Density Map for the 3n+1 Problem

range

10

Start with a number

x

and repeat: if

x

is even, halve it; if

x

is odd, triple it and add one. For example, starting with 3 gives 3, 10, 5, 16, 8, 4, 2, 1. Rearrange the numbers in ascending order and mark those places across row

x

so that the third row has marks at the places 1, 2, 3, 4, 5, 10, 16.