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%I #7 Apr 26 2023 10:03:21
%S 2,5,8,14,23,41,92,179,353,716,1427,2849,5708,11411
%N Smallest positive integer of the form 3k+2 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 {1,-2,-2,-5,-5,10,-5,-5,10,-5,-5,10,-5,...}.
%C (2) See A139217 for the corresponding sequence using integers of the form 3k+1.
%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)+2*a(n-3), for n>6.
%Y Cf. A001045, A139217.
%K nonn
%O 1,1
%A _John W. Layman_, Apr 11 2008