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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
##### Keywords:
primes; sumsets; distribution of primes
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