Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence.
Thanks Sundi
Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence. Thanks Sundi 

closed as offtopic by Ricardo Andrade, Evan Jenkins, Steven Landsburg, Andres Caicedo, Andrey Rekalo Oct 19 '13 at 7:39This question appears to be offtopic. The users who voted to close gave this specific reason:



got it, thanks, just a gp series would do. 1,2,4,8,16... 


Other sequences that immediately come to mind are vectorlike expressions $$(1, 0, 0, 0, 0, ...), (0, 1, 0, 0, 0, ...) , (0, 0, 1, 0, 0, ...), ...$$ (or matrices or tensors) or the sequence $(a_n)$ of approximations of transcendentals like Liouville's number $$a_n = \sum_{k=0}^{n} \frac{1}{k!}$$ or just terminating rationals with different points of termination behind the decimal point $$0.1, 0.11, 0.111, ...$$ or before$$1, 10, 100, ... $$ But that's already very close to the first answer. 

