A123504 Sequence generated from the first nontrivial zero of the Riemann zeta function.

1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 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, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0

Offset: 2

Author

Gary W. Adamson, Oct 01 2006

Keywords

• nonn

Comments

A123505 records the lengths of runs. A123506 uses the second zero.

Examples

			a(8) = 1 since (1/8)^z = (0.353553..., angle 115.943... degrees).
		

Crossrefs

Cf. A058303, A100060, A102522, A102523, A123505, A123506, A123507.

Programs

Mathematica

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

PARI

t=1/2+solve(y=14,15,imag(zeta(1/2+y*I)))*I;
a(n)=arg(n^-t)>0 \\ Charles R Greathouse IV, Mar 10 2016

Formula

Extract argument from (1/n)^z, z = (1/2 + i*14.1347251417...). a(n) = 1 if the argument is between 0 and 180 degrees, and = 0 if otherwise (n = 2, 3, 4, ...).

Extensions

More terms from Amiram Eldar, May 31 2025