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A139217 Smallest positive integer of the form 3k+1 such that all subsets of {a(1),...,a(n)} have a different sum. 3
1, 4, 7, 13, 22, 49, 97, 190, 385, 769, 1534, 3073, 6145, 12286 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

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) 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.

FORMULA

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

CROSSREFS

Cf. A001045, A139218.

Sequence in context: A008471 A156622 A111314 * A038391 A090854 A039694

Adjacent sequences:  A139214 A139215 A139216 * A139218 A139219 A139220

KEYWORD

nonn

AUTHOR

John W. Layman (layman(AT)math.vt.edu), Apr 11 2008

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Last modified February 14 14:07 EST 2012. Contains 205623 sequences.