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URL: https://oeis.org/A123504

⇱ A123504 - OEIS

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A123504
Sequence generated from the first nontrivial zero of the Riemann zeta function.
3
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
2,1
COMMENTS
A123505 records the lengths of runs. A123506 uses the second zero.
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, ...).
EXAMPLE
a(8) = 1 since (1/8)^z = (0.353553..., angle 115.943... degrees).
MATHEMATICA
a[n_] := Boole[Arg[1/n^ZetaZero[1]] > 0]; Array[a, 100, 2] (* Amiram Eldar, May 31 2025 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Oct 01 2006
EXTENSIONS
More terms from Amiram Eldar, May 31 2025
STATUS
approved