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

Offset

2,1

Comments

A123054 performs an analogous set of operations using the first nontrivial zero. A123507 records the lengths of runs in A123506.

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..57.

Formula

Let z = (1/2 + i*t), t = 21.022039639... (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. If not, then a(n) = 0.

Example

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

Crossrefs

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

Sequence in context: A157658 A296211 A341642 * A051105 A284929 A286746

Adjacent sequences: A123503 A123504 A123505 * A123507 A123508 A123509

Keyword

nonn,more

Author

Gary W. Adamson, Oct 02 2006

Status

approved