%N a(n) is the smallest number such that for, all m<n, both a(n)*a(m) and a(n)+a(m) are nonsquares.
%C No number occurs more than once in the sequence because if a(n)=m then if m occurs again then a(n)*m=m^2. a(n) is always bigger than a(n-1) because all numbers less than a(n-1) have been checked to see if they make a square and if any do then because of the uniqueness of each value of a(n) then they must have already occurred in the sequence previously.
%e a(4) = 6 because a(1)*6 = 6, a(2)*6 = 12, a(3)*6 = 30 and a(1)+6 = 7, a(2)+6 = 8, a(3)+6=11, all nonsquares
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 18 2001