The prime factors of the given numbers are 2 and 3.
If each term in the series is 2m3n for m,n≥0, we can build a series with increasing values of m and n, starting with m=n=0. The table below shows the products of 2m3n which are 144 or less:
| m |
n |
2m |
3n |
2m3n |
| 0 |
0 |
1 |
1 |
1 |
| 0 |
1 |
1 |
3 |
3 |
| 1 |
0 |
2 |
1 |
2 |
| 1 |
1 |
2 |
3 |
6 |
| 2 |
0 |
4 |
1 |
4 |
| 2 |
1 |
4 |
3 |
12 |
| 2 |
2 |
4 |
9 |
36 |
| 3 |
0 |
8 |
1 |
8 |
| 3 |
1 |
8 |
3 |
24 |
| 3 |
2 |
8 |
9 |
72 |
| 4 |
0 |
16 |
1 |
16 |
| 4 |
1 |
16 |
3 |
48 |
| 4 |
2 |
16 |
9 |
144 |
RULES
(1) The numbers in the n column cannot exceed the m number in the same row.
(2) The m numbers progressively increase by 1.
(3) The product (last column) must be between 1 and 144.
----oOo----
Numbers in green are given, and numbers in red are to fill the blanks. When these are arranged in numerical order we get:
1, 2, 3, 4, 6, 8, 12, 16, 24, 36, 48, 72, 144.
The red numbers coincide with the blanks, so they are the missing numbers.