An extremal problem in subsequence sum

Jin-Hui Fang and Guoyou Qian

Applied Mathematics and Computation, 2022, vol. 423, issue C

Abstract: Let N denote the set of all positive integers and let N0=N⋃{0}. For a strictly increasing sequence A of positive integers, let P(A) be the set of all integers which can be represented as the finite sum of distinct terms of A. Fix an integer b such that b∈{1,2,4,7,8} or b≥11. For every integer k≥1, define inductively ck(b) as the smallest positive integer r so that there exist two strictly increasing sequences A={ai}i=1∞ and B={bi}i=1∞ of positive integers such that (1) b1=c1(b)=b,b2=c2(b)=3b+5; (2) bi=ci(b) for all 3≤i≤k−1 and bk=r; (3) P(A)=N0∖{bi:i∈N} and ai≤∑jKeywords: Subsequence sum; Burr’s problem; Complement; Extremal problem (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322000832

DOI: 10.1016/j.amc.2022.126997

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