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Integer sequences avoiding prime pairwise sums. (English) Zbl 1196.11042
Summary: The following result is proved: If \(A\subseteq \{ 1,\, 2,\, \dots ,\, n\} \) is the subset of largest cardinality such that the sum of no two (distinct) elements of \(A\) is prime, then \(| A|=\lfloor(n+1)/2\rfloor\) and all the elements of \(A\) have the same parity. The following open question is posed: what is the largest cardinality of \(A\subseteq \{ 1,\, 2,\, \dots ,\, n\} \) such that the sum of no two (distinct) elements of \(A\) is prime and \(A\) contains elements of both parities?
MSC:
11B75 Other combinatorial number theory
05D05 Extremal set theory
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