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 


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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. 

