A123507 Lengths of bit runs in A123506.

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

Author

Gary W. Adamson, Oct 01 2006

Keywords

• nonn

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