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%I #5 Feb 12 2014 18:08:52
%S 1,4,7,13,22,49,97,190,385,769,1534,3073,6145,12286
%N Smallest positive integer of the form 3k+1 such that all subsets of {a(1),...,a(n)} have a different sum.
%C (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,...}.
%C (2) See A139218 for the corresponding sequence using integers of the form 3k+2.
%C (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.
%F It appears that a(n)=a(n-1)+a(n-2)+2a(n-3), for n>4.
%Y Cf. A001045, A139218.
%K nonn
%O 1,2
%A _John W. Layman_, Apr 11 2008
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