OFFSET
2,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..1000 (terms n = 2..100 from Vincenzo Librandi)
Tal Barnea, On the Riemann Zeta Function and the fractional part of rational powers, arXiv:1808.06653 [math.NT], 2018.
Tal Barnea, The Riemann Zeta Function and the Fractional Part of Rational Powers, J. Int. Seq., Vol. 22 (2019), Article 19.3.6.
FORMULA
From Franklin T. Adams-Watters, Mar 23 2010: (Start)
a(n) = floor(1/(zeta(n)-1)).
a(n) = 2^n - (4/3)^n + O(1). It appears that a(n) = 2^n - floor((4/3)^n) - k, where k is usually 2 but is sometimes 1. Up to n=1000, the only values of n where k = 1 are 4, 5, 13, 14, and 17. (End)
MATHEMATICA
a[n_] := ContinuedFraction[ Zeta[n], 2] // Last; Table[a[n], {n, 2, 31}] (* Jean-François Alcover, Feb 26 2013 *)
PROG
(Maxima) A013697(n):=floor(1/(zeta(n)-1))$
makelist(A013697(n), n, 2, 30); /* Martin Ettl, Nov 03 2012 */
(Python)
from sympy import zeta
print([1//(zeta(n) - 1) for n in range(2, 32)]) # Karl V. Keller, Jr., Jul 21 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Apr 22 2001
STATUS
approved