Journal of Integer Sequences, Vol. 11 (2008), Article 08.5.6

Integer Sequences Avoiding Prime Pairwise Sums

Yong-Gao Chen
Department of Mathematics
Nanjing Normal University
Nanjing 210097


The following result is proved: If $A\subseteq \{
1,\, 2,\, \ldots ,\, n\} $ is the subset of largest cardinality such that the sum of no two (distinct) elements of $A$ is prime, then $\vert A\vert=\lfloor(n+1)/2\rfloor$ 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,\, \ldots ,\, n\} $ such that the sum of no two (distinct) elements of $A$ is prime and $A$ contains elements of both parities?

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Received April 16 2008; revised version received December 13 2008. Published in Journal of Integer Sequences, December 13 2008.

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