This list has, for n=1,2,...,100, the path of least cost to n, and shows both addition and multiplication steps. When there is a tie, the shortest path is shown. Further ties are broken by using the lexicographically first path.

{1, {1}}
{2, {1, 2}}
{3, {1, 2, 3}}
{4, {1, 2, 4}}
{5, {1, 2, 4, 5}}
{6, {1, 2, 3, 6}}
{7, {1, 2, 3, 4, 7}}
{8, {1, 2, 4, 8}}
{9, {1, 2, 3, 9}}
{10, {1, 2, 4, 5, 10}}
{11, {1, 2, 3, 9, 11}}
{12, {1, 2, 3, 4, 12}}
{13, {1, 2, 3, 4, 9, 13}}
{14, {1, 2, 3, 4, 7, 14}}
{15, {1, 2, 3, 5, 15}}
{16, {1, 2, 4, 16}}
{17, {1, 2, 4, 16, 17}}
{18, {1, 2, 3, 6, 18}}
{19, {1, 2, 3, 4, 16, 19}}
{20, {1, 2, 4, 5, 20}}
{21, {1, 2, 3, 4, 7, 21}}
{22, {1, 2, 3, 9, 11, 22}}
{23, {1, 2, 3, 4, 5, 20, 23}}
{24, {1, 2, 4, 6, 24}}
{25, {1, 2, 4, 5, 25}}
{26, {1, 2, 4, 5, 25, 26}}
{27, {1, 2, 3, 9, 27}}
{28, {1, 2, 3, 4, 7, 28}}
{29, {1, 2, 3, 9, 27, 29}}
{30, {1, 2, 3, 5, 6, 30}}
{31, {1, 2, 3, 4, 9, 27, 31}}
{32, {1, 2, 4, 8, 32}}
{33, {1, 2, 4, 8, 32, 33}}
{34, {1, 2, 4, 8, 32, 34}}
{35, {1, 2, 4, 5, 7, 35}}
{36, {1, 2, 3, 6, 36}}
{37, {1, 2, 3, 6, 36, 37}}
{38, {1, 2, 3, 6, 36, 38}}
{39, {1, 2, 3, 6, 36, 39}}
{40, {1, 2, 4, 5, 8, 40}}
{41, {1, 2, 4, 5, 8, 40, 41}}
{42, {1, 2, 3, 6, 7, 42}}
{43, {1, 2, 3, 4, 9, 16, 27, 43}}
{44, {1, 2, 3, 4, 8, 11, 44}}
{45, {1, 2, 3, 5, 9, 45}}
{46, {1, 2, 3, 5, 9, 45, 46}}
{47, {1, 2, 3, 5, 9, 45, 47}}
{48, {1, 2, 3, 4, 12, 48}}
{49, {1, 2, 3, 4, 7, 49}}
{50, {1, 2, 4, 5, 10, 50}}
{51, {1, 2, 3, 4, 12, 48, 51}}
{52, {1, 2, 3, 4, 9, 13, 52}}
{53, {1, 2, 3, 4, 7, 49, 53}}
{54, {1, 2, 3, 6, 9, 54}}
{55, {1, 2, 3, 6, 9, 54, 55}}
{56, {1, 2, 3, 4, 7, 8, 56}}
{57, {1, 2, 3, 4, 16, 19, 57}}
{58, {1, 2, 3, 9, 27, 29, 58}}
{59, {1, 2, 3, 4, 8, 9, 27, 32, 59}}
{60, {1, 2, 4, 6, 10, 60}}
{61, {1, 2, 4, 6, 10, 60, 61}}
{62, {1, 2, 3, 4, 9, 27, 31, 62}}
{63, {1, 2, 3, 4, 7, 9, 63}}
{64, {1, 2, 4, 8, 64}}
{65, {1, 2, 4, 8, 64, 65}}
{66, {1, 2, 4, 8, 64, 66}}
{67, {1, 2, 3, 4, 8, 64, 67}}
{68, {1, 2, 4, 8, 64, 68}}
{69, {1, 2, 4, 5, 8, 64, 69}}
{70, {1, 2, 4, 5, 7, 10, 70}}
{71, {1, 2, 3, 4, 7, 8, 64, 71}}
{72, {1, 2, 3, 6, 12, 72}}
{73, {1, 2, 3, 6, 12, 72, 73}}
{74, {1, 2, 3, 6, 12, 72, 74}}
{75, {1, 2, 3, 5, 15, 75}}
{76, {1, 2, 3, 4, 16, 19, 76}}
{77, {1, 2, 3, 4, 7, 11, 77}}
{78, {1, 2, 3, 6, 12, 13, 78}}
{79, {1, 2, 3, 4, 5, 15, 75, 79}}
{80, {1, 2, 4, 5, 16, 80}}
{81, {1, 2, 3, 9, 81}}
{82, {1, 2, 3, 9, 81, 82}}
{83, {1, 2, 3, 9, 81, 83}}
{84, {1, 2, 3, 9, 81, 84}}
{85, {1, 2, 3, 4, 9, 81, 85}}
{86, {1, 2, 3, 4, 9, 16, 27, 43, 86}}
{87, {1, 2, 3, 6, 9, 81, 87}}
{88, {1, 2, 3, 4, 8, 11, 88}}
{89, {1, 2, 4, 8, 9, 81, 89}}
{90, {1, 2, 3, 9, 10, 90}}
{91, {1, 2, 3, 4, 8, 9, 27, 64, 91}}
{92, {1, 2, 3, 9, 10, 90, 92}}
{93, {1, 2, 3, 4, 9, 12, 81, 93}}
{94, {1, 2, 3, 4, 9, 10, 90, 94}}
{95, {1, 2, 3, 4, 5, 15, 19, 95}}
{96, {1, 2, 4, 6, 16, 96}}
{97, {1, 2, 4, 6, 16, 96, 97}}
{98, {1, 2, 3, 4, 7, 14, 98}}
{99, {1, 2, 3, 9, 11, 99}}
{100, {1, 2, 4, 5, 10, 100}}