Integer Sequences Avoiding Prime Pairwise Sums

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

is prime, then $\vert A\vert=\lfloor(n+1)/2\rfloor$ and all the elements of

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

is prime and

contains elements of both parities?

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

Integer Sequences Avoiding Prime Pairwise Sums

Yong-Gao Chen Department of Mathematics Nanjing Normal University Nanjing 210097 P. R. CHINA

Yong-Gao Chen
Department of Mathematics
Nanjing Normal University
Nanjing 210097
P. R. CHINA