The following pictures show n tans (with short side 1) packed inside the smallest known hexagons (with side s).
1. 
s = .74062+
Trivial.
2. 
s = (3+√3)/6 = .78867+
Found by Jonathan Viquerat
in May 2026.
3. 
s = .98883+
Found by Jonathan Viquerat
in May 2026.
4. 
s = 1.05845+
Found by Jonathan Viquerat
in May 2026.
5. 
s = 1.13976+
Found by Jonathan Viquerat
in May 2026.
6. 
s = 1.20610+
Found by Jonathan Viquerat
in May 2026.
7. 
s = 1.30962+
Found by Jonathan Viquerat
in May 2026.
8. 
s = 1.37884+
Found by Jonathan Viquerat
in May 2026.
9. 
s = 1.46147+
Found by Jonathan Viquerat
in May 2026.
10. 
s = 1.55742+
Found by Jonathan Viquerat
in May 2026.
11. 
s = 1.59264+
Found by Jonathan Viquerat
in May 2026.
12. 
s = 1.67995+
Found by Jonathan Viquerat
in May 2026.
13. 
s = 1.75387+
Found by Jonathan Viquerat
in May 2026.
14. 
s = 1.83513+
Found by Jonathan Viquerat
in May 2026.
15. 
s = 1.87908+
Found by Jonathan Viquerat
in May 2026.
16. 
s = 1.90884+
Found by Jonathan Viquerat
in May 2026.
17. 
s = 1.99246+
Found by Jonathan Viquerat
in May 2026.
18. 
s = 2.03807+
Found by Jonathan Viquerat
in May 2026.
19. 
s = 2.12378+
Found by Jonathan Viquerat
in May 2026.
20. 
s = 2.16065+
Found by Jonathan Viquerat
in May 2026.