 2, 3, ...

Crossrefs

Cf. A100060, A102522, A102523, A123504, A123506, A123507.

Programs

  • Mathematica
    Length /@ Split[Table[Boole[Arg[1/n^ZetaZero[1]] > 0], {n, 2, 10^6}]] (* Amiram Eldar, May 31 2025 *)

Extensions

More terms from Amiram Eldar, May 31 2025

A123506 Sequence generated from the second nontrivial zero of the Riemann zeta function.

Original entry on oeis.org

0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 2

Views

Author

Gary W. Adamson, Oct 02 2006

Keywords

Comments

A123504 performs an analogous set of operations using the first nontrivial zero. A123507 records the lengths of runs in this sequence.
Let z = (1/2 + i*t), t = 21.0220396387... (the second nontrivial Riemann zeta function zero). Perform (1/n)^z, (n = 2, 3, 4, ...) extracting the argument. If the argument is between 0 and 180 degrees, a(n) = 1, otherwise a(n) = 0.

Examples

			a(7) = 1 since (1/7)^z = (0.37796447..., angle 176.201... degrees) and the argument is between 0 and 180 degrees.

References

  • John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Plume - a Penguin Group, NY, 2003, pp. 198-199.

Crossrefs

Cf. A065434, A102522, A102523, A123504, A123505, A123507.

Programs

  • Mathematica
    a[n_] := Boole[Arg[1/n^ZetaZero[2]] > 0]; Array[a, 100, 2] (* Amiram Eldar, May 31 2025 *)

Extensions

More terms from Amiram Eldar, May 31 2025

A123507 Lengths of bit runs in A123506.

Original entry on oeis.org

1, 2, 1, 3, 1, 1, 2, 2, 3, 2, 4, 3, 5, 5, 5, 7, 8, 9, 11, 12, 14, 17, 19, 22, 26, 31, 34, 41, 47, 55, 64, 73, 86, 100, 115, 135, 156, 181, 210, 244, 283, 329, 383, 443, 516, 598, 695, 807, 936, 1088, 1263, 1467, 1703, 1978, 2297, 2666, 3097, 3595, 4176, 4848, 5630
Offset: 2

Views

Author

Gary W. Adamson, Oct 01 2006

Keywords

Comments

The sequence uses operations based on the second nontrivial Riemann zero: (1/2 + i*t), t = 21.022039639... A123504 and A123505 use the first nontrivial zero.
Record the numbers of consecutive bit runs of A123506, see example.

Examples

			a(4) = 3 since A123506 = 0, 1, 1, 0, 1, 1, 1, ...

References

  • John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Plume - a Penguin Group, NY, 2003, pp. 198-199.

Crossrefs

Cf. A100060, A102522, A102523, A123504, A123505, A123506.

Programs

  • Mathematica
    Length /@ Split[Table[Boole[Arg[1/n^ZetaZero[2]] > 0], {n, 2, 10^6}]] (* Amiram Eldar, May 31 2025 *)

Extensions

More terms from Amiram Eldar, May 31 2025
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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