The greedy algorithm was used to generate sets of positive integers containing no subset of the form
{
x
,
x
+
y
,
x
+
2
y
}
\{ x,x + y,x + 2y\}
,
{
x
,
x
+
y
,
x
+
3
y
}
\{ x,x + y,x + 3y\}
,
{
x
,
x
+
2
y
,
x
+
3
y
}
\{ x,x + 2y,x + 3y\}
,
{
x
,
x
+
3
y
,
x
+
4
y
}
\{ x,x + 3y,x + 4y\}
,
{
x
,
x
+
3
y
,
x
+
5
y
}
\{ x,x + 3y,x + 5y\}
, and
{
x
,
x
+
y
,
x
+
2
y
,
x
+
3
y
}
\{ x,x + y,x + 2y,x + 3y\}
, respectively. All of these sets have peaks of density in roughly geometric progression.