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Finding FF(2)...
step 2: 1/3 + 1/4 + 1/5 + 1/9 + 2/15 + 1/25 + 1/-30 + 1/-45 + 1/-75 + 1/900
step 5: 1/3 + 1/4 + 1/5 + 1/9 + 1/15 + 1/25 + 1/30 + 1/-30 + 1/-45 + 1/45 + 1/75 + 1/-75 + 1/-450 + 1/900
step 4: 1/3 + 1/4 + 1/5 + 1/9 + 1/15 + 1/25 + 1/-450 + 1/900
FF(2) = [3 4 5 9 15 25 -450 900]
Finding FF(3)...
step 2: 1/5 + 1/6 + 1/9 + 1/10 + 1/16 + 1/18 + 1/25 + 2/27 + 1/30 + 4/45 + 1/50 + 1/81 + 2/125 + 2/135 + 2/375 + 1/625 + 1/-675 + 1/-900 + 1/-1125 + 1/1350 + 1/1800 + 1/-2025 + 1/2250 + 1/-3375 + 1/4050 + 1/-5625 + 1/6750 + 1/11250 + 1/-202500 + 1/202500 + 1/810000
step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/16 + 1/18 + 1/25 + 2/27 + 1/30 + 4/45 + 1/50 + 1/81 + 2/125 + 2/135 + 2/375 + 1/625 + 1/-675 + 1/-900 + 1/-1125 + 1/1350 + 1/1800 + 1/-2025 + 1/2250 + 1/-3375 + 1/4050 + 1/-5625 + 1/6750 + 1/11250 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/16 + 1/18 + 1/25 + 1/27 + 1/30 + 1/45 + 1/50 + 1/54 + 2/81 + 3/90 + 1/125 + 5/135 + 3/225 + 1/250 + 1/270 + 2/375 + 1/405 + 2/625 + 1/-675 + 1/675 + 1/750 + 1/-810 + 1/-900 + 1/1125 + 1/-1125 + 1/1350 + 3/-1350 + 1/1800 + 1/1875 + 1/-2025 + 1/2250 + 1/-3375 + 1/-3750 + 1/4050 + 1/-4050 + 1/-5625 + 1/6750 + 1/11250 + 1/-11250 + 1/810000
step 2: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 2/27 + 1/45 + 1/50 + 1/54 + 1/75 + 2/81 + 1/125 + 1/250 + 1/270 + 2/375 + 1/405 + 1/-450 + 2/625 + 1/-675 + 1/675 + 1/750 + 1/-810 + 1/-900 + 1/1125 + 1/-1125 + 1/1350 + 1/1800 + 1/1875 + 1/-2025 + 1/2250 + 1/-3375 + 1/-3750 + 1/4050 + 1/-4050 + 1/-5625 + 1/6750 + 1/11250 + 1/-11250 + 1/810000
step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 2/27 + 1/45 + 1/50 + 1/54 + 1/75 + 2/81 + 1/125 + 1/250 + 1/270 + 2/375 + 1/405 + 1/-450 + 2/625 + 1/750 + 1/-810 + 1/-900 + 1/1350 + 1/1800 + 1/1875 + 1/-2025 + 1/2250 + 1/-3375 + 1/-3750 + 1/-5625 + 1/6750 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 2/54 + 1/75 + 2/81 + 1/125 + 1/135 + 1/162 + 1/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-450 + 1/625 + 2/750 + 2/-810 + 1/-900 + 1/1125 + 1/1250 + 1/1350 + 1/1800 + 3/1875 + 1/-2025 + 1/2250 + 1/-2430 + 1/3125 + 1/-3375 + 1/-3750 + 1/-5625 + 1/6750 + 1/-11250 + 1/-18750 + 1/810000
step 2: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 2/27 + 1/45 + 1/50 + 1/75 + 2/81 + 1/125 + 1/135 + 1/162 + 1/243 + 1/250 + 1/270 + 2/375 + 2/405 + 1/-405 + 1/-450 + 2/625 + 1/-900 + 1/1125 + 1/1250 + 1/1350 + 1/1800 + 1/-2025 + 1/2250 + 1/-2430 + 1/3125 + 1/-3375 + 1/-3750 + 1/-5625 + 1/6750 + 1/-11250 + 1/-18750 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 2/81 + 1/125 + 2/135 + 2/162 + 2/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-405 + 1/-450 + 1/625 + 1/750 + 1/810 + 1/-810 + 1/-900 + 2/1125 + 1/1215 + 2/1250 + 1/1350 + 1/1800 + 2/1875 + 1/-2025 + 1/2025 + 1/2250 + 2/-2430 + 2/3125 + 1/-3375 + 1/-3750 + 1/-5625 + 1/6750 + 2/-11250 + 1/-12150 + 2/-18750 + 1/810000
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step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 2/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/125 + 2/135 + 2/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-405 + 1/-450 + 2/625 + 1/750 + 1/-900 + 2/1125 + 1/1350 + 1/1800 + 2/1875 + 1/2250 + 2/3125 + 1/-3375 + 1/-3750 + 2/-5625 + 1/6750 + 1/-9375 + 1/-12150 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 2/54 + 1/75 + 1/81 + 1/125 + 2/135 + 1/243 + 1/250 + 2/270 + 1/375 + 1/-405 + 2/405 + 1/-450 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/-810 + 1/810 + 1/-900 + 1/1125 + 2/1215 + 1/1250 + 1/1350 + 1/1800 + 2/1875 + 1/2025 + 2/2250 + 2/3125 + 1/3375 + 1/-3375 + 1/-3750 + 1/3750 + 1/-4050 + 2/5625 + 1/-5625 + 1/6250 + 1/6750 + 1/-7290 + 2/9375 + 1/-9375 + 1/-11250 + 2/-12150 + 1/15625 + 1/-16875 + 1/-18750 + 1/-28125 + 1/-33750 + 1/-56250 + 1/-93750 + 1/168750 + 1/810000
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step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 2/27 + 2/45 + 1/50 + 1/75 + 1/81 + 1/125 + 1/243 + 1/250 + 1/375 + 2/405 + 1/-405 + 1/-450 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/-900 + 2/1125 + 2/1215 + 1/1250 + 1/1350 + 1/1800 + 2/1875 + 1/2025 + 2/3125 + 1/-4050 + 2/5625 + 1/-5625 + 1/-6075 + 1/6250 + 1/6750 + 1/-7290 + 1/-9375 + 2/9375 + 1/-11250 + 1/15625 + 1/-16875 + 1/-18750 + 1/-28125 + 1/-33750 + 1/-56250 + 1/-93750 + 1/168750 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 2/81 + 1/90 + 1/125 + 2/135 + 1/225 + 1/243 + 1/250 + 1/375 + 1/-405 + 1/405 + 1/-450 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/-810 + 1/810 + 1/-900 + 1/1125 + 2/1215 + 1/1250 + 1/1350 + 1/-1350 + 1/1800 + 1/1875 + 2/2025 + 1/2250 + 1/2430 + 1/3125 + 1/3375 + 1/3645 + 1/3750 + 1/-4050 + 3/5625 + 1/-5625 + 1/6075 + 1/-6075 + 2/6250 + 1/6750 + 1/-7290 + 3/9375 + 1/-9375 + 1/11250 + 1/-11250 + 1/-12150 + 2/15625 + 1/16875 + 1/-16875 + 1/-18750 + 1/18750 + 1/-28125 + 2/28125 + 2/-33750 + 1/-36450 + 1/46875 + 2/-56250 + 2/-93750 + 1/-168750 + 1/168750 + 1/-281250 + 1/810000
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step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 2/81 + 1/90 + 1/125 + 2/135 + 1/225 + 1/243 + 1/250 + 1/375 + 1/-450 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/-900 + 1/1125 + 2/1215 + 1/1250 + 1/1800 + 2/1875 + 2/2025 + 1/2250 + 1/2430 + 3/3125 + 1/3375 + 1/3645 + 1/3750 + 1/-4050 + 1/-5625 + 1/6750 + 1/-7290 + 1/-9375 + 1/-12150 + 2/15625 + 1/16875 + 2/-16875 + 1/-36450 + 1/-281250 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 2/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-450 + 1/486 + 1/625 + 2/675 + 1/729 + 1/750 + 1/-900 + 1/1125 + 1/1215 + 1/1250 + 1/1800 + 1/1875 + 1/2025 + 1/2250 + 1/-2430 + 2/2430 + 1/3125 + 1/3375 + 2/3645 + 2/3750 + 1/4050 + 2/-4050 + 1/5625 + 1/-5625 + 2/6075 + 2/6250 + 1/6750 + 1/-7290 + 3/9375 + 1/-9375 + 1/10125 + 1/-12150 + 3/15625 + 1/16875 + 1/-16875 + 1/31250 + 1/-33750 + 2/-36450 + 1/46875 + 1/-50625 + 1/-56250 + 1/-60750 + 1/78125 + 1/-84375 + 2/-93750 + 1/-281250 + 1/-468750 + 1/506250 + 1/810000
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step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 2/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-450 + 1/486 + 1/625 + 2/675 + 1/729 + 1/750 + 1/-900 + 1/1125 + 2/1215 + 1/1250 + 1/1800 + 2/1875 + 1/2250 + 1/-2430 + 3/3125 + 1/3375 + 2/3645 + 1/4050 + 2/6075 + 1/6750 + 1/-7290 + 1/-9375 + 1/10125 + 1/-12150 + 3/15625 + 1/-18225 + 1/31250 + 1/-33750 + 1/-50625 + 1/-56250 + 1/-60750 + 1/78125 + 1/-84375 + 1/-281250 + 1/-468750 + 1/506250 + 1/810000
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 1/243 + 1/250 + 1/270 + 1/375 + 1/405 + 1/-450 + 2/486 + 1/625 + 1/675 + 2/729 + 1/750 + 1/810 + 1/-900 + 1/1125 + 3/1215 + 1/1250 + 1/1350 + 1/1800 + 1/1875 + 2/2025 + 1/2250 + 1/-2430 + 1/2430 + 1/3125 + 2/3375 + 2/3645 + 1/3750 + 1/4050 + 1/5625 + 2/6075 + 2/6250 + 1/6750 + 1/7290 + 2/-7290 + 3/9375 + 1/-9375 + 1/10125 + 1/10935 + 2/-12150 + 1/12150 + 3/15625 + 1/-18225 + 2/18225 + 1/-20250 + 1/30375 + 3/31250 + 1/-33750 + 1/-36450 + 2/46875 + 1/-50625 + 2/-56250 + 1/-60750 + 3/78125 + 1/-84375 + 2/-93750 + 1/-109350 + 1/-182250 + 1/-281250 + 3/-468750 + 1/506250 + 1/810000
step 2: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 2/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-450 + 1/625 + 1/675 + 2/729 + 1/750 + 1/810 + 1/-900 + 1/1125 + 1/1250 + 1/1350 + 1/1800 + 1/1875 + 2/2025 + 1/2250 + 1/-2430 + 1/2430 + 3/3125 + 2/3375 + 2/3645 + 1/-3645 + 1/3750 + 1/4050 + 1/5625 + 2/6075 + 1/-6075 + 1/6750 + 1/7290 + 1/-9375 + 1/10125 + 1/10935 + 1/12150 + 3/15625 + 1/-18225 + 2/18225 + 1/-20250 + 1/-28125 + 1/30375 + 3/31250 + 1/-33750 + 1/-36450 + 1/-46875 + 2/46875 + 1/-50625 + 1/-60750 + 3/78125 + 1/-84375 + 1/-109350 + 1/-156250 + 1/-182250 + 1/-281250 + 1/506250 + 1/810000
step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 2/243 + 1/250 + 1/270 + 1/375 + 2/405 + 1/-450 + 1/625 + 1/675 + 2/729 + 1/750 + 1/810 + 1/-900 + 1/1125 + 1/1250 + 1/1350 + 1/1800 + 1/1875 + 2/2025 + 1/2250 + 3/3125 + 2/3375 + 2/3645 + 1/-3645 + 1/3750 + 1/4050 + 1/5625 + 2/6075 + 1/-6075 + 1/6750 + 1/7290 + 1/-9375 + 1/10125 + 1/10935 + 1/12150 + 3/15625 + 1/-18225 + 2/18225 + 1/-20250 + 1/-28125 + 1/30375 + 3/31250 + 1/-33750 + 1/-36450 + 1/-46875 + 2/46875 + 1/-50625 + 1/-60750 + 3/78125 + 1/-84375 + 1/-109350 + 1/-156250 + 1/-182250 + 1/-281250 + 1/506250 + 1/810000
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step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 2/135 + 1/162 + 1/225 + 1/243 + 1/250 + 1/270 + 1/375 + 1/-450 + 1/486 + 1/625 + 2/675 + 2/729 + 1/750 + 1/-900 + 2/1125 + 1/1250 + 1/1350 + 1/1458 + 1/1800 + 1/1875 + 1/2187 + 1/2250 + 2/3125 + 1/-3645 + 1/3750 + 1/5625 + 4/6075 + 1/-6075 + 1/6250 + 1/-7290 + 2/9375 + 1/-9375 + 2/10935 + 1/-12150 + 4/15625 + 1/16875 + 1/-18225 + 1/-20250 + 1/-21870 + 1/-28125 + 2/30375 + 1/-30375 + 1/-33750 + 2/-46875 + 1/-50625 + 6/78125 + 1/-84375 + 1/-101250 + 1/140625 + 1/-156250 + 1/-234375 + 1/-281250 + 2/390625 + 1/-468750 + 1/506250 + 1/-546750 + 1/810000 + 1/-1171875 + 1/-1406250
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step 2: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 1/243 + 1/250 + 1/270 + 1/375 + 1/405 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/810 + 1/-900 + 1/1125 + 1/1215 + 3/1250 + 1/1350 + 1/1458 + 1/1800 + 2/1875 + 1/2025 + 1/2187 + 1/2250 + 4/3125 + 1/-3125 + 1/3375 + 1/3645 + 1/3750 + 1/4374 + 1/5625 + 1/6075 + 1/-6250 + 1/6561 + 2/9375 + 1/10935 + 1/-12150 + 1/13122 + 7/15625 + 1/-16875 + 1/18225 + 1/19683 + 1/-20250 + 1/-28125 + 1/-31250 + 1/31250 + 1/32805 + 1/39366 + 8/46875 + 2/-46875 + 1/50625 + 1/54675 + 1/-56250 + 1/59049 + 1/-60750 + 8/78125 + 1/-78125 + 1/91125 + 2/98415 + 1/109350 + 1/118098 + 1/140625 + 1/-151875 + 3/156250 + 1/-168750 + 2/177147 + 1/-182250 + 1/196830 + 1/234375 + 4/-234375 + 1/-253125 + 1/-295245 + 1/-303750 + 2/390625 + 1/-390625 + 1/421875 + 1/-455625 + 2/492075 + 1/-506250 + 2/531441 + 1/590490 + 2/-703125 + 1/-759375 + 1/781250 + 1/810000 + 1/820125 + 1/-843750 + 1/-911250 + 1/984150 + 7/1171875 + 2/-1171875 + 1/-1265625 + 1/1366875 + 2/1476225 + 1/-1518750 + 1/-1640250 + 1/-1771470 + 8/1953125 + 1/-1953125 + 1/-2109375 + 1/-2278125 + 1/2460375 + 1/-2657205 + 1/-2952450 + 8/3515625 + 2/-3515625 + 1/3796875 + 1/3906250 + 1/-4100625 + 1/-4218750 + 1/-4428675 + 1/4428675 + 1/-4556250 + 1/5859375 + 14/-5859375 + 1/-6328125 + 1/-6834375 + 31/7031250 + 1/-7031250 + 1/-7381125 + 1/7381125 + 4/9765625 + 13/-9765625 + 4/-10546875 + 1/-13668750 + 1/14762250 + 2/-17578125 + 1/17578125 + 1/-18984375 + 3/19531250 + 1/-20503125 + 1/21093750 + 1/22143375 + 1/-24603750 + 8/-29296875 + 2/-34171875 + 1/35156250 + 17/-35156250 + 1/36905625 + 1/37968750 + 1/-44286750 + 7/-48828125 + 7/48828125 + 7/-52734375 + 1/56953125 + 1/-56953125 + 1/-58593750 + 1/68343750 + 1/-68343750 + 1/-73811250 + 22/-87890625 + 1/-97656250 + 1/102515625 + 1/-102515625 + 1/-113906250 + 1/123018750 + 1/146484375 + 1/158203125 + 2/-170859375 + 1/170859375 + 1/-175781250 + 1/-189843750 + 1/-221433750 + 1/244140625 + 3/-244140625 + 11/-263671875 + 1/-284765625 + 1/-292968750 + 1/316406250 + 4/439453125 + 1/474609375 + 3/-488281250 + 7/-791015625 + 2/791015625 + 1/-878906250 + 1/1025156250 + 7/-1220703125 + 13/1220703125 + 19/-1318359375 + 1/1318359375 + 7/-1582031250 + 1/1708593750 + 44/2197265625 + 31/2441406250 + 1/-2441406250 + 1/2636718750 + 7/-3662109375 + 68/3662109375 + 19/-3955078125 + 1/3955078125 + 1/-4746093750 + 26/-6103515625 + 17/6103515625 + 1/6591796875 + 23/-7324218750 + 7/7910156250 + 7/-7910156250 + 16/-10986328125 + 1/13183593750 + 29/-18310546875 + 49/18310546875 + 43/-21972656250 + 23/-30517578125 + 1/-32958984375 + 17/39550781250 + 4/-54931640625 + 3/61035156250 + 1/-65917968750 + 11/-91552734375 + 29/91552734375 + 1/98876953125 + 73/-109863281250 + 1/164794921875 + 16/-164794921875 + 1/-197753906250 + 16/-274658203125 + 1/-549316406250 + 11/549316406250 + 4/823974609375 + 1/-988769531250
step 4: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 1/243 + 1/250 + 1/270 + 1/375 + 1/405 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/810 + 1/-900 + 1/1125 + 1/1215 + 3/1250 + 1/1350 + 1/1458 + 1/1800 + 2/1875 + 1/2025 + 1/2187 + 1/2250 + 4/3125 + 1/-3125 + 1/3375 + 1/3645 + 1/3750 + 1/4374 + 1/5625 + 1/6075 + 1/-6250 + 1/6561 + 2/9375 + 1/10935 + 1/-12150 + 1/13122 + 7/15625 + 1/-16875 + 1/18225 + 1/19683 + 1/-20250 + 1/-28125 + 1/32805 + 1/39366 + 8/46875 + 2/-46875 + 1/50625 + 1/54675 + 1/-56250 + 1/59049 + 1/-60750 + 8/78125 + 1/-78125 + 1/91125 + 2/98415 + 1/109350 + 1/118098 + 1/140625 + 1/-151875 + 3/156250 + 1/-168750 + 2/177147 + 1/-182250 + 1/196830 + 1/234375 + 4/-234375 + 1/-253125 + 1/-295245 + 1/-303750 + 2/390625 + 1/-390625 + 1/421875 + 1/-455625 + 2/492075 + 1/-506250 + 2/531441 + 1/590490 + 2/-703125 + 1/-759375 + 1/781250 + 1/810000 + 1/820125 + 1/-843750 + 1/-911250 + 1/984150 + 7/1171875 + 2/-1171875 + 1/-1265625 + 1/1366875 + 2/1476225 + 1/-1518750 + 1/-1640250 + 1/-1771470 + 8/1953125 + 1/-1953125 + 1/-2109375 + 1/-2278125 + 1/2460375 + 1/-2657205 + 1/-2952450 + 8/3515625 + 2/-3515625 + 1/3796875 + 1/3906250 + 1/-4100625 + 1/-4218750 + 1/-4556250 + 1/5859375 + 14/-5859375 + 1/-6328125 + 1/-6834375 + 31/7031250 + 1/-7031250 + 4/9765625 + 13/-9765625 + 4/-10546875 + 1/-13668750 + 1/14762250 + 2/-17578125 + 1/17578125 + 1/-18984375 + 3/19531250 + 1/-20503125 + 1/21093750 + 1/22143375 + 1/-24603750 + 8/-29296875 + 2/-34171875 + 1/35156250 + 17/-35156250 + 1/36905625 + 1/37968750 + 1/-44286750 + 7/-52734375 + 1/-58593750 + 1/-73811250 + 22/-87890625 + 1/-97656250 + 1/-113906250 + 1/123018750 + 1/146484375 + 1/158203125 + 2/-170859375 + 1/170859375 + 1/-175781250 + 1/-189843750 + 1/-221433750 + 1/244140625 + 3/-244140625 + 11/-263671875 + 1/-284765625 + 1/-292968750 + 1/316406250 + 4/439453125 + 1/474609375 + 3/-488281250 + 7/-791015625 + 2/791015625 + 1/-878906250 + 1/1025156250 + 7/-1220703125 + 13/1220703125 + 19/-1318359375 + 1/1318359375 + 7/-1582031250 + 1/1708593750 + 44/2197265625 + 31/2441406250 + 1/-2441406250 + 1/2636718750 + 7/-3662109375 + 68/3662109375 + 19/-3955078125 + 1/3955078125 + 1/-4746093750 + 26/-6103515625 + 17/6103515625 + 1/6591796875 + 23/-7324218750 + 16/-10986328125 + 1/13183593750 + 29/-18310546875 + 49/18310546875 + 43/-21972656250 + 23/-30517578125 + 1/-32958984375 + 17/39550781250 + 4/-54931640625 + 3/61035156250 + 1/-65917968750 + 11/-91552734375 + 29/91552734375 + 1/98876953125 + 73/-109863281250 + 1/164794921875 + 16/-164794921875 + 1/-197753906250 + 16/-274658203125 + 11/549316406250 + 1/-549316406250 + 4/823974609375 + 1/-988769531250
step 5: 1/5 + 1/6 + 1/9 + 1/10 + 1/15 + 1/16 + 1/18 + 1/25 + 1/27 + 1/45 + 1/50 + 1/54 + 1/75 + 1/81 + 1/90 + 1/125 + 1/135 + 1/162 + 1/225 + 1/243 + 1/250 + 1/270 + 1/375 + 1/405 + 1/486 + 1/625 + 1/675 + 1/729 + 1/750 + 1/810 + 1/-900 + 1/1125 + 1/1215 + 1/1250 + 1/1350 + 1/1458 + 1/1800 + 1/1875 + 1/2025 + 1/2187 + 1/2250 + 2/2500 + 1/3125 + 1/-3125 + 1/3375 + 1/3645 + 4/3750 + 1/4374 + 2/5625 + 1/6075 + 1/-6250 + 5/6250 + 1/6561 + 5/9375 + 1/10935 + 1/-12150 + 1/13122 + 4/15625 + 1/-16875 + 1/18225 + 1/18750 + 1/19683 + 1/-20250 + 1/-28125 + 1/28125 + 6/31250 + 1/32805 + 2/-37500 + 1/39366 + 8/46875 + 1/-46875 + 1/50625 + 1/54675 + 2/-56250 + 1/59049 + 1/-60750 + 7/78125 + 1/-78125 + 1/91125 + 7/93750 + 4/-93750 + 1/98415 + 1/109350 + 1/118098 + 8/140625 + 1/-140625 + 1/-151875 + 8/156250 + 1/-168750 + 1/177147 + 1/-182250 + 2/196830 + 15/234375 + 2/-234375 + 1/-253125 + 1/-281250 + 1/295245 + 1/-295245 + 1/-303750 + 2/312500 + 1/354294 + 8/390625 + 1/-390625 + 1/421875 + 1/-455625 + 2/468750 + 9/-468750 + 2/492075 + 1/-506250 + 2/531441 + 1/590490 + 4/-703125 + 1/-759375 + 4/781250 + 1/810000 + 1/820125 + 1/-843750 + 1/885735 + 1/-911250 + 2/984150 + 1/1062882 + 2/1171875 + 4/-1171875 + 1/-1265625 + 1/1366875 + 8/-1406250 + 1/1406250 + 2/1476225 + 1/-1518750 + 1/1594323 + 1/-1640250 + 1/-1771470 + 2/1953125 + 1/-1953125 + 2/-2109375 + 1/-2278125 + 8/-2343750 + 6/2343750 + 2/2460375 + 1/2657205 + 1/-2657205 + 1/2952450 + 2/-2952450 + 7/3515625 + 3/-3515625 + 1/3796875 + 8/3906250 + 1/-4100625 + 1/-4218750 + 1/4428675 + 1/-4556250 + 2/-4687500 + 1/-5314410 + 14/5859375 + 2/-5859375 + 1/-6328125 + 1/-6834375 + 11/7031250 + 2/-7031250 + 1/7381125 + 8/9765625 + 1/-9765625 + 2/-10546875 + 7/10546875 + 14/-11718750 + 1/-13668750 + 30/14062500 + 1/14762250 + 1/-14762250 + 1/-15943230 + 15/-17578125 + 8/17578125 + 1/-18984375 + 4/19531250 + 12/-19531250 + 1/-20503125 + 3/-21093750 + 32/21093750 + 1/22143375 + 1/-24603750 + 26/-29296875 + 3/29296875 + 3/-31640625 + 1/-34171875 + 32/35156250 + 8/-35156250 + 1/36905625 + 1/37968750 + 2/39062500 + 2/-44286750 + 12/-48828125 + 3/48828125 + 5/-52734375 + 2/58593750 + 15/-58593750 + 1/-68343750 + 16/-70312500 + 1/-73811250 + 9/-87890625 + 2/97656250 + 1/-97656250 + 1/-102515625 + 29/-105468750 + 1/105468750 + 1/-113906250 + 1/123018750 + 7/-146484375 + 1/146484375 + 6/-158203125 + 1/158203125 + 2/-170859375 + 1/170859375 + 38/-175781250 + 13/175781250 + 1/-189843750 + 30/-210937500 + 1/-221433750 + 1/244140625 + 1/-244140625 + 28/-263671875 + 1/-284765625 + 12/292968750 + 4/-292968750 + 4/316406250 + 1/-341718750 + 21/-439453125 + 1/439453125 + 1/474609375 + 3/-488281250 + 1/-512578125 + 10/-527343750 + 1/527343750 + 2/-585937500 + 2/-732421875 + 11/-791015625 + 1/791015625 + 1/-854296875 + 1/-878906250 + 10/878906250 + 2/-976562500 + 2/1025156250 + 16/1054687500 + 3/-1220703125 + 1/1220703125 + 11/-1318359375 + 4/1318359375 + 2/-1464843750 + 7/-1582031250 + 7/1582031250 + 1/1708593750 + 4/2197265625 + 6/-2373046875 + 1/2373046875 + 13/2441406250 + 9/-2441406250 + 18/-2636718750 + 22/2636718750 + 6/-3164062500 + 7/-3662109375 + 13/3662109375 + 25/-3955078125 + 2/3955078125 + 43/4394531250 + 7/-4746093750 + 30/4882812500 + 1/5125781250 + 7/-6103515625 + 13/6103515625 + 44/6591796875 + 18/-6591796875 + 99/7324218750 + 7/-7324218750 + 10/7910156250 + 24/-7910156250 + 7/-10986328125 + 110/10986328125 + 18/-11865234375 + 25/-12207031250 + 46/12207031250 + 1/13183593750 + 3/-13183593750 + 2/14648437500 + 22/-14648437500 + 32/-18310546875 + 84/18310546875 + 18/-19775390625 + 38/-21972656250 + 1/-23730468750 + 6/23730468750 + 26/-30517578125 + 16/30517578125 + 16/-32958984375 + 62/-36621093750 + 54/36621093750 + 19/39550781250 + 42/-43945312500 + 6/47460937500 + 48/54931640625 + 44/-54931640625 + 1/61035156250 + 22/-61035156250 + 86/-65917968750 + 30/-73242187500 + 16/79101562500 + 51/-91552734375 + 49/91552734375 + 1/98876953125 + 113/-109863281250 + 6/109863281250 + 34/118652343750 + 2/122070312500 + 22/-152587890625 + 1/164794921875 + 4/-164794921875 + 55/183105468750 + 26/-183105468750 + 16/197753906250 + 1/-197753906250 + 72/-219726562500 + 22/219726562500 + 28/274658203125 + 14/-274658203125 + 2/305175781250 + 15/329589843750 + 87/-329589843750 + 28/457763671875 + 10/-457763671875 + 15/-494384765625 + 29/549316406250 + 136/-549316406250 + 42/659179687500 + 1/823974609375 + 30/-823974609375 + 22/915527343750 + 1/-988769531250 + 10/1098632812500 + 16/-1186523437500 + 15/-1373291015625 + 16/1647949218750 + 2/-1831054687500 + 3/2471923828125 + 20/2746582031250 + 28/-2746582031250 + 72/3295898437500 + 3/4119873046875 + 15/4943847656250 + 15/8239746093750 + 10/-16479492187500 + 3/-24719238281250
Reached 20 iterations of steps 1-5; Aborting.
#!/usr/bin/env perl6
my \ff1 = (2, 3, 5, -30);
.say for (ff1, &next-ff ... *)[^3];
#| Generates FF(n) from FF(n-1).
#| Both input and output are represented as a list of denominators.
sub next-ff (@denominators) {
debug-output "Finding FF({2 + $++})...";
my $bag = (@denominators X* @denominators).Bag;
$bag.&converge: {
$bag = $bag.&converge: *.kv.map(&simplify-fraction).flat.pairup.Bag;
debug-output "step 2", $bag;
$bag = $bag.grep({ $bag{-.key} != .value }).Bag;
debug-output "step 4", $bag;
$bag = $bag.kv.map(-> $denominator, $numerator {
$denominator,
(($denominator xx $numerator-1) X* ff1)
}).flat.Bag;
debug-output "step 5", $bag;
debug-output "Reached 20 iterations of steps 1-5; Aborting." and exit
if ++$ == 20;
$bag
}
debug-output "FF({2 + $++}) = [{ $bag.keys.sort(*.abs) }]";
$bag.keys.sort(*.abs).cache
}
#| Simplifies a fraction. (Both input and output are given as two integers.)
sub simplify-fraction ($numerator, $denominator) {
($numerator / $denominator).nude
}
#| Repeatedly applies a function to a value until it doesn't change anymore.
sub converge ($initial, &step) {
($initial, &step ... &[eqv])[*-1]
}
#| Helper function for printing intermediate results to stderr.
multi debug-output ($label, %bag) {
state $last = '';
my $string = %bag.sort(*.key.abs).map({ "{.value}/{.key}" }).join(' + ');
if $last ne $string {
note "$label: $string";
$last = $string;
}
1
}
multi debug-output ($string) {
note "\n$string\n";
}
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