Take the tour ×  Probably, I should call it a sequence, anyway,
is there a sequence/set (Fibonacci is a valid answer for this
question (minus the first three Fibonacci numbers including
zero), but too big) where any $k$-subset (subset/aggregation of
terms within sequence, with $k$ elements) will have a unique sum
that can't be achieved by any other k-subset?  This PDF is
somewhere along the same lines... Thanks all.  Edit I'm asking
for the smallest such series, and it must satisfy (as one
commenter asked) for all $k$ (well, if that's not possible, just
odd or even $k$ will do)  share|improve this question Just in
case anyone missed out, I've already given one possible answer,
the Fibonacci sequence with the initial $0, 1, 1$ removed. – 
Mach9 Apr 11 '12 at 13:16 The powers of two, $a_k=2^k$ have this
property. Actually, for any integer $b>1$, $a_k=b^k$ have this
property. –  Thomas Andrews Apr 11 '12 at 13:21 D you want this
property to be true for all $k$, or do you want it true just for
a single value of $