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

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

Author

Gary W. Adamson, Oct 02 2006

Keywords

• nonn

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