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Search: id:A079798
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| A079798 |
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Partition of positive integers into shortest possible groups, starting with (1), (2,3), (4,5,6), (7,8,9,10,11), such that a(n) = the sum of the terms of the n-th group is a multiple of a(n-1) and a(n) > a(n-1). |
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+0
6
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| 1, 5, 15, 45, 495, 16830, 4358970, 1159486020, 196818113950920, 3151092455396895169036800, 136084696980410308844836382925537725529600, 9996588705394796239042140065772174939073840705818917941136700639014745600
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Dropping requirement a(n) > a(n-1) leads to a different partition: (1), (2, 3), (4, 5, 6), (7, 8), ... - see A160275.
For partition starting with (1), (2), (3,4,5), see A075631.
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FORMULA
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a(n) = A000217(A079801(n)) - A000217(A079801(n-1)) [From R. J. Mathar and Max Alekseyev]
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PROGRAM
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(PARI) A000217(n)= { return(n*(n+1)/2) ; } upto(first, osum, strict)= { local(trifirst, tstsu) ; trifirst=A000217(first-1) ; for(lst=first+1, first+100000000, tstsu=A000217(lst)-trifirst ; if(strict==1 && tstsu<= osum, next ; ) ; if( tstsu % osum == 0, return(lst) ; ) ; ) ; return(-1) ; } { a=1 ; first=2 ; for(n=2, 40, last=upto(first, a, 1) ; a=A000217(last)-A000217(first-1) ; print(a, ", ") ; first=last+1 ; ) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2006
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CROSSREFS
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Cf. A079799, A079800, A079801, A075631.
Sequence in context: A035069 A001869 A058425 this_sequence A037504 A105465 A089040
Adjacent sequences: A079795 A079796 A079797 this_sequence A079799 A079800 A079801
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 05 2003
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2006
Edited and extended by Max Alekseyev (maxale(AT)gmail.com), May 08 2009
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