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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

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OFFSET

2,1

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.

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..88.

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A065434, A102522, A102523, A123504, A123505, A123507.

Sequence in context: A157658 A296211 A341642 * A051105 A284929 A286746

Adjacent sequences: A123503 A123504 A123505 * A123507 A123508 A123509