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Search: id:A051717
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| A051717 |
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Denominators of Bernoulli twin numbers C(n). |
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+0
16
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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]
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LINKS
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M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.
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EXAMPLE
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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, ...
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MAPLE
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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;
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CROSSREFS
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Cf. A051716, A129825, A129826, A129724, A051714, A051715.
Sequence in context: A144857 A090445 A018318 this_sequence A108326 A002234 A074005
Adjacent sequences: A051714 A051715 A051716 this_sequence A051718 A051719 A051720
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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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
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