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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

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OFFSET

2,2

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=2..62.

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A138618 A140583 A237266 * A384009 A188804 A122580