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A139217
Smallest positive integer of the form 3k+1 such that all subsets of {a(1),...,a(n)} have a different sum.
3
1, 4, 7, 13, 22, 49, 97, 190, 385, 769, 1534, 3073, 6145, 12286
OFFSET
1,2
COMMENTS
(1) It appears that {a(n+1)-2a(n)} is eventually periodic, with values {2,-1,-1,-4,5,-1,-4,5,-1,-4,5,-1,-4,...}.
(2) See A139218 for the corresponding sequence using integers of the form 3k+2.
(3) M. F. Hasler, in a SeqFan memo dated Apr 09 2008, notes that the Jacobsthal sequence (A001045) from a(2) on (i.e., 1,3,5,11,21,...) gives the smallest positive odd integer such that all subsets of {a(2),...,a(n)} have a different sum.
FORMULA
It appears that a(n)=a(n-1)+a(n-2)+2a(n-3), for n>4.
CROSSREFS
Sequence in context: A111314 A316861 A298354 * A038391 A073832 A265160
KEYWORD
nonn
AUTHOR
John W. Layman, Apr 11 2008
STATUS
approved