|
| |
|
|
A051717
|
|
Denominators of Bernoulli twin numbers C(n).
|
|
19
| |
|
|
1, 2, 3, 6, 30, 30, 42, 42, 30, 30, 66, 66, 2730, 2730, 6, 6, 510, 510, 798, 798, 330, 330, 138, 138, 2730, 2730, 6, 6, 870, 870, 14322, 14322, 510, 510, 6, 6, 1919190, 1919190, 6, 6, 13530, 13530, 1806, 1806, 690, 690, 282, 282, 46410, 46410, 66, 66, 1590, 1590
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| The Bernoulli twin numbers C(n) are defined by C(0) = 1, then C(2n) = B(2n)+B(2n-1), C(2n+1) = -B(2n+1)-B(2n), where B() are the Bernoulli numbers A027641/A027642. The definition is due to Paul Curtz.
Denominators of column 1 of table described in A051714/A051715.
A simpler definition is: If n=0 then 1 else denominator(B(i)-B(i-1)). [From Peter Luschny (peter(AT)luschny.de), Jul 04 2009]
|
|
|
LINKS
| M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.
|
|
|
EXAMPLE
| Sequence of C(n)'s begins: 1, -1/2, -1/3, -1/6, -1/30, 1/30, 1/42, -1/42, -1/30, 1/30, 5/66, -5/66, -691/2730, 691/2730, 7/6, -7/6, ...
|
|
|
MAPLE
| C:=proc(n) if n=0 then RETURN(1); fi; if n mod 2 = 0 then RETURN(bernoulli(n)+bernoulli(n-1)); else RETURN(-bernoulli(n)-bernoulli(n-1)); fi; end;
|
|
|
MATHEMATICA
| c[0] = 1; c[n_?EvenQ] := BernoulliB[n] + BernoulliB[n-1]; c[n_?OddQ] := -BernoulliB[n] - BernoulliB[n-1]; Table[ Denominator[c[n]], {n, 0, 53}] (* From Jean-François Alcover, Dec 19 2011 *)
|
|
|
CROSSREFS
| Cf. A051716, A129825, A129826, A129724, A051714, A051715.
Sequence in context: A144857 A090445 A018318 * A192441 A108326 A002234
Adjacent sequences: A051714 A051715 A051716 * A051718 A051719 A051720
|
|
|
KEYWORD
| nonn,easy,nice,frac
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999
Edited by N. J. A. Sloane (njas(AT)research.att.com), May 25 2008
|
| |
|
|
