Existence Table

1=unit

2=prime

3=prime

4=X   PoP (4=/=1+2)

5=prime

6=3+2+1

7=prime

8=X   PoP (8=/=4+2+1)

9=X   PoP (9=/=3+3+1)

10=X  2p (10=/=5+2+1)

11=prime

12=6+3+2+1 (12=4+4+3+1, but if two 4s, a domino must tile)

13=prime

14=X   2p (14=/=7+2+1)

15=X   (15=5+3+3+3+1, but there aren’t three trominoes)

16=X   PoP (16=/=8+4+2+1) (16=8+4+4, but if two 4s, a domino must tile)

17=prime

18=9+3+3+2+1=9+6+2+1

19=prime

20=10+5+4+1=5+5+5+4+1=10=?

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