A079798 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).

1, 5, 15, 45, 495, 16830, 4358970, 1159486020, 196818113950920, 3151092455396895169036800, 136084696980410308844836382925537725529600, 9996588705394796239042140065772174939073840705818917941136700639014745600

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = A000217(A079801(n)) - A000217(A079801(n-1)) [From R. J. Mathar and Max Alekseyev]

Prog

(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, May 06 2006

Crossrefs

Cf. A079799, A079800, A079801, A075631.

Sequence in context: A176611 A001869 A058425 * A344814 A037504 A197237

Adjacent sequences: A079795 A079796 A079797 * A079799 A079800 A079801

Keyword

nonn

Author

Amarnath Murthy, Feb 05 2003

Extensions

More terms from R. J. Mathar, May 06 2006

Edited and extended by Max Alekseyev, May 08 2009

Status

approved