1492 - List of Creatable Rationals

This is a list of all possible rational numbers which can be created using regular or repeated digits with only at most 1 occurrence of 1, 4, 9, or 2.  They are in lowest terms and in ascending order.  There are 678 different numbers.  The numbers 1, 1/5, 2, 21/50, 21/5, and 42 can all be created in two ways, but the rest can only be created in one way.

Here is some Mathematica code that can be used to generate this list:

DigitCombinations=Block[{n=Length[#]},Reap[Do[Sow[FromDigits[{Append[Take[p,{1,r}],Take[p,{r+1,n}]],d}]],{p,Permutations[#]},{d,0,n},{r,d,n}]][[2,1]]]&;
Sort[DeleteDuplicates[Flatten[Map[DigitCombinations,Rest[Subsets[{1,4,9,2}]],{1}]]],Less]

{1/10, 1/9, 3/25, 4/33, 11/90, 31/250, 124/999, 41/330, 28/225, 1249/10000, 1249/9999, 208/1665, 1237/9900, 1/8, 129/1000, 43/333, 64/495, 647/5000, 1294/9999, 431/3330, 233/1800, 641/4950, 13/100, 7/50, 14/99, 71/500, 142/999, 32/225, 47/330, 1429/10000, 1429/9999, 283/1980, 238/1665, 143/1000, 13/90, 149/1000, 149/999, 373/2500, 1492/9999, 1343/9000, 497/3330, 739/4950, 74/495, 3/20, 19/100, 19/99, 24/125, 64/333, 173/900, 481/2500, 1924/9999, 127/660, 433/2250, 641/3330, 191/990, 97/500, 194/999, 971/5000, 1942/9999, 437/2250, 641/3300, 647/3330, 7/36, 193/990, 1/5, 21/100, 19/90, 7/33, 107/500, 106/495, 214/999, 193/900, 2149/10000, 2147/9990, 2149/9999, 532/2475, 43/200, 219/1000, 217/990, 73/333, 1097/5000, 1096/4995, 2194/9999, 79/360, 2173/9900, 11/50, 2/9, 6/25, 241/1000, 217/900, 241/999, 239/990, 2419/10000, 479/1980, 2419/9999, 2417/9990, 121/500, 8/33, 11/45, 249/1000, 2491/10000, 1121/4500, 2491/9999, 2489/9990, 2467/9900, 83/333, 247/990, 1/4, 29/100, 291/1000, 131/450, 97/333, 1457/5000, 577/1980, 2914/9999, 2623/9000, 1456/4995, 289/990, 29/99, 147/500, 2941/10000, 2647/9000, 2941/9999, 728/2475, 2939/9990, 98/333, 53/180, 146/495, 3/10, 2/5, 41/100, 37/90, 103/250, 68/165, 371/900, 412/999, 4129/10000, 275/666, 1022/2475, 4129/9999, 413/1000, 41/99, 419/1000, 83/198, 262/625, 698/1665, 3773/9000, 4192/9999, 4151/9900, 419/999, 21/50, 421/1000, 379/900, 139/330, 421/999, 4219/10000, 4177/9900, 281/666, 4219/9999, 211/500, 19/45, 14/33, 429/1000, 4291/10000, 1931/4500, 1429/3330, 4291/9999, 4249/9900, 85/198, 143/333, 43/100, 4/9, 49/100, 491/1000, 221/450, 307/625, 1621/3300, 4421/9000, 4912/9999, 818/1665, 491/999, 487/990, 123/250, 4921/10000, 4429/9000, 406/825, 4921/9999, 1639/3330, 443/900, 164/333, 244/495, 49/99, 1/2, 9/10, 91/100, 41/45, 114/125, 301/330, 821/900, 2281/2500, 1823/1998, 3011/3300, 2053/2250, 9124/9999, 304/333, 457/500, 181/198, 4571/5000, 9133/9990, 2057/2250, 3017/3300, 9142/9999, 823/900, 914/999, 91/99, 23/25, 921/1000, 829/900, 152/165, 4607/5000, 4561/4950, 1841/1998, 8293/9000, 9214/9999, 307/333, 83/90, 231/250, 9241/10000, 8317/9000, 4616/4995, 9149/9900, 9241/9999, 61/66, 208/225, 308/333, 92/99, 47/50, 941/1000, 847/900, 2353/2500, 1553/1650, 8471/9000, 9403/9990, 9412/9999, 466/495, 941/999, 471/500, 9421/10000, 8479/9000, 3109/3300, 4706/4995, 9421/9999, 212/225, 311/330, 314/333, 17/18, 94/99, 1, 6/5, 11/9, 31/25, 41/33, 56/45, 1249/1000, 416/333, 1237/990, 5/4, 129/100, 128/99, 647/500, 431/333, 233/180, 641/495, 13/10, 7/5, 71/50, 64/45, 47/33, 1429/1000, 283/198, 476/333, 143/100, 13/9, 149/100, 373/250, 1343/900, 497/333, 739/495, 148/99, 3/2, 19/10, 48/25, 173/90, 481/250, 127/66, 433/225, 641/333, 191/99, 97/50, 971/500, 437/225, 641/330, 647/333, 35/18, 193/99, 2, 21/10, 19/9, 107/50, 212/99, 193/90, 2149/1000, 2147/999, 1064/495, 43/20, 219/100, 217/99, 1097/500, 2192/999, 79/36, 2173/990, 11/5, 12/5, 241/100, 217/90, 239/99, 2419/1000, 479/198, 2417/999, 121/50, 22/9, 249/100, 2491/1000, 1121/450, 2489/999, 2467/990, 247/99, 5/2, 29/10, 291/100, 131/45, 1457/500, 577/198, 2623/900, 2912/999, 289/99, 147/50, 2941/1000, 2647/900, 1456/495, 2939/999, 53/18, 292/99, 3, 4, 41/10, 37/9, 103/25, 136/33, 371/90, 4129/1000, 1375/333, 2044/495, 413/100, 419/100, 415/99, 524/125, 1396/333, 3773/900, 4151/990, 21/5, 421/100, 379/90, 139/33, 4219/1000, 4177/990, 1405/333, 211/50, 38/9, 429/100, 4291/1000, 1931/450, 1429/333, 4249/990, 425/99, 43/10, 49/10, 491/100, 221/45, 614/125, 1621/330, 4421/900, 1636/333, 487/99, 123/25, 4921/1000, 4429/900, 812/165, 1639/333, 443/90, 488/99, 5, 9, 91/10, 82/9, 228/25, 301/33, 821/90, 2281/250, 9115/999, 3011/330, 2053/225, 457/50, 905/99, 4571/500, 9133/999, 2057/225, 3017/330, 823/90, 46/5, 921/100, 829/90, 304/33, 4607/500, 4561/495, 9205/999, 8293/900, 83/9, 231/25, 9241/1000, 8317/900, 9232/999, 9149/990, 305/33, 416/45, 47/5, 941/100, 847/90, 2353/250, 1553/165, 8471/900, 9403/999, 932/99, 471/50, 9421/1000, 8479/900, 3109/330, 9412/999, 424/45, 311/33, 85/9, 12, 62/5, 112/9, 1249/100, 1237/99, 25/2, 129/10, 647/50, 233/18, 1282/99, 13, 14, 71/5, 128/9, 1429/100, 1415/99, 143/10, 149/10, 373/25, 1343/90, 1478/99, 15, 19, 96/5, 173/9, 481/25, 635/33, 866/45, 97/5, 971/50, 874/45, 641/33, 175/9, 21, 107/5, 193/9, 2149/100, 2128/99, 43/2, 219/10, 1097/50, 395/18, 2173/99, 22, 24, 241/10, 217/9, 2419/100, 2395/99, 121/5, 249/10, 2491/100, 1121/45, 2467/99, 25, 29, 291/10, 262/9, 1457/50, 2885/99, 2623/90, 147/5, 2941/100, 2647/90, 2912/99, 265/9, 41, 206/5, 371/9, 4129/100, 4088/99, 413/10, 419/10, 1048/25, 3773/90, 4151/99, 42, 421/10, 379/9, 4219/100, 4177/99, 211/5, 429/10, 4291/100, 1931/45, 4249/99, 43, 49, 491/10, 442/9, 1228/25, 1621/33, 4421/90, 246/5, 4921/100, 4429/90, 1624/33, 443/9, 91, 456/5, 821/9, 2281/25, 3011/33, 4106/45, 457/5, 4571/50, 4114/45, 3017/33, 823/9, 92, 921/10, 829/9, 4607/50, 9122/99, 8293/90, 462/5, 9241/100, 8317/90, 9149/99, 832/9, 94, 941/10, 847/9, 2353/25, 3106/33, 8471/90, 471/5, 9421/100, 8479/90, 3109/33, 848/9, 124, 1249/10, 125, 129, 647/5, 1165/9, 142, 1429/10, 143, 149, 746/5, 1343/9, 192, 962/5, 1732/9, 194, 971/5, 1748/9, 214, 2149/10, 215, 219, 1097/5, 1975/9, 241, 2419/10, 242, 249, 2491/10, 2242/9, 291, 1457/5, 2623/9, 294, 2941/10, 2647/9, 412, 4129/10, 413, 419, 2096/5, 3773/9, 421, 4219/10, 422, 429, 4291/10, 3862/9, 491, 2456/5, 4421/9, 492, 4921/10, 4429/9, 912, 4562/5, 8212/9, 914, 4571/5, 8228/9, 921, 4607/5, 8293/9, 924, 9241/10, 8317/9, 941, 4706/5, 8471/9, 942, 9421/10, 8479/9, 1249, 1294, 1429, 1492, 1924, 1942, 2149, 2194, 2419, 2491, 2914, 2941, 4129, 4192, 4219, 4291, 4912, 4921, 9124, 9142, 9214, 9241, 9412, 9421}