The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 EXTENSIONS More terms from James A. Sellers, Dec 08 1999 Edited by N. J. A. Sloane, May 25 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 26 12:33 EST 2020. Contains 332279 sequences. (Running on oeis4.)