A139218 Smallest positive integer of the form 3k+2 such that all subsets of {a(1),...,a(n)} have a different sum.

2, 5, 8, 14, 23, 41, 92, 179, 353, 716, 1427, 2849, 5708, 11411

Offset: 1

Author

John W. Layman, Apr 11 2008

Keywords

• nonn

Comments

(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,...}.

(2) See A139217 for the corresponding sequence using integers of the form 3k+1.

(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.

Crossrefs

Cf. A001045, A139217.

Formula

It appears that a(n) = a(n-1)+a(n-2)+2*a(n-3), for n>6.