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A051717 Denominators of Bernoulli twin numbers C(n). 30
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; text; 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)). - Peter Luschny, Jul 04 2009

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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}] (* Jean-François Alcover, Dec 19 2011 *)

Join[{1}, Denominator[Total/@Partition[BernoulliB[Range[0, 60]], 2, 1]]] (* Harvey P. Dale, Mar 09 2013 *)

PROG

(PARI) a(n)=if(n<3, n+1, denominator(bernfrac(n)-bernfrac(n-1))) \\ Charles R Greathouse IV, May 18 2015

CROSSREFS

Cf. A051716, A129825, A129826, A129724, A051714, A051715.

Sequence in context: A269996 A018318 A277809 * A192441 A108326 A002234

Adjacent sequences:  A051714 A051715 A051716 * A051718 A051719 A051720

KEYWORD

nonn,easy,nice,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Dec 08 1999

Edited by N. J. A. Sloane, May 25 2008

STATUS

approved

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Last modified August 24 14:36 EDT 2019. Contains 326285 sequences. (Running on oeis4.)