|
|
A013697
|
|
Second term in continued fraction for zeta(n).
|
|
4
|
|
|
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, 4294957340, 8589921317, 17179851485
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
LINKS
|
|
|
FORMULA
|
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))$
(Python)
from sympy import zeta
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|