Search: id:A139218
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%I A139218
%S A139218 2,5,8,14,23,41,92,179,353,716,1427,2849,5708,11411
%N A139218 Smallest positive integer of the form 3k+2 such that all subsets of {a(1),
               ...,a(n)} have a different sum.
%C A139218 (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 A139218 (2) See A139217 for the corresponding sequence using integers of the 
               form 3k+1.
%C A139218 (3) Maximilian Hasler, in a SeqFan memo dated Apr. 9, 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 A139218 It appears that a(n)=a(n-1)+a(n-2)+2a(n-3), for n>6.
%Y A139218 Cf. A001045, A139217.
%Y A139218 Sequence in context: A000094 A058578 A023674 this_sequence A017988 A103077 
               A090980
%Y A139218 Adjacent sequences: A139215 A139216 A139217 this_sequence A139219 A139220 
               A139221
%K A139218 nonn
%O A139218 1,1
%A A139218 John W. Layman (layman(AT)math.vt.edu), Apr 11 2008

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