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A013697
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Second term in continued fraction for zeta(n).
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4
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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2,2
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LINKS
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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.
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FORMULA
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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)
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MATHEMATICA
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a[n_] := ContinuedFraction[ Zeta[n], 2] // Last; Table[a[n], {n, 2, 31}] (* Jean-François Alcover, Feb 26 2013 *)
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PROG
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(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
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CROSSREFS
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Bisections: A190297, A190584.
Sequence in context: A007009 A188814 A104384 * A306055 A212522 A207408
Adjacent sequences: A013694 A013695 A013696 * A013698 A013699 A013700
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Vladeta Jovovic, Apr 22 2001
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STATUS
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approved
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