The following pictures show n unit equilateral triangles packed inside the smallest known tan (with short side length s).
1. 
s = √(3/2) = 1.22474+
Trivial.
2. 
s = √3 = 1.73205+
Trivial.
3. 
s = (√3+1)/√2 = 1.93185+
Trivial.
4. 
s = (3+√3)/2 = 2.36602+
Found by Jonathan Viquerat
in May 2026.
5. 
s = (3√2+√6+2√3)/4 = 2.53905+
Found by Jonathan Viquerat
in May 2026.
6. 
s = √2+√(3/2) = 2.63895+
Found by Jonathan Viquerat
in May 2026.
7. 
s = 2.78972+
Found by Jonathan Viquerat
in May 2026.
8. 
s = 3.07313+
Found by Jonathan Viquerat
in May 2026.
9. 
s = 3.18252+
Found by Jonathan Viquerat
in May 2026.
10. 
s = 3.34084+
Found by Jonathan Viquerat
in May 2026.
11. 
s = 3.46951+
Found by Jonathan Viquerat
in May 2026.
12. 
s = 3.62487+
Found by Bhavithran Ananthan
in July 2026.
13. 
s = 3.71163+
Found by Jonathan Viquerat
in May 2026.
14. 
s = 3.88268+
Found by Jonathan Viquerat
in May 2026.
15. 
s = 3.98382+
Found by Thomas Greenleaf
in June 2026.
16. 
s = 4.03901+
Found by Thomas Greenleaf
in June 2026.
17. 
s = 4.20127+
Found by Bhavithran Ananthan
in July 2026.
18. 
s = 4.27120+
Found by Thomas Greenleaf
in June 2026.
19. 
s = 4.45701+
Found by Thomas Greenleaf
in June 2026.
20. 
s = 4.56124+
Found by Bhavithran Ananthan
in July 2026.
21. 
s = 4.64141+
Found by Akshaj Shandilya
in July 2026.
22. 
s = 4.73276+
Found by Akshaj Shandilya
in July 2026.
23. 
s = 4.82974+
Found by Akshaj Shandilya
in July 2026.
24. 
s = 4.91168+
Found by Akshaj Shandilya
in July 2026.
25. 
s = 5.05586+
Found by Akshaj Shandilya
in July 2026.
26. 
s = 5.10960+
Found by Akshaj Shandilya
in July 2026.
27. 
s = 5.19773+
Found by Akshaj Shandilya
in July 2026.
28. 
s = 5.32367+
Found by Akshaj Shandilya
in July 2026.
29. 
s = 5.40552+
Found by Akshaj Shandilya
in July 2026.
30. 
s = 5.46262+
Found by Akshaj Shandilya
in July 2026.