A139217 Smallest positive integer of the form 3k+1 such that all subsets of {a(1),...,a(n)} have a different sum.

1, 4, 7, 13, 22, 49, 97, 190, 385, 769, 1534, 3073, 6145, 12286

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 {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.

Crossrefs

Cf. A001045, A139218.

Formula

It appears that a(n)=a(n-1)+a(n-2)+2a(n-3), for n>4.