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A013697 Second term in continued fraction for zeta(n). 3
1, 4, 12, 27, 57, 119, 245, 497, 1005, 2023, 4063, 8149, 16327, 32692, 65435, 130938, 261965, 524050, 1048259, 2096730, 4193742, 8387859, 16776218, 33553102, 67107091, 134215364, 268432305, 536866711, 1073736223, 2147476180 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Vincenzo Librandi and 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-Fran├žois Alcover, Feb 26 2013 *)

PROG

(Maxima) A013697(n):=floor(1/(zeta(n)-1))$

makelist(A013697(n), n, 2, 30); /* Martin Ettl, Nov 03 2012 */

CROSSREFS

Bisections: A190297, A190584.

Sequence in context: A007009 A188814 A104384 * A306055 A212522 A207408

Adjacent sequences:  A013694 A013695 A013696 * A013698 A013699 A013700

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladeta Jovovic, Apr 22 2001

STATUS

approved

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Last modified July 14 09:22 EDT 2020. Contains 335720 sequences. (Running on oeis4.)