I hope this is readable. Obiously merges with 5 are best. But in the puzzles you have chain reactions and for home you can deactivate those.
Read notation from right to left. So starting with 5 yields 2 better level and 0 starting level. Since for 6 and 7 you effectifly loose a starting item, those are worse. With no chaining you get the optimal output with multiples of 5. 20 looks interesting, probably bc 20 yields 8 with one lvl higher and 8 yield 2+1 level higher, thus having 3 to get to new level. Any higher item # is really tedious to get the number of items right.
# Chained Only 5er Home - no Chain 3 1.0 3 1.0 4 1.1 4 1.1 5 2.0 2-0 2.0 6 2.0 2-1 2.0 7 2.1 2-2 2.1 8 1.0.0 2-3 3.0 9 1.0.0 2-4 3.0 10 1.1.0 4-0 4.0 11 1.1.0 4-1 4.0 12 1.1.1 4-2 4.1 13 2.0.0 4-3 5.0 14 2.0.0 4-4 15 2.0.0 2-1-0 16 2.0.0 2-1-1 17 2.0.1 2-1-2 18 2.1.0 2-1-3 19 2.1.0 2-1-4 20 1.0.0.0 2-3-0