given any two numbers k,j(adsbygoogle = window.adsbygoogle || []).push({});

what is the largest sequence of integers such that the sum of any k consecutive terms is negative and the sum of any j consecutive terms is positive

and

how may we find a subset containing k of the first n numbers such that out of all subsets with k elements, this subset has the smallest arithmetic progression with common difference j. and out of all subsets with k elements, does this subset contain the largest arithmetic progression for some other integer?

ideas would be very much appreciated

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# Sequence of integers and arithmetic progressions

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