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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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closed as off-topic by Ricardo Andrade, Evan Jenkins, Steven Landsburg, Andrés E. Caicedo, Andrey Rekalo Oct 19 '13 at 7:39

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The sequence $.1, .01, .001, .0001,\ldots$ will do the trick. – Barry Cipra May 9 '13 at 13:53

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

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Other sequences that immediately come to mind are vector-like 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.

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Thanks a lot Sundi – jyotirmoy sundi Apr 26 '13 at 1:34

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