[seqfan] Smallest sum- and product-sets

[Charles Greathouse]

Let A+B = {a+b: a in A, b in B} and AB = {ab: a in A, b in B}. Then define
a(n) = min_S ( max(|S+S|, |S^2|) )
where the minimum is over all n-element subsets of the real numbers.

It is conjectured that a(n) is large -- that is, greater than n^(2-e) for
any positive e and all large enough n based on e (even though the sumset
and productset sequences alone are O(n)). Is this sequence in the OEIS? Is
the sequence altered by replacing "real numbers" with "integers"?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University