A125642 Divide the circle into ten "decants" (each of 36 degrees). Let z = 1/2 + i*14.134725142... be the first nontrivial zero of the Riemann zeta function. Then a(n) is the decant containing the argument of 1/n^z.

1, 5, -5, -2, 4, -1, -4, 4, 1, -2, -4, 5, 3, 1, -1, -3, -4, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -5, 5, 4, 3, 3, 2, 1, 1, -1, -2, -2, -3, -3, -4, -5, -5, 5, 5, 4, 4, 3, 3, 2

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Formula

Given the first Riemann nontrivial zero, z = (1/2 + i*14.134725142...), extract the argument of 1/n^z (in polar coordinates) and map it on a unit circle by decants: (0 to 36 deg. = 1), (36 to 72 deg. = 2), (72 to 108 deg. = 3), (108 to 144 deg. = 4), (144 to 180 deg. = 5), (0 to -36 deg. = -1), (-36 to -72 deg. = -2), (-72 to -108 deg. = -3), (-108 to -144 deg. = -4), (-144 to -180 deg. = -5).

Example

a(5) = 4 since 1/4^z = has angle 136.58045... and the argument is between 108 and 144 deg., which is the 4th decant.

Crossrefs

Cf. A100060.

Sequence in context: A319593 A335321 A172125 * A247039 A011335 A021185

Adjacent sequences: A125639 A125640 A125641 * A125643 A125644 A125645

Keyword

more,sign

Author

Gary W. Adamson, Nov 28 2006

Extensions

Edited by N. J. A. Sloane, Aug 10 2019

Status

approved