Ensamma Bråk

[WASD]

Körde en massa primtal upp till 500 med försök att summera ner till 1/1000 och de flesta kunde bildas på många olika sätt.
 

1/479 == 1/921 + 1/998
1/479 == 1/922 + 1/997
1/479 == 1/928 + 1/990
1/479 == 1/936 + 1/981
1/479 == 1/937 + 1/980
1/479 == 1/952 + 1/964
1/479 == 1/953 + 1/963
1/479 == 1/954 + 1/962
1/479 == 1/955 + 1/961
1/479 == 1/956 + 1/960
1/479 == 1/957 + 1/959

Mezox har du skype? Jag och davve snackar där.

Här är alla resultat. Första primtalsensammabråket att ha mer än en möjlighet är 103
Edit: Och de primtalen som inte står med uppfylls endast av 1/(2b)+1/(2b).

 

Edit: På grund av avrundningsfel är denna listan inkorrekt. Ensamma bråk av primtal verkar bara ha en lösning utöver 1/(2b)+1/(2b)

1/3 == 1/4 + 1/12
1/5 == 1/6 + 1/30
1/7 == 1/8 + 1/56
1/11 == 1/12 + 1/132
1/13 == 1/14 + 1/182
1/17 == 1/18 + 1/306
1/19 == 1/20 + 1/380
1/23 == 1/24 + 1/552
1/29 == 1/30 + 1/870
1/31 == 1/32 + 1/992
1/101 == 1/113 + 1/951
1/103 == 1/115 + 1/987
1/103 == 1/116 + 1/919
1/109 == 1/124 + 1/901
1/109 == 1/127 + 1/769
1/113 == 1/129 + 1/911
1/113 == 1/132 + 1/785
1/113 == 1/134 + 1/721
1/127 == 1/148 + 1/895
1/127 == 1/151 + 1/799
1/127 == 1/155 + 1/703
1/127 == 1/159 + 1/631
1/127 == 1/163 + 1/575
1/127 == 1/169 + 1/511
1/127 == 1/175 + 1/463
1/131 == 1/151 + 1/989
1/131 == 1/153 + 1/911
1/131 == 1/155 + 1/846
1/131 == 1/157 + 1/791
1/131 == 1/161 + 1/703
1/131 == 1/164 + 1/651
1/131 == 1/170 + 1/571
1/131 == 1/171 + 1/560
1/131 == 1/175 + 1/521
1/131 == 1/183 + 1/461
1/131 == 1/186 + 1/443
1/131 == 1/191 + 1/417
1/131 == 1/196 + 1/395
1/131 == 1/197 + 1/391
1/137 == 1/160 + 1/953
1/137 == 1/161 + 1/919
1/137 == 1/171 + 1/689
1/137 == 1/183 + 1/545
1/137 == 1/185 + 1/528
1/137 == 1/188 + 1/505
1/137 == 1/205 + 1/413
1/137 == 1/206 + 1/409
1/137 == 1/229 + 1/341
1/137 == 1/239 + 1/321
1/137 == 1/273 + 1/275
1/139 == 1/162 + 1/979
1/139 == 1/163 + 1/944
1/139 == 1/167 + 1/829
1/139 == 1/169 + 1/783
1/139 == 1/174 + 1/691
1/139 == 1/179 + 1/622
1/139 == 1/181 + 1/599
1/139 == 1/185 + 1/559
1/139 == 1/195 + 1/484
1/139 == 1/199 + 1/461
1/139 == 1/208 + 1/419
1/139 == 1/209 + 1/415
1/139 == 1/223 + 1/369
1/139 == 1/231 + 1/349
1/139 == 1/244 + 1/323
1/139 == 1/254 + 1/307
1/139 == 1/259 + 1/300
1/139 == 1/277 + 1/279
1/149 == 1/179 + 1/889
1/149 == 1/183 + 1/802
1/149 == 1/186 + 1/749
1/149 == 1/189 + 1/704
1/149 == 1/199 + 1/593
1/149 == 1/209 + 1/519
1/149 == 1/223 + 1/449
1/149 == 1/224 + 1/445
1/149 == 1/249 + 1/371
1/149 == 1/260 + 1/349
1/149 == 1/269 + 1/334
1/149 == 1/297 + 1/299
1/151 == 1/181 + 1/911
1/151 == 1/184 + 1/842
1/151 == 1/189 + 1/751
1/151 == 1/191 + 1/721
1/151 == 1/199 + 1/626
1/151 == 1/201 + 1/607
1/151 == 1/208 + 1/551
1/151 == 1/211 + 1/531
1/151 == 1/226 + 1/455
1/151 == 1/227 + 1/451
1/151 == 1/231 + 1/436
1/151 == 1/246 + 1/391
1/151 == 1/251 + 1/379
1/151 == 1/265 + 1/351
1/151 == 1/271 + 1/341
1/151 == 1/301 + 1/303
1/157 == 1/190 + 1/904
1/157 == 1/191 + 1/882
1/157 == 1/196 + 1/789
1/157 == 1/206 + 1/660
1/157 == 1/207 + 1/650
1/157 == 1/209 + 1/631
1/157 == 1/215 + 1/582
1/157 == 1/235 + 1/473
1/157 == 1/236 + 1/469
1/157 == 1/242 + 1/447
1/157 == 1/261 + 1/394
1/157 == 1/302 + 1/327
1/157 == 1/313 + 1/315
1/163 == 1/199 + 1/901
1/163 == 1/204 + 1/811
1/163 == 1/214 + 1/684
1/163 == 1/217 + 1/655
1/163 == 1/235 + 1/532
1/163 == 1/244 + 1/491
1/163 == 1/245 + 1/487
1/163 == 1/271 + 1/409
1/163 == 1/286 + 1/379
1/163 == 1/325 + 1/327
1/167 == 1/205 + 1/901
1/167 == 1/209 + 1/831
1/167 == 1/215 + 1/748
1/167 == 1/223 + 1/665
1/167 == 1/246 + 1/520
1/167 == 1/250 + 1/503
1/167 == 1/251 + 1/499
1/167 == 1/279 + 1/416
1/167 == 1/333 + 1/335
1/173 == 1/214 + 1/903
1/173 == 1/216 + 1/869
1/173 == 1/231 + 1/689
1/173 == 1/246 + 1/583
1/173 == 1/255 + 1/538
1/173 == 1/259 + 1/521
1/173 == 1/260 + 1/517
1/173 == 1/289 + 1/431
1/173 == 1/302 + 1/405
1/173 == 1/319 + 1/378
1/173 == 1/345 + 1/347
1/179 == 1/219 + 1/980
1/179 == 1/224 + 1/891
1/179 == 1/239 + 1/713
1/179 == 1/251 + 1/624
1/179 == 1/253 + 1/612
1/179 == 1/268 + 1/539
1/179 == 1/269 + 1/535
1/179 == 1/299 + 1/446
1/179 == 1/340 + 1/378
1/179 == 1/357 + 1/359
1/181 == 1/221 + 1/1000
1/181 == 1/222 + 1/980
1/181 == 1/223 + 1/961
1/181 == 1/226 + 1/909
1/181 == 1/228 + 1/878
1/181 == 1/233 + 1/811
1/181 == 1/237 + 1/766
1/181 == 1/241 + 1/727
1/181 == 1/244 + 1/701
1/181 == 1/246 + 1/685
1/181 == 1/248 + 1/670
1/181 == 1/251 + 1/649
1/181 == 1/253 + 1/636
1/181 == 1/259 + 1/601
1/181 == 1/265 + 1/571
1/181 == 1/271 + 1/545
1/181 == 1/272 + 1/541
1/181 == 1/285 + 1/496
1/181 == 1/286 + 1/493
1/181 == 1/298 + 1/461
1/181 == 1/301 + 1/454
1/181 == 1/307 + 1/441
1/181 == 1/311 + 1/433
1/181 == 1/321 + 1/415
1/181 == 1/337 + 1/391
1/181 == 1/344 + 1/382
1/181 == 1/349 + 1/376
1/181 == 1/361 + 1/363
1/191 == 1/237 + 1/984
1/191 == 1/239 + 1/951
1/191 == 1/248 + 1/831
1/191 == 1/249 + 1/820
1/191 == 1/251 + 1/799
1/191 == 1/252 + 1/789
1/191 == 1/255 + 1/761
1/191 == 1/265 + 1/684
1/191 == 1/267 + 1/671
1/191 == 1/271 + 1/647
1/191 == 1/286 + 1/575
1/191 == 1/287 + 1/571
1/191 == 1/305 + 1/511
1/191 == 1/311 + 1/495
1/191 == 1/319 + 1/476
1/191 == 1/343 + 1/431
1/191 == 1/351 + 1/419
1/191 == 1/381 + 1/383
1/193 == 1/241 + 1/969
1/193 == 1/243 + 1/938
1/193 == 1/257 + 1/775
1/193 == 1/260 + 1/749
1/193 == 1/289 + 1/581
1/193 == 1/290 + 1/577
1/193 == 1/312 + 1/506
1/193 == 1/318 + 1/491
1/193 == 1/321 + 1/484
1/193 == 1/342 + 1/443
1/193 == 1/385 + 1/387
1/197 == 1/246 + 1/989
1/197 == 1/248 + 1/958
1/197 == 1/253 + 1/890
1/197 == 1/259 + 1/823
1/197 == 1/260 + 1/813
1/197 == 1/262 + 1/794
1/197 == 1/263 + 1/785
1/197 == 1/269 + 1/736
1/197 == 1/274 + 1/701
1/197 == 1/281 + 1/659
1/197 == 1/285 + 1/638
1/197 == 1/295 + 1/593
1/197 == 1/296 + 1/589
1/197 == 1/321 + 1/510
1/197 == 1/323 + 1/505
1/197 == 1/329 + 1/491
1/197 == 1/344 + 1/461
1/197 == 1/348 + 1/454
1/197 == 1/351 + 1/449
1/197 == 1/365 + 1/428
1/197 == 1/393 + 1/395
1/199 == 1/249 + 1/991
1/199 == 1/254 + 1/919
1/199 == 1/259 + 1/859
1/199 == 1/265 + 1/799
1/199 == 1/266 + 1/790
1/199 == 1/271 + 1/749
1/199 == 1/274 + 1/727
1/199 == 1/279 + 1/694
1/199 == 1/287 + 1/649
1/199 == 1/289 + 1/639
1/199 == 1/298 + 1/599
1/199 == 1/299 + 1/595
1/199 == 1/309 + 1/559
1/199 == 1/319 + 1/529
1/199 == 1/328 + 1/506
1/199 == 1/331 + 1/499
1/199 == 1/343 + 1/474
1/199 == 1/349 + 1/463
1/199 == 1/364 + 1/439
1/199 == 1/375 + 1/424
1/199 == 1/379 + 1/419
1/199 == 1/397 + 1/399
1/211 == 1/268 + 1/992
1/211 == 1/271 + 1/953
1/211 == 1/273 + 1/929
1/211 == 1/276 + 1/896
1/211 == 1/281 + 1/847
1/211 == 1/282 + 1/838
1/211 == 1/295 + 1/741
1/211 == 1/308 + 1/670
1/211 == 1/316 + 1/635
1/211 == 1/317 + 1/631
1/211 == 1/324 + 1/605
1/211 == 1/331 + 1/582
1/211 == 1/351 + 1/529
1/211 == 1/364 + 1/502
1/211 == 1/370 + 1/491
1/211 == 1/379 + 1/476
1/211 == 1/408 + 1/437
1/211 == 1/421 + 1/423
1/223 == 1/287 + 1/1000
1/223 == 1/288 + 1/988
1/223 == 1/297 + 1/895
1/223 == 1/298 + 1/886
1/223 == 1/304 + 1/837
1/223 == 1/307 + 1/815
1/223 == 1/308 + 1/808
1/223 == 1/317 + 1/752
1/223 == 1/319 + 1/741
1/223 == 1/334 + 1/671
1/223 == 1/335 + 1/667
1/223 == 1/340 + 1/648
1/223 == 1/344 + 1/634
1/223 == 1/360 + 1/586
1/223 == 1/371 + 1/559
1/223 == 1/376 + 1/548
1/223 == 1/391 + 1/519
1/223 == 1/415 + 1/482
1/223 == 1/418 + 1/478
1/223 == 1/444 + 1/448
1/223 == 1/445 + 1/447
1/227 == 1/294 + 1/996
1/227 == 1/302 + 1/914
1/227 == 1/303 + 1/905
1/227 == 1/316 + 1/806
1/227 == 1/340 + 1/683
1/227 == 1/341 + 1/679
1/227 == 1/346 + 1/660
1/227 == 1/353 + 1/636
1/227 == 1/379 + 1/566
1/227 == 1/420 + 1/494
1/227 == 1/452 + 1/456
1/227 == 1/453 + 1/455
1/229 == 1/298 + 1/989
1/229 == 1/305 + 1/919
1/229 == 1/306 + 1/910
1/229 == 1/314 + 1/846
1/229 == 1/321 + 1/799
1/229 == 1/324 + 1/781
1/229 == 1/343 + 1/689
1/229 == 1/344 + 1/685
1/229 == 1/349 + 1/666
1/229 == 1/367 + 1/609
1/229 == 1/381 + 1/574
1/229 == 1/386 + 1/563
1/229 == 1/396 + 1/543
1/229 == 1/413 + 1/514
1/229 == 1/419 + 1/505
1/229 == 1/456 + 1/460
1/229 == 1/457 + 1/459
1/233 == 1/305 + 1/987
1/233 == 1/310 + 1/938
1/233 == 1/311 + 1/929
1/233 == 1/315 + 1/895
1/233 == 1/320 + 1/857
1/233 == 1/322 + 1/843
1/233 == 1/331 + 1/787
1/233 == 1/337 + 1/755
1/233 == 1/338 + 1/750
1/233 == 1/349 + 1/701
1/233 == 1/350 + 1/697
1/233 == 1/355 + 1/678
1/233 == 1/374 + 1/618
1/233 == 1/377 + 1/610
1/233 == 1/389 + 1/581
1/233 == 1/397 + 1/564
1/233 == 1/398 + 1/562
1/233 == 1/407 + 1/545
1/233 == 1/411 + 1/538
1/233 == 1/429 + 1/510
1/233 == 1/441 + 1/494
1/233 == 1/464 + 1/468
1/233 == 1/465 + 1/467
1/239 == 1/318 + 1/962
1/239 == 1/319 + 1/953
1/239 == 1/323 + 1/919
1/239 == 1/324 + 1/911
1/239 == 1/335 + 1/834
1/239 == 1/338 + 1/816
1/239 == 1/341 + 1/799
1/239 == 1/344 + 1/783
1/239 == 1/348 + 1/763
1/239 == 1/351 + 1/749
1/239 == 1/358 + 1/719
1/239 == 1/359 + 1/715
1/239 == 1/364 + 1/696
1/239 == 1/370 + 1/675
1/239 == 1/375 + 1/659
1/239 == 1/379 + 1/647
1/239 == 1/399 + 1/596
1/239 == 1/407 + 1/579
1/239 == 1/408 + 1/577
1/239 == 1/409 + 1/575
1/239 == 1/443 + 1/519
1/239 == 1/449 + 1/511
1/239 == 1/457 + 1/501
1/239 == 1/463 + 1/494
1/239 == 1/476 + 1/480
1/239 == 1/477 + 1/479
1/241 == 1/321 + 1/967
1/241 == 1/322 + 1/958
1/241 == 1/329 + 1/901
1/241 == 1/337 + 1/846
1/241 == 1/342 + 1/816
1/241 == 1/351 + 1/769
1/241 == 1/354 + 1/755
1/241 == 1/356 + 1/746
1/241 == 1/361 + 1/725
1/241 == 1/362 + 1/721
1/241 == 1/367 + 1/702
1/241 == 1/373 + 1/681
1/241 == 1/383 + 1/650
1/241 == 1/401 + 1/604
1/241 == 1/406 + 1/593
1/241 == 1/417 + 1/571
1/241 == 1/461 + 1/505
1/241 == 1/467 + 1/498
1/241 == 1/480 + 1/484
1/241 == 1/481 + 1/483
1/251 == 1/339 + 1/967
1/251 == 1/341 + 1/951
1/251 == 1/351 + 1/881
1/251 == 1/356 + 1/851
1/251 == 1/360 + 1/829
1/251 == 1/371 + 1/776
1/251 == 1/376 + 1/755
1/251 == 1/377 + 1/751
1/251 == 1/391 + 1/701
1/251 == 1/401 + 1/671
1/251 == 1/419 + 1/626
1/251 == 1/426 + 1/611
1/251 == 1/431 + 1/601
1/251 == 1/451 + 1/566
1/251 == 1/461 + 1/551
1/251 == 1/466 + 1/544
1/251 == 1/469 + 1/540
1/251 == 1/476 + 1/531
1/251 == 1/500 + 1/504
1/251 == 1/501 + 1/503
1/257 == 1/349 + 1/975
1/257 == 1/353 + 1/945
1/257 == 1/354 + 1/938
1/257 == 1/355 + 1/931
1/257 == 1/358 + 1/911
1/257 == 1/362 + 1/886
1/257 == 1/366 + 1/863
1/257 == 1/368 + 1/852
1/257 == 1/376 + 1/812
1/257 == 1/380 + 1/794
1/257 == 1/385 + 1/773
1/257 == 1/386 + 1/769
1/257 == 1/415 + 1/675
1/257 == 1/429 + 1/641
1/257 == 1/436 + 1/626
1/257 == 1/442 + 1/614
1/257 == 1/449 + 1/601
1/257 == 1/453 + 1/594
1/257 == 1/459 + 1/584
1/257 == 1/466 + 1/573
1/257 == 1/468 + 1/570
1/257 == 1/475 + 1/560
1/257 == 1/512 + 1/516
1/257 == 1/513 + 1/515
1/263 == 1/358 + 1/991
1/263 == 1/360 + 1/976
1/263 == 1/385 + 1/830
1/263 == 1/389 + 1/812
1/263 == 1/394 + 1/791
1/263 == 1/395 + 1/787
1/263 == 1/408 + 1/740
1/263 == 1/422 + 1/698
1/263 == 1/425 + 1/690
1/263 == 1/439 + 1/656
1/263 == 1/446 + 1/641
1/263 == 1/452 + 1/629
1/263 == 1/484 + 1/576
1/263 == 1/504 + 1/550
1/263 == 1/524 + 1/528
1/263 == 1/525 + 1/527
1/269 == 1/368 + 1/1000
1/269 == 1/377 + 1/939
1/269 == 1/381 + 1/915
1/269 == 1/388 + 1/877
1/269 == 1/389 + 1/872
1/269 == 1/390 + 1/867
1/269 == 1/398 + 1/830
1/269 == 1/403 + 1/809
1/269 == 1/404 + 1/805
1/269 == 1/412 + 1/775
1/269 == 1/414 + 1/768
1/269 == 1/422 + 1/742
1/269 == 1/427 + 1/727
1/269 == 1/449 + 1/671
1/269 == 1/455 + 1/658
1/269 == 1/456 + 1/656
1/269 == 1/463 + 1/642
1/269 == 1/470 + 1/629
1/269 == 1/474 + 1/622
1/269 == 1/485 + 1/604
1/269 == 1/498 + 1/585
1/269 == 1/511 + 1/568
1/269 == 1/522 + 1/555
1/269 == 1/536 + 1/540
1/269 == 1/537 + 1/539
1/271 == 1/373 + 1/991
1/271 == 1/374 + 1/984
1/271 == 1/379 + 1/951
1/271 == 1/384 + 1/921
1/271 == 1/391 + 1/883
1/271 == 1/392 + 1/878
1/271 == 1/393 + 1/873
1/271 == 1/401 + 1/836
1/271 == 1/406 + 1/815
1/271 == 1/407 + 1/811
1/271 == 1/415 + 1/781
1/271 == 1/417 + 1/774
1/271 == 1/424 + 1/751
1/271 == 1/431 + 1/730
1/271 == 1/441 + 1/703
1/271 == 1/443 + 1/698
1/271 == 1/451 + 1/679
1/271 == 1/456 + 1/668
1/271 == 1/475 + 1/631
1/271 == 1/487 + 1/611
1/271 == 1/511 + 1/577
1/271 == 1/515 + 1/572
1/271 == 1/526 + 1/559
1/271 == 1/540 + 1/544
1/271 == 1/541 + 1/543
1/277 == 1/384 + 1/994
1/277 == 1/386 + 1/981
1/277 == 1/389 + 1/962
1/277 == 1/390 + 1/956
1/277 == 1/391 + 1/950
1/277 == 1/399 + 1/906
1/277 == 1/403 + 1/886
1/277 == 1/414 + 1/837
1/277 == 1/415 + 1/833
1/277 == 1/416 + 1/829
1/277 == 1/417 + 1/825
1/277 == 1/424 + 1/799
1/277 == 1/426 + 1/792
1/277 == 1/432 + 1/772
1/277 == 1/442 + 1/742
1/277 == 1/446 + 1/731
1/277 == 1/451 + 1/718
1/277 == 1/453 + 1/713
1/277 == 1/461 + 1/694
1/277 == 1/466 + 1/683
1/277 == 1/480 + 1/655
1/277 == 1/495 + 1/629
1/277 == 1/502 + 1/618
1/277 == 1/504 + 1/615
1/277 == 1/538 + 1/571
1/277 == 1/552 + 1/556
1/277 == 1/553 + 1/555
1/281 == 1/393 + 1/986
1/281 == 1/401 + 1/939
1/281 == 1/404 + 1/923
1/281 == 1/420 + 1/849
1/281 == 1/421 + 1/845
1/281 == 1/422 + 1/841
1/281 == 1/423 + 1/837
1/281 == 1/430 + 1/811
1/281 == 1/449 + 1/751
1/281 == 1/469 + 1/701
1/281 == 1/475 + 1/688
1/281 == 1/484 + 1/670
1/281 == 1/491 + 1/657
1/281 == 1/495 + 1/650
1/281 == 1/516 + 1/617
1/281 == 1/521 + 1/610
1/281 == 1/527 + 1/602
1/281 == 1/560 + 1/564
1/281 == 1/561 + 1/563
1/283 == 1/395 + 1/998
1/283 == 1/402 + 1/956
1/283 == 1/413 + 1/899
1/283 == 1/423 + 1/855
1/283 == 1/424 + 1/851
1/283 == 1/425 + 1/847
1/283 == 1/426 + 1/843
1/283 == 1/437 + 1/803
1/283 == 1/459 + 1/738
1/283 == 1/465 + 1/723
1/283 == 1/471 + 1/709
1/283 == 1/476 + 1/698
1/283 == 1/491 + 1/668
1/283 == 1/496 + 1/659
1/283 == 1/503 + 1/647
1/283 == 1/543 + 1/591
1/283 == 1/563 + 1/569
1/283 == 1/564 + 1/568
1/283 == 1/565 + 1/567
1/293 == 1/416 + 1/991
1/293 == 1/420 + 1/969
1/293 == 1/428 + 1/929
1/293 == 1/438 + 1/885
1/293 == 1/439 + 1/881
1/293 == 1/440 + 1/877
1/293 == 1/441 + 1/873
1/293 == 1/452 + 1/833
1/293 == 1/461 + 1/804
1/293 == 1/462 + 1/801
1/293 == 1/463 + 1/798
1/293 == 1/464 + 1/795
1/293 == 1/470 + 1/778
1/293 == 1/478 + 1/757
1/293 == 1/489 + 1/731
1/293 == 1/495 + 1/718
1/293 == 1/506 + 1/696
1/293 == 1/512 + 1/685
1/293 == 1/516 + 1/678
1/293 == 1/525 + 1/663
1/293 == 1/539 + 1/642
1/293 == 1/544 + 1/635
1/293 == 1/547 + 1/631
1/293 == 1/583 + 1/589
1/293 == 1/584 + 1/588
1/293 == 1/585 + 1/587
1/307 == 1/443 + 1/1000
1/307 == 1/444 + 1/995
1/307 == 1/445 + 1/990
1/307 == 1/446 + 1/985
1/307 == 1/450 + 1/966
1/307 == 1/452 + 1/957
1/307 == 1/459 + 1/927
1/307 == 1/460 + 1/923
1/307 == 1/461 + 1/919
1/307 == 1/462 + 1/915
1/307 == 1/467 + 1/896
1/307 == 1/475 + 1/868
1/307 == 1/479 + 1/855
1/307 == 1/490 + 1/822
1/307 == 1/494 + 1/811
1/307 == 1/497 + 1/803
1/307 == 1/505 + 1/783
1/307 == 1/511 + 1/769
1/307 == 1/516 + 1/758
1/307 == 1/533 + 1/724
1/307 == 1/538 + 1/715
1/307 == 1/545 + 1/703
1/307 == 1/555 + 1/687
1/307 == 1/557 + 1/684
1/307 == 1/559 + 1/681
1/307 == 1/571 + 1/664
1/307 == 1/574 + 1/660
1/307 == 1/581 + 1/651
1/307 == 1/585 + 1/646
1/307 == 1/590 + 1/640
1/307 == 1/597 + 1/632
1/307 == 1/611 + 1/617
1/307 == 1/612 + 1/616
1/307 == 1/613 + 1/615
1/311 == 1/452 + 1/997
1/311 == 1/456 + 1/978
1/311 == 1/458 + 1/969
1/311 == 1/465 + 1/939
1/311 == 1/466 + 1/935
1/311 == 1/467 + 1/931
1/311 == 1/468 + 1/927
1/311 == 1/473 + 1/908
1/311 == 1/481 + 1/880
1/311 == 1/497 + 1/831
1/311 == 1/501 + 1/820
1/311 == 1/506 + 1/807
1/311 == 1/508 + 1/802
1/311 == 1/510 + 1/797
1/311 == 1/519 + 1/776
1/311 == 1/525 + 1/763
1/311 == 1/537 + 1/739
1/311 == 1/551 + 1/714
1/311 == 1/554 + 1/709
1/311 == 1/559 + 1/701
1/311 == 1/571 + 1/683
1/311 == 1/576 + 1/676
1/311 == 1/585 + 1/664
1/311 == 1/593 + 1/654
1/311 == 1/598 + 1/648
1/311 == 1/605 + 1/640
1/311 == 1/619 + 1/625
1/311 == 1/620 + 1/624
1/311 == 1/621 + 1/623
1/313 == 1/456 + 1/998
1/313 == 1/459 + 1/984
1/313 == 1/461 + 1/975
1/313 == 1/468 + 1/945
1/313 == 1/469 + 1/941
1/313 == 1/470 + 1/937
1/313 == 1/471 + 1/933
1/313 == 1/476 + 1/914
1/313 == 1/487 + 1/876
1/313 == 1/507 + 1/818
1/313 == 1/515 + 1/798
1/313 == 1/521 + 1/784
1/313 == 1/526 + 1/773
1/313 == 1/543 + 1/739
1/313 == 1/561 + 1/708
1/313 == 1/589 + 1/668
1/313 == 1/597 + 1/658
1/313 == 1/602 + 1/652
1/313 == 1/609 + 1/644
1/313 == 1/623 + 1/629
1/313 == 1/624 + 1/628
1/313 == 1/625 + 1/627
1/317 == 1/465 + 1/996
1/317 == 1/467 + 1/987
1/317 == 1/474 + 1/957
1/317 == 1/475 + 1/953
1/317 == 1/476 + 1/949
1/317 == 1/477 + 1/945
1/317 == 1/482 + 1/926
1/317 == 1/493 + 1/888
1/317 == 1/511 + 1/835
1/317 == 1/516 + 1/822
1/317 == 1/518 + 1/817
1/317 == 1/520 + 1/812
1/317 == 1/529 + 1/791
1/317 == 1/535 + 1/778
1/317 == 1/548 + 1/752
1/317 == 1/554 + 1/741
1/317 == 1/558 + 1/734
1/317 == 1/567 + 1/719
1/317 == 1/574 + 1/708
1/317 == 1/576 + 1/705
1/317 == 1/578 + 1/702
1/317 == 1/585 + 1/692
1/317 == 1/610 + 1/660
1/317 == 1/617 + 1/652
1/317 == 1/631 + 1/637
1/317 == 1/632 + 1/636
1/317 == 1/633 + 1/635
1/331 == 1/495 + 1/999
1/331 == 1/496 + 1/995
1/331 == 1/497 + 1/991
1/331 == 1/498 + 1/987
1/331 == 1/503 + 1/968
1/331 == 1/506 + 1/957
1/331 == 1/508 + 1/950
1/331 == 1/510 + 1/943
1/331 == 1/513 + 1/933
1/331 == 1/517 + 1/920
1/331 == 1/527 + 1/890
1/331 == 1/535 + 1/868
1/331 == 1/545 + 1/843
1/331 == 1/551 + 1/829
1/331 == 1/556 + 1/818
1/331 == 1/575 + 1/780
1/331 == 1/580 + 1/771
1/331 == 1/584 + 1/764
1/331 == 1/587 + 1/759
1/331 == 1/590 + 1/754
1/331 == 1/595 + 1/746
1/331 == 1/607 + 1/728
1/331 == 1/632 + 1/695
1/331 == 1/637 + 1/689
1/331 == 1/644 + 1/681
1/331 == 1/659 + 1/665
1/331 == 1/660 + 1/664
1/331 == 1/661 + 1/663
1/337 == 1/512 + 1/986
1/337 == 1/515 + 1/975
1/337 == 1/517 + 1/968
1/337 == 1/519 + 1/961
1/337 == 1/538 + 1/902
1/337 == 1/542 + 1/891
1/337 == 1/545 + 1/883
1/337 == 1/555 + 1/858
1/337 == 1/561 + 1/844
1/337 == 1/566 + 1/833
1/337 == 1/585 + 1/795
1/337 == 1/603 + 1/764
1/337 == 1/610 + 1/753
1/337 == 1/612 + 1/750
1/337 == 1/614 + 1/747
1/337 == 1/626 + 1/730
1/337 == 1/632 + 1/722
1/337 == 1/649 + 1/701
1/337 == 1/656 + 1/693
1/337 == 1/671 + 1/677
1/337 == 1/672 + 1/676
1/337 == 1/673 + 1/675
1/347 == 1/536 + 1/984
1/347 == 1/546 + 1/952
1/347 == 1/547 + 1/949
1/347 == 1/548 + 1/946
1/347 == 1/549 + 1/943
1/347 == 1/559 + 1/915
1/347 == 1/562 + 1/907
1/347 == 1/570 + 1/887
1/347 == 1/579 + 1/866
1/347 == 1/584 + 1/855
1/347 == 1/601 + 1/821
1/347 == 1/614 + 1/798
1/347 == 1/617 + 1/793
1/347 == 1/620 + 1/788
1/347 == 1/627 + 1/777
1/347 == 1/629 + 1/774
1/347 == 1/631 + 1/771
1/347 == 1/633 + 1/768
1/347 == 1/640 + 1/758
1/347 == 1/648 + 1/747
1/347 == 1/663 + 1/728
1/347 == 1/676 + 1/713
1/347 == 1/690 + 1/698
1/347 == 1/691 + 1/697
1/347 == 1/692 + 1/696
1/347 == 1/693 + 1/695
1/349 == 1/539 + 1/990
1/349 == 1/542 + 1/980
1/349 == 1/548 + 1/961
1/349 == 1/549 + 1/958
1/349 == 1/550 + 1/955
1/349 == 1/551 + 1/952
1/349 == 1/552 + 1/949
1/349 == 1/553 + 1/946
1/349 == 1/559 + 1/929
1/349 == 1/575 + 1/888
1/349 == 1/581 + 1/874
1/349 == 1/586 + 1/863
1/349 == 1/606 + 1/823
1/349 == 1/629 + 1/784
1/349 == 1/639 + 1/769
1/349 == 1/649 + 1/755
1/349 == 1/652 + 1/751
1/349 == 1/655 + 1/747
1/349 == 1/667 + 1/732
1/349 == 1/680 + 1/717
1/349 == 1/694 + 1/702
1/349 == 1/695 + 1/701
1/349 == 1/696 + 1/700
1/349 == 1/697 + 1/699
1/353 == 1/548 + 1/992
1/353 == 1/553 + 1/976
1/353 == 1/554 + 1/973
1/353 == 1/560 + 1/955
1/353 == 1/561 + 1/952
1/353 == 1/566 + 1/938
1/353 == 1/572 + 1/922
1/353 == 1/580 + 1/902
1/353 == 1/589 + 1/881
1/353 == 1/594 + 1/870
1/353 == 1/611 + 1/836
1/353 == 1/617 + 1/825
1/353 == 1/621 + 1/818
1/353 == 1/633 + 1/798
1/353 == 1/649 + 1/774
1/353 == 1/654 + 1/767
1/353 == 1/663 + 1/755
1/353 == 1/675 + 1/740
1/353 == 1/688 + 1/725
1/353 == 1/702 + 1/710
1/353 == 1/703 + 1/709
1/353 == 1/704 + 1/708
1/353 == 1/705 + 1/707
1/359 == 1/561 + 1/997
1/359 == 1/571 + 1/967
1/359 == 1/572 + 1/964
1/359 == 1/576 + 1/953
1/359 == 1/582 + 1/937
1/359 == 1/590 + 1/917
1/359 == 1/599 + 1/896
1/359 == 1/604 + 1/885
1/359 == 1/622 + 1/849
1/359 == 1/635 + 1/826
1/359 == 1/638 + 1/821
1/359 == 1/641 + 1/816
1/359 == 1/646 + 1/808
1/359 == 1/648 + 1/805
1/359 == 1/656 + 1/793
1/359 == 1/658 + 1/790
1/359 == 1/663 + 1/783
1/359 == 1/678 + 1/763
1/359 == 1/682 + 1/758
1/359 == 1/692 + 1/746
1/359 == 1/700 + 1/737
1/359 == 1/714 + 1/722
1/359 == 1/715 + 1/721
1/359 == 1/716 + 1/720
1/359 == 1/717 + 1/719
1/367 == 1/586 + 1/982
1/367 == 1/590 + 1/971
1/367 == 1/593 + 1/963
1/367 == 1/598 + 1/950
1/367 == 1/600 + 1/945
1/367 == 1/605 + 1/933
1/367 == 1/611 + 1/919
1/367 == 1/616 + 1/908
1/367 == 1/625 + 1/889
1/367 == 1/626 + 1/887
1/367 == 1/627 + 1/885
1/367 == 1/628 + 1/883
1/367 == 1/638 + 1/864
1/367 == 1/643 + 1/855
1/367 == 1/647 + 1/848
1/367 == 1/650 + 1/843
1/367 == 1/653 + 1/838
1/367 == 1/656 + 1/833
1/367 == 1/663 + 1/822
1/367 == 1/665 + 1/819
1/367 == 1/667 + 1/816
1/367 == 1/669 + 1/813
1/367 == 1/671 + 1/810
1/367 == 1/681 + 1/796
1/367 == 1/690 + 1/784
1/367 == 1/702 + 1/769
1/367 == 1/708 + 1/762
1/367 == 1/715 + 1/754
1/367 == 1/730 + 1/738
1/367 == 1/731 + 1/737
1/367 == 1/732 + 1/736
1/367 == 1/733 + 1/735
1/373 == 1/600 + 1/986
1/373 == 1/603 + 1/978
1/373 == 1/608 + 1/965
1/373 == 1/610 + 1/960
1/373 == 1/615 + 1/948
1/373 == 1/621 + 1/934
1/373 == 1/626 + 1/923
1/373 == 1/634 + 1/906
1/373 == 1/635 + 1/904
1/373 == 1/636 + 1/902
1/373 == 1/637 + 1/900
1/373 == 1/638 + 1/898
1/373 == 1/639 + 1/896
1/373 == 1/648 + 1/879
1/373 == 1/669 + 1/843
1/373 == 1/714 + 1/781
1/373 == 1/720 + 1/774
1/373 == 1/727 + 1/766
1/373 == 1/742 + 1/750
1/373 == 1/743 + 1/749
1/373 == 1/744 + 1/748
1/373 == 1/745 + 1/747
1/379 == 1/616 + 1/985
1/379 == 1/618 + 1/980
1/379 == 1/620 + 1/975
1/379 == 1/631 + 1/949
1/379 == 1/636 + 1/938
1/379 == 1/644 + 1/921
1/379 == 1/645 + 1/919
1/379 == 1/646 + 1/917
1/379 == 1/647 + 1/915
1/379 == 1/648 + 1/913
1/379 == 1/649 + 1/911
1/379 == 1/650 + 1/909
1/379 == 1/659 + 1/892
1/379 == 1/664 + 1/883
1/379 == 1/668 + 1/876
1/379 == 1/677 + 1/861
1/379 == 1/682 + 1/853
1/379 == 1/684 + 1/850
1/379 == 1/694 + 1/835
1/379 == 1/704 + 1/821
1/379 == 1/710 + 1/813
1/379 == 1/713 + 1/809
1/379 == 1/717 + 1/804
1/379 == 1/721 + 1/799
1/379 == 1/726 + 1/793
1/379 == 1/739 + 1/778
1/379 == 1/754 + 1/762
1/379 == 1/755 + 1/761
1/379 == 1/756 + 1/760
1/379 == 1/757 + 1/759
1/383 == 1/639 + 1/956
1/383 == 1/644 + 1/945
1/383 == 1/664 + 1/905
1/383 == 1/677 + 1/882
1/383 == 1/683 + 1/872
1/383 == 1/688 + 1/864
1/383 == 1/704 + 1/840
1/383 == 1/709 + 1/833
1/383 == 1/721 + 1/817
1/383 == 1/729 + 1/807
1/383 == 1/739 + 1/795
1/383 == 1/747 + 1/786
1/383 == 1/762 + 1/770
1/383 == 1/763 + 1/769
1/383 == 1/764 + 1/768
1/383 == 1/765 + 1/767
1/389 == 1/649 + 1/971
1/389 == 1/654 + 1/960
1/389 == 1/674 + 1/920
1/389 == 1/680 + 1/909
1/389 == 1/684 + 1/902
1/389 == 1/691 + 1/890
1/389 == 1/701 + 1/874
1/389 == 1/711 + 1/859
1/389 == 1/713 + 1/856
1/389 == 1/718 + 1/849
1/389 == 1/723 + 1/842
1/389 == 1/726 + 1/838
1/389 == 1/729 + 1/834
1/389 == 1/745 + 1/814
1/389 == 1/751 + 1/807
1/389 == 1/759 + 1/798
1/389 == 1/774 + 1/782
1/389 == 1/775 + 1/781
1/389 == 1/776 + 1/780
1/389 == 1/777 + 1/779
1/397 == 1/661 + 1/994
1/397 == 1/665 + 1/985
1/397 == 1/666 + 1/983
1/397 == 1/673 + 1/968
1/397 == 1/674 + 1/966
1/397 == 1/675 + 1/964
1/397 == 1/680 + 1/954
1/397 == 1/681 + 1/952
1/397 == 1/682 + 1/950
1/397 == 1/683 + 1/948
1/397 == 1/690 + 1/935
1/397 == 1/691 + 1/933
1/397 == 1/703 + 1/912
1/397 == 1/706 + 1/907
1/397 == 1/711 + 1/899
1/397 == 1/716 + 1/891
1/397 == 1/718 + 1/888
1/397 == 1/720 + 1/885
1/397 == 1/722 + 1/882
1/397 == 1/724 + 1/879
1/397 == 1/726 + 1/876
1/397 == 1/733 + 1/866
1/397 == 1/748 + 1/846
1/397 == 1/752 + 1/841
1/397 == 1/756 + 1/836
1/397 == 1/761 + 1/830
1/397 == 1/767 + 1/823
1/397 == 1/774 + 1/815
1/397 == 1/775 + 1/814
1/397 == 1/789 + 1/799
1/397 == 1/790 + 1/798
1/397 == 1/791 + 1/797
1/397 == 1/792 + 1/796
1/397 == 1/793 + 1/795
1/401 == 1/674 + 1/990
1/401 == 1/695 + 1/948
1/401 == 1/696 + 1/946
1/401 == 1/701 + 1/937
1/401 == 1/705 + 1/930
1/401 == 1/709 + 1/923
1/401 == 1/712 + 1/918
1/401 == 1/720 + 1/905
1/401 == 1/722 + 1/902
1/401 == 1/736 + 1/881
1/401 == 1/741 + 1/874
1/401 == 1/749 + 1/863
1/401 == 1/756 + 1/854
1/401 == 1/764 + 1/844
1/401 == 1/769 + 1/838
1/401 == 1/775 + 1/831
1/401 == 1/782 + 1/823
1/401 == 1/783 + 1/822
1/401 == 1/797 + 1/807
1/401 == 1/798 + 1/806
1/401 == 1/799 + 1/805
1/401 == 1/800 + 1/804
1/401 == 1/801 + 1/803
1/409 == 1/692 + 1/1000
1/409 == 1/693 + 1/998
1/409 == 1/694 + 1/996
1/409 == 1/702 + 1/980
1/409 == 1/703 + 1/978
1/409 == 1/704 + 1/976
1/409 == 1/711 + 1/963
1/409 == 1/712 + 1/961
1/409 == 1/724 + 1/940
1/409 == 1/727 + 1/935
1/409 == 1/737 + 1/919
1/409 == 1/749 + 1/901
1/409 == 1/756 + 1/891
1/409 == 1/759 + 1/887
1/409 == 1/768 + 1/875
1/409 == 1/775 + 1/866
1/409 == 1/790 + 1/848
1/409 == 1/798 + 1/839
1/409 == 1/813 + 1/823
1/409 == 1/814 + 1/822
1/409 == 1/815 + 1/821
1/409 == 1/816 + 1/820
1/409 == 1/817 + 1/819
1/419 == 1/727 + 1/989
1/419 == 1/737 + 1/971
1/419 == 1/740 + 1/966
1/419 == 1/749 + 1/951
1/419 == 1/754 + 1/943
1/419 == 1/756 + 1/940
1/419 == 1/766 + 1/925
1/419 == 1/768 + 1/922
1/419 == 1/773 + 1/915
1/419 == 1/778 + 1/908
1/419 == 1/781 + 1/904
1/419 == 1/784 + 1/900
1/419 == 1/787 + 1/896
1/419 == 1/791 + 1/891
1/419 == 1/799 + 1/881
1/419 == 1/804 + 1/875
1/419 == 1/810 + 1/868
1/419 == 1/818 + 1/859
1/419 == 1/833 + 1/843
1/419 == 1/834 + 1/842
1/419 == 1/835 + 1/841
1/419 == 1/836 + 1/840
1/419 == 1/837 + 1/839
1/421 == 1/732 + 1/991
1/421 == 1/733 + 1/989
1/421 == 1/745 + 1/968
1/421 == 1/748 + 1/963
1/421 == 1/756 + 1/950
1/421 == 1/758 + 1/947
1/421 == 1/772 + 1/926
1/421 == 1/782 + 1/912
1/421 == 1/785 + 1/908
1/421 == 1/788 + 1/904
1/421 == 1/791 + 1/900
1/421 == 1/803 + 1/885
1/421 == 1/808 + 1/879
1/421 == 1/814 + 1/872
1/421 == 1/822 + 1/863
1/421 == 1/837 + 1/847
1/421 == 1/838 + 1/846
1/421 == 1/839 + 1/845
1/421 == 1/840 + 1/844
1/421 == 1/841 + 1/843
1/431 == 1/758 + 1/999
1/431 == 1/761 + 1/994
1/431 == 1/770 + 1/979
1/431 == 1/775 + 1/971
1/431 == 1/791 + 1/947
1/431 == 1/796 + 1/940
1/431 == 1/801 + 1/933
1/431 == 1/804 + 1/929
1/431 == 1/807 + 1/925
1/431 == 1/814 + 1/916
1/431 == 1/818 + 1/911
1/431 == 1/834 + 1/892
1/431 == 1/841 + 1/884
1/431 == 1/842 + 1/883
1/431 == 1/857 + 1/867
1/431 == 1/858 + 1/866
1/431 == 1/859 + 1/865
1/431 == 1/860 + 1/864
1/431 == 1/861 + 1/863
1/433 == 1/766 + 1/996
1/433 == 1/769 + 1/991
1/433 == 1/772 + 1/986
1/433 == 1/777 + 1/978
1/433 == 1/795 + 1/951
1/433 == 1/797 + 1/948
1/433 == 1/805 + 1/937
1/433 == 1/808 + 1/933
1/433 == 1/811 + 1/929
1/433 == 1/818 + 1/920
1/433 == 1/822 + 1/915
1/433 == 1/826 + 1/910
1/433 == 1/831 + 1/904
1/433 == 1/838 + 1/896
1/433 == 1/845 + 1/888
1/433 == 1/846 + 1/887
1/433 == 1/861 + 1/871
1/433 == 1/862 + 1/870
1/433 == 1/863 + 1/869
1/433 == 1/864 + 1/868
1/433 == 1/865 + 1/867
1/439 == 1/785 + 1/996
1/439 == 1/790 + 1/988
1/439 == 1/792 + 1/985
1/439 == 1/802 + 1/970
1/439 == 1/804 + 1/967
1/439 == 1/811 + 1/957
1/439 == 1/814 + 1/953
1/439 == 1/826 + 1/937
1/439 == 1/838 + 1/922
1/439 == 1/843 + 1/916
1/439 == 1/849 + 1/909
1/439 == 1/857 + 1/900
1/439 == 1/858 + 1/899
1/439 == 1/873 + 1/883
1/439 == 1/874 + 1/882
1/439 == 1/875 + 1/881
1/439 == 1/876 + 1/880
1/439 == 1/877 + 1/879
1/443 == 1/796 + 1/999
1/443 == 1/814 + 1/972
1/443 == 1/819 + 1/965
1/443 == 1/824 + 1/958
1/443 == 1/827 + 1/954
1/443 == 1/834 + 1/945
1/443 == 1/846 + 1/930
1/443 == 1/851 + 1/924
1/443 == 1/857 + 1/917
1/443 == 1/865 + 1/908
1/443 == 1/866 + 1/907
1/443 == 1/881 + 1/891
1/443 == 1/882 + 1/890
1/443 == 1/883 + 1/889
1/443 == 1/884 + 1/888
1/443 == 1/885 + 1/887
1/449 == 1/821 + 1/991
1/449 == 1/823 + 1/988
1/449 == 1/828 + 1/981
1/449 == 1/833 + 1/974
1/449 == 1/836 + 1/970
1/449 == 1/839 + 1/966
1/449 == 1/842 + 1/962
1/449 == 1/849 + 1/953
1/449 == 1/853 + 1/948
1/449 == 1/858 + 1/942
1/449 == 1/863 + 1/936
1/449 == 1/869 + 1/929
1/449 == 1/877 + 1/920
1/449 == 1/878 + 1/919
1/449 == 1/892 + 1/904
1/449 == 1/893 + 1/903
1/449 == 1/894 + 1/902
1/449 == 1/895 + 1/901
1/449 == 1/896 + 1/900
1/449 == 1/897 + 1/899
1/457 == 1/843 + 1/998
1/457 == 1/851 + 1/987
1/457 == 1/854 + 1/983
1/457 == 1/861 + 1/974
1/457 == 1/869 + 1/964
1/457 == 1/873 + 1/959
1/457 == 1/878 + 1/953
1/457 == 1/885 + 1/945
1/457 == 1/893 + 1/936
1/457 == 1/894 + 1/935
1/457 == 1/908 + 1/920
1/457 == 1/909 + 1/919
1/457 == 1/910 + 1/918
1/457 == 1/911 + 1/917
1/457 == 1/912 + 1/916
1/457 == 1/913 + 1/915
1/461 == 1/856 + 1/999
1/461 == 1/859 + 1/995
1/461 == 1/862 + 1/991
1/461 == 1/865 + 1/987
1/461 == 1/872 + 1/978
1/461 == 1/881 + 1/967
1/461 == 1/886 + 1/961
1/461 == 1/892 + 1/954
1/461 == 1/893 + 1/953
1/461 == 1/901 + 1/944
1/461 == 1/916 + 1/928
1/461 == 1/917 + 1/927
1/461 == 1/918 + 1/926
1/461 == 1/919 + 1/925
1/461 == 1/920 + 1/924
1/461 == 1/921 + 1/923
1/463 == 1/863 + 1/999
1/463 == 1/866 + 1/995
1/463 == 1/869 + 1/991
1/463 == 1/876 + 1/982
1/463 == 1/880 + 1/977
1/463 == 1/885 + 1/971
1/463 == 1/890 + 1/965
1/463 == 1/896 + 1/958
1/463 == 1/897 + 1/957
1/463 == 1/905 + 1/948
1/463 == 1/920 + 1/932
1/463 == 1/921 + 1/931
1/463 == 1/922 + 1/930
1/463 == 1/923 + 1/929
1/463 == 1/924 + 1/928
1/463 == 1/925 + 1/927
1/467 == 1/877 + 1/999
1/467 == 1/880 + 1/995
1/467 == 1/884 + 1/990
1/467 == 1/888 + 1/985
1/467 == 1/893 + 1/979
1/467 == 1/898 + 1/973
1/467 == 1/904 + 1/966
1/467 == 1/905 + 1/965
1/467 == 1/912 + 1/957
1/467 == 1/913 + 1/956
1/467 == 1/928 + 1/940
1/467 == 1/929 + 1/939
1/467 == 1/930 + 1/938
1/467 == 1/931 + 1/937
1/467 == 1/932 + 1/936
1/467 == 1/933 + 1/935
1/479 == 1/921 + 1/998
1/479 == 1/922 + 1/997
1/479 == 1/928 + 1/990
1/479 == 1/936 + 1/981
1/479 == 1/937 + 1/980
1/479 == 1/952 + 1/964
1/479 == 1/953 + 1/963
1/479 == 1/954 + 1/962
1/479 == 1/955 + 1/961
1/479 == 1/956 + 1/960
1/479 == 1/957 + 1/959
1/487 == 1/952 + 1/997
1/487 == 1/953 + 1/996
1/487 == 1/968 + 1/980
1/487 == 1/969 + 1/979
1/487 == 1/970 + 1/978
1/487 == 1/971 + 1/977
1/487 == 1/972 + 1/976
1/487 == 1/973 + 1/975
1/491 == 1/976 + 1/988
1/491 == 1/977 + 1/987
1/491 == 1/978 + 1/986
1/491 == 1/979 + 1/985
1/491 == 1/980 + 1/984
1/491 == 1/981 + 1/983
1/499 == 1/996 + 1/1000
1/499 == 1/997 + 1/999

Körde som sagt bara ner till 1/1000 för summeringarna.

Redigerat 31 Mars 2013 av WASD

[Dave37]

Det där kan inte stämma, WA säger att de enda bråken som finns för 1/479 är:

1/480 + 1/229920

1/958 + 1/958

 

Alltså talföljden

480, 958, 229920

 

Så det måste vara något avrundningsfel eller nått i ditt program. Felet blir i storleksordningen 10^-8, så se till att ditt program är jävligt noggrant, annars kommer det snabbt misslyckas att räkna så stora bråk.

Redigerat 31 Mars 2013 av Dave37

[WASD]

Som sagt så räknade jag bara ner till 1/1000. Inte 1/229920. Det skulle ta enormt mycket längre tid.

 

Varje enskilt bråk tar n^2/2 iterationer med min algoritm. Tar för lång tid om jag ska räkna så högt.

[Dave37]

Då låter vi bli tal lägre än 1/100 då för säkerhets skull. Kan du generera fram en lite längre lista än den jag har i #12 med liknande uppställning men då måste du ha med de som är "halva"?

Redigerat 31 Mars 2013 av Dave37

[WASD]

Ensamma bråken 1/1 till 1/100 inklusive 1/(2b)+1/(2b) med summeringsförsök ner till 1/10000 i samma format som inlägg #12.

 

 

1: 

1/1 = 1/2 + 1/2

2, 

 

2: 

1/2 = 1/3 + 1/6

1/2 = 1/4 + 1/4

3, 4, 6, 

 

3: 

1/3 = 1/4 + 1/12

1/3 = 1/6 + 1/6

4, 6, 12, 

 

4: 

1/4 = 1/5 + 1/20

1/4 = 1/6 + 1/12

1/4 = 1/8 + 1/8

5, 6, 8, 12, 20, 

 

5: 

1/5 = 1/6 + 1/30

1/5 = 1/10 + 1/10

6, 10, 30, 

 

6: 

1/6 = 1/7 + 1/42

1/6 = 1/8 + 1/24

1/6 = 1/9 + 1/18

1/6 = 1/10 + 1/15

1/6 = 1/12 + 1/12

7, 8, 9, 10, 12, 15, 18, 24, 42, 

 

7: 

1/7 = 1/8 + 1/56

1/7 = 1/14 + 1/14

8, 14, 56, 

 

8: 

1/8 = 1/9 + 1/72

1/8 = 1/10 + 1/40

1/8 = 1/12 + 1/24

1/8 = 1/16 + 1/16

9, 10, 12, 16, 24, 40, 72, 

 

9: 

1/9 = 1/10 + 1/90

1/9 = 1/12 + 1/36

1/9 = 1/18 + 1/18

10, 12, 18, 36, 90, 

 

10: 

1/10 = 1/11 + 1/110

1/10 = 1/12 + 1/60

1/10 = 1/14 + 1/35

1/10 = 1/15 + 1/30

1/10 = 1/20 + 1/20

11, 12, 14, 15, 20, 30, 35, 60, 110, 

 

11: 

1/11 = 1/12 + 1/132

1/11 = 1/22 + 1/22

12, 22, 132, 

 

12: 

1/12 = 1/13 + 1/156

1/12 = 1/14 + 1/84

1/12 = 1/15 + 1/60

1/12 = 1/16 + 1/48

1/12 = 1/18 + 1/36

1/12 = 1/20 + 1/30

1/12 = 1/21 + 1/28

1/12 = 1/24 + 1/24

13, 14, 15, 16, 18, 20, 21, 24, 28, 30, 36, 48, 60, 84, 156, 

 

13: 

1/13 = 1/14 + 1/182

1/13 = 1/26 + 1/26

14, 26, 182, 

 

14: 

1/14 = 1/15 + 1/210

1/14 = 1/16 + 1/112

1/14 = 1/18 + 1/63

1/14 = 1/21 + 1/42

1/14 = 1/28 + 1/28

15, 16, 18, 21, 28, 42, 63, 112, 210, 

 

15: 

1/15 = 1/16 + 1/240

1/15 = 1/18 + 1/90

1/15 = 1/20 + 1/60

1/15 = 1/24 + 1/40

1/15 = 1/30 + 1/30

16, 18, 20, 24, 30, 40, 60, 90, 240, 

 

16: 

1/16 = 1/17 + 1/272

1/16 = 1/18 + 1/144

1/16 = 1/20 + 1/80

1/16 = 1/24 + 1/48

1/16 = 1/32 + 1/32

17, 18, 20, 24, 32, 48, 80, 144, 272, 

 

17: 

1/17 = 1/18 + 1/306

1/17 = 1/34 + 1/34

18, 34, 306, 

 

18: 

1/18 = 1/19 + 1/342

1/18 = 1/20 + 1/180

1/18 = 1/21 + 1/126

1/18 = 1/22 + 1/99

1/18 = 1/24 + 1/72

1/18 = 1/27 + 1/54

1/18 = 1/30 + 1/45

1/18 = 1/36 + 1/36

19, 20, 21, 22, 24, 27, 30, 36, 45, 54, 72, 99, 126, 180, 342, 

 

19: 

1/19 = 1/20 + 1/380

1/19 = 1/38 + 1/38

20, 38, 380, 

 

20: 

1/20 = 1/21 + 1/420

1/20 = 1/22 + 1/220

1/20 = 1/24 + 1/120

1/20 = 1/25 + 1/100

1/20 = 1/28 + 1/70

1/20 = 1/30 + 1/60

1/20 = 1/36 + 1/45

1/20 = 1/40 + 1/40

21, 22, 24, 25, 28, 30, 36, 40, 45, 60, 70, 100, 120, 220, 420, 

 

21: 

1/21 = 1/22 + 1/462

1/21 = 1/24 + 1/168

1/21 = 1/28 + 1/84

1/21 = 1/30 + 1/70

1/21 = 1/42 + 1/42

22, 24, 28, 30, 42, 70, 84, 168, 462, 

 

22: 

1/22 = 1/23 + 1/506

1/22 = 1/24 + 1/264

1/22 = 1/26 + 1/143

1/22 = 1/33 + 1/66

1/22 = 1/44 + 1/44

23, 24, 26, 33, 44, 66, 143, 264, 506, 

 

23: 

1/23 = 1/24 + 1/552

1/23 = 1/46 + 1/46

24, 46, 552, 

 

24: 

1/24 = 1/25 + 1/600

1/24 = 1/26 + 1/312

1/24 = 1/27 + 1/216

1/24 = 1/28 + 1/168

1/24 = 1/30 + 1/120

1/24 = 1/32 + 1/96

1/24 = 1/33 + 1/88

1/24 = 1/36 + 1/72

1/24 = 1/40 + 1/60

1/24 = 1/42 + 1/56

1/24 = 1/48 + 1/48

25, 26, 27, 28, 30, 32, 33, 36, 40, 42, 48, 56, 60, 72, 88, 96, 120, 168, 216, 312, 600, 

 

25: 

1/25 = 1/26 + 1/650

1/25 = 1/30 + 1/150

1/25 = 1/50 + 1/50

26, 30, 50, 150, 650, 

 

26: 

1/26 = 1/27 + 1/702

1/26 = 1/28 + 1/364

1/26 = 1/30 + 1/195

1/26 = 1/39 + 1/78

1/26 = 1/52 + 1/52

27, 28, 30, 39, 52, 78, 195, 364, 702, 

 

27: 

1/27 = 1/28 + 1/756

1/27 = 1/30 + 1/270

1/27 = 1/36 + 1/108

1/27 = 1/54 + 1/54

28, 30, 36, 54, 108, 270, 756, 

 

28: 

1/28 = 1/29 + 1/812

1/28 = 1/30 + 1/420

1/28 = 1/32 + 1/224

1/28 = 1/35 + 1/140

1/28 = 1/36 + 1/126

1/28 = 1/42 + 1/84

1/28 = 1/44 + 1/77

1/28 = 1/56 + 1/56

29, 30, 32, 35, 36, 42, 44, 56, 77, 84, 126, 140, 224, 420, 812, 

 

29: 

1/29 = 1/30 + 1/870

1/29 = 1/58 + 1/58

30, 58, 870, 

 

30: 

1/30 = 1/31 + 1/930

1/30 = 1/32 + 1/480

1/30 = 1/33 + 1/330

1/30 = 1/34 + 1/255

1/30 = 1/35 + 1/210

1/30 = 1/36 + 1/180

1/30 = 1/39 + 1/130

1/30 = 1/40 + 1/120

1/30 = 1/42 + 1/105

1/30 = 1/45 + 1/90

1/30 = 1/48 + 1/80

1/30 = 1/50 + 1/75

1/30 = 1/55 + 1/66

1/30 = 1/60 + 1/60

31, 32, 33, 34, 35, 36, 39, 40, 42, 45, 48, 50, 55, 60, 66, 75, 80, 90, 105, 120, 130, 180, 210, 255, 330, 480, 930, 

 

31: 

1/31 = 1/32 + 1/992

1/31 = 1/62 + 1/62

32, 62, 992, 

 

32: 

1/32 = 1/33 + 1/1056

1/32 = 1/34 + 1/544

1/32 = 1/36 + 1/288

1/32 = 1/40 + 1/160

1/32 = 1/48 + 1/96

1/32 = 1/64 + 1/64

33, 34, 36, 40, 48, 64, 96, 160, 288, 544, 1056, 

 

33: 

1/33 = 1/34 + 1/1122

1/33 = 1/36 + 1/396

1/33 = 1/42 + 1/154

1/33 = 1/44 + 1/132

1/33 = 1/66 + 1/66

34, 36, 42, 44, 66, 132, 154, 396, 1122, 

 

34: 

1/34 = 1/35 + 1/1190

1/34 = 1/36 + 1/612

1/34 = 1/38 + 1/323

1/34 = 1/51 + 1/102

1/34 = 1/68 + 1/68

35, 36, 38, 51, 68, 102, 323, 612, 1190, 

 

35: 

1/35 = 1/36 + 1/1260

1/35 = 1/40 + 1/280

1/35 = 1/42 + 1/210

1/35 = 1/60 + 1/84

1/35 = 1/70 + 1/70

36, 40, 42, 60, 70, 84, 210, 280, 1260, 

 

36: 

1/36 = 1/37 + 1/1332

1/36 = 1/38 + 1/684

1/36 = 1/39 + 1/468

1/36 = 1/40 + 1/360

1/36 = 1/42 + 1/252

1/36 = 1/44 + 1/198

1/36 = 1/45 + 1/180

1/36 = 1/48 + 1/144

1/36 = 1/52 + 1/117

1/36 = 1/54 + 1/108

1/36 = 1/60 + 1/90

1/36 = 1/63 + 1/84

1/36 = 1/72 + 1/72

37, 38, 39, 40, 42, 44, 45, 48, 52, 54, 60, 63, 72, 84, 90, 108, 117, 144, 180, 198, 252, 360, 468, 684, 1332, 

 

37: 

1/37 = 1/38 + 1/1406

1/37 = 1/74 + 1/74

38, 74, 1406, 

 

38: 

1/38 = 1/39 + 1/1482

1/38 = 1/40 + 1/760

1/38 = 1/42 + 1/399

1/38 = 1/57 + 1/114

1/38 = 1/76 + 1/76

39, 40, 42, 57, 76, 114, 399, 760, 1482, 

 

39: 

1/39 = 1/40 + 1/1560

1/39 = 1/42 + 1/546

1/39 = 1/48 + 1/208

1/39 = 1/52 + 1/156

1/39 = 1/78 + 1/78

40, 42, 48, 52, 78, 156, 208, 546, 1560, 

 

40: 

1/40 = 1/41 + 1/1640

1/40 = 1/42 + 1/840

1/40 = 1/44 + 1/440

1/40 = 1/45 + 1/360

1/40 = 1/48 + 1/240

1/40 = 1/50 + 1/200

1/40 = 1/56 + 1/140

1/40 = 1/60 + 1/120

1/40 = 1/65 + 1/104

1/40 = 1/72 + 1/90

1/40 = 1/80 + 1/80

41, 42, 44, 45, 48, 50, 56, 60, 65, 72, 80, 90, 104, 120, 140, 200, 240, 360, 440, 840, 1640, 

 

41: 

1/41 = 1/42 + 1/1722

1/41 = 1/82 + 1/82

42, 82, 1722, 

 

42: 

1/42 = 1/43 + 1/1806

1/42 = 1/44 + 1/924

1/42 = 1/45 + 1/630

1/42 = 1/46 + 1/483

1/42 = 1/48 + 1/336

1/42 = 1/49 + 1/294

1/42 = 1/51 + 1/238

1/42 = 1/54 + 1/189

1/42 = 1/56 + 1/168

1/42 = 1/60 + 1/140

1/42 = 1/63 + 1/126

1/42 = 1/70 + 1/105

1/42 = 1/78 + 1/91

1/42 = 1/84 + 1/84

43, 44, 45, 46, 48, 49, 51, 54, 56, 60, 63, 70, 78, 84, 91, 105, 126, 140, 168, 189, 238, 294, 336, 483, 630, 924, 1806, 

 

43: 

1/43 = 1/44 + 1/1892

1/43 = 1/86 + 1/86

44, 86, 1892, 

 

44: 

1/44 = 1/45 + 1/1980

1/44 = 1/46 + 1/1012

1/44 = 1/48 + 1/528

1/44 = 1/52 + 1/286

1/44 = 1/55 + 1/220

1/44 = 1/60 + 1/165

1/44 = 1/66 + 1/132

1/44 = 1/88 + 1/88

45, 46, 48, 52, 55, 60, 66, 88, 132, 165, 220, 286, 528, 1012, 1980, 

 

45: 

1/45 = 1/46 + 1/2070

1/45 = 1/48 + 1/720

1/45 = 1/50 + 1/450

1/45 = 1/54 + 1/270

1/45 = 1/60 + 1/180

1/45 = 1/70 + 1/126

1/45 = 1/72 + 1/120

1/45 = 1/90 + 1/90

46, 48, 50, 54, 60, 70, 72, 90, 120, 126, 180, 270, 450, 720, 2070, 

 

46: 

1/46 = 1/47 + 1/2162

1/46 = 1/48 + 1/1104

1/46 = 1/50 + 1/575

1/46 = 1/69 + 1/138

1/46 = 1/92 + 1/92

47, 48, 50, 69, 92, 138, 575, 1104, 2162, 

 

47: 

1/47 = 1/48 + 1/2256

1/47 = 1/94 + 1/94

48, 94, 2256, 

 

48: 

1/48 = 1/49 + 1/2352

1/48 = 1/50 + 1/1200

1/48 = 1/51 + 1/816

1/48 = 1/52 + 1/624

1/48 = 1/54 + 1/432

1/48 = 1/56 + 1/336

1/48 = 1/57 + 1/304

1/48 = 1/60 + 1/240

1/48 = 1/64 + 1/192

1/48 = 1/66 + 1/176

1/48 = 1/72 + 1/144

1/48 = 1/80 + 1/120

1/48 = 1/84 + 1/112

1/48 = 1/96 + 1/96

49, 50, 51, 52, 54, 56, 57, 60, 64, 66, 72, 80, 84, 96, 112, 120, 144, 176, 192, 240, 304, 336, 432, 624, 816, 1200, 2352, 

 

49: 

1/49 = 1/50 + 1/2450

1/49 = 1/56 + 1/392

1/49 = 1/98 + 1/98

50, 56, 98, 392, 2450, 

 

50: 

1/50 = 1/51 + 1/2550

1/50 = 1/52 + 1/1300

1/50 = 1/54 + 1/675

1/50 = 1/55 + 1/550

1/50 = 1/60 + 1/300

1/50 = 1/70 + 1/175

1/50 = 1/75 + 1/150

1/50 = 1/100 + 1/100

51, 52, 54, 55, 60, 70, 75, 100, 150, 175, 300, 550, 675, 1300, 2550, 

 

51: 

1/51 = 1/52 + 1/2652

1/51 = 1/54 + 1/918

1/51 = 1/60 + 1/340

1/51 = 1/68 + 1/204

1/51 = 1/102 + 1/102

52, 54, 60, 68, 102, 204, 340, 918, 2652, 

 

52: 

1/52 = 1/53 + 1/2756

1/52 = 1/54 + 1/1404

1/52 = 1/56 + 1/728

1/52 = 1/60 + 1/390

1/52 = 1/65 + 1/260

1/52 = 1/68 + 1/221

1/52 = 1/78 + 1/156

1/52 = 1/104 + 1/104

53, 54, 56, 60, 65, 68, 78, 104, 156, 221, 260, 390, 728, 1404, 2756, 

 

53: 

1/53 = 1/54 + 1/2862

1/53 = 1/106 + 1/106

54, 106, 2862, 

 

54: 

1/54 = 1/55 + 1/2970

1/54 = 1/56 + 1/1512

1/54 = 1/57 + 1/1026

1/54 = 1/58 + 1/783

1/54 = 1/60 + 1/540

1/54 = 1/63 + 1/378

1/54 = 1/66 + 1/297

1/54 = 1/72 + 1/216

1/54 = 1/81 + 1/162

1/54 = 1/90 + 1/135

1/54 = 1/108 + 1/108

55, 56, 57, 58, 60, 63, 66, 72, 81, 90, 108, 135, 162, 216, 297, 378, 540, 783, 1026, 1512, 2970, 

 

55: 

1/55 = 1/56 + 1/3080

1/55 = 1/60 + 1/660

1/55 = 1/66 + 1/330

1/55 = 1/80 + 1/176

1/55 = 1/110 + 1/110

56, 60, 66, 80, 110, 176, 330, 660, 3080, 

 

56: 

1/56 = 1/57 + 1/3192

1/56 = 1/58 + 1/1624

1/56 = 1/60 + 1/840

1/56 = 1/63 + 1/504

1/56 = 1/64 + 1/448

1/56 = 1/70 + 1/280

1/56 = 1/72 + 1/252

1/56 = 1/84 + 1/168

1/56 = 1/88 + 1/154

1/56 = 1/105 + 1/120

1/56 = 1/112 + 1/112

57, 58, 60, 63, 64, 70, 72, 84, 88, 105, 112, 120, 154, 168, 252, 280, 448, 504, 840, 1624, 3192, 

 

57: 

1/57 = 1/58 + 1/3306

1/57 = 1/60 + 1/1140

1/57 = 1/66 + 1/418

1/57 = 1/76 + 1/228

1/57 = 1/114 + 1/114

58, 60, 66, 76, 114, 228, 418, 1140, 3306, 

 

58: 

1/58 = 1/59 + 1/3422

1/58 = 1/60 + 1/1740

1/58 = 1/62 + 1/899

1/58 = 1/87 + 1/174

1/58 = 1/116 + 1/116

59, 60, 62, 87, 116, 174, 899, 1740, 3422, 

 

59: 

1/59 = 1/60 + 1/3540

1/59 = 1/118 + 1/118

60, 118, 3540, 

 

60: 

1/60 = 1/61 + 1/3660

1/60 = 1/62 + 1/1860

1/60 = 1/63 + 1/1260

1/60 = 1/64 + 1/960

1/60 = 1/65 + 1/780

1/60 = 1/66 + 1/660

1/60 = 1/68 + 1/510

1/60 = 1/69 + 1/460

1/60 = 1/70 + 1/420

1/60 = 1/72 + 1/360

1/60 = 1/75 + 1/300

1/60 = 1/76 + 1/285

1/60 = 1/78 + 1/260

1/60 = 1/80 + 1/240

1/60 = 1/84 + 1/210

1/60 = 1/85 + 1/204

1/60 = 1/90 + 1/180

1/60 = 1/96 + 1/160

1/60 = 1/100 + 1/150

1/60 = 1/105 + 1/140

1/60 = 1/108 + 1/135

1/60 = 1/110 + 1/132

1/60 = 1/120 + 1/120

61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 78, 80, 84, 85, 90, 96, 100, 105, 108, 110, 120, 132, 135, 140, 150, 160, 180, 204, 210, 240, 260, 285, 300, 360, 420, 460, 510, 660, 780, 960, 1260, 1860, 3660, 

 

61: 

1/61 = 1/62 + 1/3782

1/61 = 1/122 + 1/122

62, 122, 3782, 

 

62: 

1/62 = 1/63 + 1/3906

1/62 = 1/64 + 1/1984

1/62 = 1/66 + 1/1023

1/62 = 1/93 + 1/186

1/62 = 1/124 + 1/124

63, 64, 66, 93, 124, 186, 1023, 1984, 3906, 

 

63: 

1/63 = 1/64 + 1/4032

1/63 = 1/66 + 1/1386

1/63 = 1/70 + 1/630

1/63 = 1/72 + 1/504

1/63 = 1/84 + 1/252

1/63 = 1/90 + 1/210

1/63 = 1/112 + 1/144

1/63 = 1/126 + 1/126

64, 66, 70, 72, 84, 90, 112, 126, 144, 210, 252, 504, 630, 1386, 4032, 

 

64: 

1/64 = 1/65 + 1/4160

1/64 = 1/66 + 1/2112

1/64 = 1/68 + 1/1088

1/64 = 1/72 + 1/576

1/64 = 1/80 + 1/320

1/64 = 1/96 + 1/192

1/64 = 1/128 + 1/128

65, 66, 68, 72, 80, 96, 128, 192, 320, 576, 1088, 2112, 4160, 

 

65: 

1/65 = 1/66 + 1/4290

1/65 = 1/70 + 1/910

1/65 = 1/78 + 1/390

1/65 = 1/90 + 1/234

1/65 = 1/130 + 1/130

66, 70, 78, 90, 130, 234, 390, 910, 4290, 

 

66: 

1/66 = 1/67 + 1/4422

1/66 = 1/68 + 1/2244

1/66 = 1/69 + 1/1518

1/66 = 1/70 + 1/1155

1/66 = 1/72 + 1/792

1/66 = 1/75 + 1/550

1/66 = 1/77 + 1/462

1/66 = 1/78 + 1/429

1/66 = 1/84 + 1/308

1/66 = 1/88 + 1/264

1/66 = 1/99 + 1/198

1/66 = 1/102 + 1/187

1/66 = 1/110 + 1/165

1/66 = 1/132 + 1/132

67, 68, 69, 70, 72, 75, 77, 78, 84, 88, 99, 102, 110, 132, 165, 187, 198, 264, 308, 429, 462, 550, 792, 1155, 1518, 2244, 4422, 

 

67: 

1/67 = 1/68 + 1/4556

1/67 = 1/134 + 1/134

68, 134, 4556, 

 

68: 

1/68 = 1/69 + 1/4692

1/68 = 1/70 + 1/2380

1/68 = 1/72 + 1/1224

1/68 = 1/76 + 1/646

1/68 = 1/84 + 1/357

1/68 = 1/85 + 1/340

1/68 = 1/102 + 1/204

1/68 = 1/136 + 1/136

69, 70, 72, 76, 84, 85, 102, 136, 204, 340, 357, 646, 1224, 2380, 4692, 

 

69: 

1/69 = 1/70 + 1/4830

1/69 = 1/72 + 1/1656

1/69 = 1/78 + 1/598

1/69 = 1/92 + 1/276

1/69 = 1/138 + 1/138

70, 72, 78, 92, 138, 276, 598, 1656, 4830, 

 

70: 

1/70 = 1/71 + 1/4970

1/70 = 1/72 + 1/2520

1/70 = 1/74 + 1/1295

1/70 = 1/75 + 1/1050

1/70 = 1/77 + 1/770

1/70 = 1/80 + 1/560

1/70 = 1/84 + 1/420

1/70 = 1/90 + 1/315

1/70 = 1/95 + 1/266

1/70 = 1/98 + 1/245

1/70 = 1/105 + 1/210

1/70 = 1/119 + 1/170

1/70 = 1/120 + 1/168

1/70 = 1/140 + 1/140

71, 72, 74, 75, 77, 80, 84, 90, 95, 98, 105, 119, 120, 140, 168, 170, 210, 245, 266, 315, 420, 560, 770, 1050, 1295, 2520, 4970, 

 

71: 

1/71 = 1/72 + 1/5112

1/71 = 1/142 + 1/142

72, 142, 5112, 

 

72: 

1/72 = 1/73 + 1/5256

1/72 = 1/74 + 1/2664

1/72 = 1/75 + 1/1800

1/72 = 1/76 + 1/1368

1/72 = 1/78 + 1/936

1/72 = 1/80 + 1/720

1/72 = 1/81 + 1/648

1/72 = 1/84 + 1/504

1/72 = 1/88 + 1/396

1/72 = 1/90 + 1/360

1/72 = 1/96 + 1/288

1/72 = 1/99 + 1/264

1/72 = 1/104 + 1/234

1/72 = 1/108 + 1/216

1/72 = 1/120 + 1/180

1/72 = 1/126 + 1/168

1/72 = 1/136 + 1/153

1/72 = 1/144 + 1/144

73, 74, 75, 76, 78, 80, 81, 84, 88, 90, 96, 99, 104, 108, 120, 126, 136, 144, 153, 168, 180, 216, 234, 264, 288, 360, 396, 504, 648, 720, 936, 1368, 1800, 2664, 5256, 

 

73: 

1/73 = 1/74 + 1/5402

1/73 = 1/146 + 1/146

74, 146, 5402, 

 

74: 

1/74 = 1/75 + 1/5550

1/74 = 1/76 + 1/2812

1/74 = 1/78 + 1/1443

1/74 = 1/111 + 1/222

1/74 = 1/148 + 1/148

75, 76, 78, 111, 148, 222, 1443, 2812, 5550, 

 

75: 

1/75 = 1/76 + 1/5700

1/75 = 1/78 + 1/1950

1/75 = 1/80 + 1/1200

1/75 = 1/84 + 1/700

1/75 = 1/90 + 1/450

1/75 = 1/100 + 1/300

1/75 = 1/120 + 1/200

1/75 = 1/150 + 1/150

76, 78, 80, 84, 90, 100, 120, 150, 200, 300, 450, 700, 1200, 1950, 5700, 

 

76: 

1/76 = 1/77 + 1/5852

1/76 = 1/78 + 1/2964

1/76 = 1/80 + 1/1520

1/76 = 1/84 + 1/798

1/76 = 1/92 + 1/437

1/76 = 1/95 + 1/380

1/76 = 1/114 + 1/228

1/76 = 1/152 + 1/152

77, 78, 80, 84, 92, 95, 114, 152, 228, 380, 437, 798, 1520, 2964, 5852, 

 

77: 

1/77 = 1/78 + 1/6006

1/77 = 1/84 + 1/924

1/77 = 1/88 + 1/616

1/77 = 1/126 + 1/198

1/77 = 1/154 + 1/154

78, 84, 88, 126, 154, 198, 616, 924, 6006, 

 

78: 

1/78 = 1/79 + 1/6162

1/78 = 1/80 + 1/3120

1/78 = 1/81 + 1/2106

1/78 = 1/82 + 1/1599

1/78 = 1/84 + 1/1092

1/78 = 1/87 + 1/754

1/78 = 1/90 + 1/585

1/78 = 1/91 + 1/546

1/78 = 1/96 + 1/416

1/78 = 1/104 + 1/312

1/78 = 1/114 + 1/247

1/78 = 1/117 + 1/234

1/78 = 1/130 + 1/195

1/78 = 1/156 + 1/156

79, 80, 81, 82, 84, 87, 90, 91, 96, 104, 114, 117, 130, 156, 195, 234, 247, 312, 416, 546, 585, 754, 1092, 1599, 2106, 3120, 6162, 

 

79: 

1/79 = 1/80 + 1/6320

1/79 = 1/158 + 1/158

80, 158, 6320, 

 

80: 

1/80 = 1/81 + 1/6480

1/80 = 1/82 + 1/3280

1/80 = 1/84 + 1/1680

1/80 = 1/85 + 1/1360

1/80 = 1/88 + 1/880

1/80 = 1/90 + 1/720

1/80 = 1/96 + 1/480

1/80 = 1/100 + 1/400

1/80 = 1/105 + 1/336

1/80 = 1/112 + 1/280

1/80 = 1/120 + 1/240

1/80 = 1/130 + 1/208

1/80 = 1/144 + 1/180

1/80 = 1/160 + 1/160

81, 82, 84, 85, 88, 90, 96, 100, 105, 112, 120, 130, 144, 160, 180, 208, 240, 280, 336, 400, 480, 720, 880, 1360, 1680, 3280, 6480, 

 

81: 

1/81 = 1/82 + 1/6642

1/81 = 1/84 + 1/2268

1/81 = 1/90 + 1/810

1/81 = 1/108 + 1/324

1/81 = 1/162 + 1/162

82, 84, 90, 108, 162, 324, 810, 2268, 6642, 

 

82: 

1/82 = 1/83 + 1/6806

1/82 = 1/84 + 1/3444

1/82 = 1/86 + 1/1763

1/82 = 1/123 + 1/246

1/82 = 1/164 + 1/164

83, 84, 86, 123, 164, 246, 1763, 3444, 6806, 

 

83: 

1/83 = 1/84 + 1/6972

1/83 = 1/166 + 1/166

84, 166, 6972, 

 

84: 

1/84 = 1/85 + 1/7140

1/84 = 1/86 + 1/3612

1/84 = 1/87 + 1/2436

1/84 = 1/88 + 1/1848

1/84 = 1/90 + 1/1260

1/84 = 1/91 + 1/1092

1/84 = 1/92 + 1/966

1/84 = 1/93 + 1/868

1/84 = 1/96 + 1/672

1/84 = 1/98 + 1/588

1/84 = 1/100 + 1/525

1/84 = 1/102 + 1/476

1/84 = 1/105 + 1/420

1/84 = 1/108 + 1/378

1/84 = 1/112 + 1/336

1/84 = 1/120 + 1/280

1/84 = 1/126 + 1/252

1/84 = 1/132 + 1/231

1/84 = 1/133 + 1/228

1/84 = 1/140 + 1/210

1/84 = 1/147 + 1/196

1/84 = 1/156 + 1/182

1/84 = 1/168 + 1/168

85, 86, 87, 88, 90, 91, 92, 93, 96, 98, 100, 102, 105, 108, 112, 120, 126, 132, 133, 140, 147, 156, 168, 182, 196, 210, 228, 231, 252, 280, 336, 378, 420, 476, 525, 588, 672, 868, 966, 1092, 1260, 1848, 2436, 3612, 7140, 

 

85: 

1/85 = 1/86 + 1/7310

1/85 = 1/90 + 1/1530

1/85 = 1/102 + 1/510

1/85 = 1/110 + 1/374

1/85 = 1/170 + 1/170

86, 90, 102, 110, 170, 374, 510, 1530, 7310, 

 

86: 

1/86 = 1/87 + 1/7482

1/86 = 1/88 + 1/3784

1/86 = 1/90 + 1/1935

1/86 = 1/129 + 1/258

1/86 = 1/172 + 1/172

87, 88, 90, 129, 172, 258, 1935, 3784, 7482, 

 

87: 

1/87 = 1/88 + 1/7656

1/87 = 1/90 + 1/2610

1/87 = 1/96 + 1/928

1/87 = 1/116 + 1/348

1/87 = 1/174 + 1/174

88, 90, 96, 116, 174, 348, 928, 2610, 7656, 

 

88: 

1/88 = 1/89 + 1/7832

1/88 = 1/90 + 1/3960

1/88 = 1/92 + 1/2024

1/88 = 1/96 + 1/1056

1/88 = 1/99 + 1/792

1/88 = 1/104 + 1/572

1/88 = 1/110 + 1/440

1/88 = 1/120 + 1/330

1/88 = 1/132 + 1/264

1/88 = 1/152 + 1/209

1/88 = 1/176 + 1/176

89, 90, 92, 96, 99, 104, 110, 120, 132, 152, 176, 209, 264, 330, 440, 572, 792, 1056, 2024, 3960, 7832, 

 

89: 

1/89 = 1/90 + 1/8010

1/89 = 1/178 + 1/178

90, 178, 8010, 

 

90: 

1/90 = 1/91 + 1/8190

1/90 = 1/92 + 1/4140

1/90 = 1/93 + 1/2790

1/90 = 1/94 + 1/2115

1/90 = 1/95 + 1/1710

1/90 = 1/96 + 1/1440

1/90 = 1/99 + 1/990

1/90 = 1/100 + 1/900

1/90 = 1/102 + 1/765

1/90 = 1/105 + 1/630

1/90 = 1/108 + 1/540

1/90 = 1/110 + 1/495

1/90 = 1/115 + 1/414

1/90 = 1/117 + 1/390

1/90 = 1/120 + 1/360

1/90 = 1/126 + 1/315

1/90 = 1/135 + 1/270

1/90 = 1/140 + 1/252

1/90 = 1/144 + 1/240

1/90 = 1/150 + 1/225

1/90 = 1/165 + 1/198

1/90 = 1/171 + 1/190

1/90 = 1/180 + 1/180

91, 92, 93, 94, 95, 96, 99, 100, 102, 105, 108, 110, 115, 117, 120, 126, 135, 140, 144, 150, 165, 171, 180, 190, 198, 225, 240, 252, 270, 315, 360, 390, 414, 495, 540, 630, 765, 900, 990, 1440, 1710, 2115, 2790, 4140, 8190, 

 

91: 

1/91 = 1/92 + 1/8372

1/91 = 1/98 + 1/1274

1/91 = 1/104 + 1/728

1/91 = 1/140 + 1/260

1/91 = 1/182 + 1/182

92, 98, 104, 140, 182, 260, 728, 1274, 8372, 

 

92: 

1/92 = 1/93 + 1/8556

1/92 = 1/94 + 1/4324

1/92 = 1/96 + 1/2208

1/92 = 1/100 + 1/1150

1/92 = 1/108 + 1/621

1/92 = 1/115 + 1/460

1/92 = 1/138 + 1/276

1/92 = 1/184 + 1/184

93, 94, 96, 100, 108, 115, 138, 184, 276, 460, 621, 1150, 2208, 4324, 8556, 

 

93: 

1/93 = 1/94 + 1/8742

1/93 = 1/96 + 1/2976

1/93 = 1/102 + 1/1054

1/93 = 1/124 + 1/372

1/93 = 1/186 + 1/186

94, 96, 102, 124, 186, 372, 1054, 2976, 8742, 

 

94: 

1/94 = 1/95 + 1/8930

1/94 = 1/96 + 1/4512

1/94 = 1/98 + 1/2303

1/94 = 1/141 + 1/282

1/94 = 1/188 + 1/188

95, 96, 98, 141, 188, 282, 2303, 4512, 8930, 

 

95: 

1/95 = 1/96 + 1/9120

1/95 = 1/100 + 1/1900

1/95 = 1/114 + 1/570

1/95 = 1/120 + 1/456

1/95 = 1/190 + 1/190

96, 100, 114, 120, 190, 456, 570, 1900, 9120, 

 

96: 

1/96 = 1/97 + 1/9312

1/96 = 1/98 + 1/4704

1/96 = 1/99 + 1/3168

1/96 = 1/100 + 1/2400

1/96 = 1/102 + 1/1632

1/96 = 1/104 + 1/1248

1/96 = 1/105 + 1/1120

1/96 = 1/108 + 1/864

1/96 = 1/112 + 1/672

1/96 = 1/114 + 1/608

1/96 = 1/120 + 1/480

1/96 = 1/128 + 1/384

1/96 = 1/132 + 1/352

1/96 = 1/144 + 1/288

1/96 = 1/160 + 1/240

1/96 = 1/168 + 1/224

1/96 = 1/192 + 1/192

97, 98, 99, 100, 102, 104, 105, 108, 112, 114, 120, 128, 132, 144, 160, 168, 192, 224, 240, 288, 352, 384, 480, 608, 672, 864, 1120, 1248, 1632, 2400, 3168, 4704, 9312, 

 

97: 

1/97 = 1/98 + 1/9506

1/97 = 1/194 + 1/194

98, 194, 9506, 

 

98: 

1/98 = 1/99 + 1/9702

1/98 = 1/100 + 1/4900

1/98 = 1/102 + 1/2499

1/98 = 1/105 + 1/1470

1/98 = 1/112 + 1/784

1/98 = 1/126 + 1/441

1/98 = 1/147 + 1/294

1/98 = 1/196 + 1/196

99, 100, 102, 105, 112, 126, 147, 196, 294, 441, 784, 1470, 2499, 4900, 9702, 

 

99: 

1/99 = 1/100 + 1/9900

1/99 = 1/102 + 1/3366

1/99 = 1/108 + 1/1188

1/99 = 1/110 + 1/990

1/99 = 1/126 + 1/462

1/99 = 1/132 + 1/396

1/99 = 1/180 + 1/220

1/99 = 1/198 + 1/198

100, 102, 108, 110, 126, 132, 180, 198, 220, 396, 462, 990, 1188, 3366, 9900, 

 

100: 

1/100 = 1/102 + 1/5100

1/100 = 1/104 + 1/2600

1/100 = 1/105 + 1/2100

1/100 = 1/108 + 1/1350

1/100 = 1/110 + 1/1100

1/100 = 1/116 + 1/725

1/100 = 1/120 + 1/600

1/100 = 1/125 + 1/500

1/100 = 1/140 + 1/350

1/100 = 1/150 + 1/300

1/100 = 1/180 + 1/225

1/100 = 1/200 + 1/200

102, 104, 105, 108, 110, 116, 120, 125, 140, 150, 180, 200, 225, 300, 350, 500, 600, 725, 1100, 1350, 2100, 2600, 5100, 

 

BUILD SUCCESSFUL (total time: 1 minute 11 seconds)

Redigerat 31 Mars 2013 av WASD

[Dave37]

Jag skrev min egna kod (18 rader) och fick fram denna matrisen för de olika nämnarna för bråken 1/1 till 1/20

 

 

Motsatta siffror ger bråket i fråga, t.ex. om man tar 12 kolumnen, och så tar man fjärde nämnaren uppifrån (16) och fjärde nedifrån (48) så borde detta resultera i 1/12 = 1/16 + 1/48

 

Vilket det gör.

 

Vad jag inte fattar är varför antalet ändras så mycket. Ok om det hade ökat på något trevligt speciellt sätt, men det här ser ju bara ut som värsta röran.

Redigerat 31 Mars 2013 av Dave37

[Mezox]

Jag tittade inte här igår kväll så kunde inte vara med i diskussionen men jo jag har skype. :p

 

Som ni har märkt har 1/p för p primtal bara två sätt att skrivas som en sådan summa. Jag kan avslöja att det finns sätt att förhand (utan räknare eller dator) hitta representationer av 1/n för rimligt stora n (upp till några tusen) inom några minuter.

 

Dave: I din tabell ser jag ett väldigt intressant mönster, kan man kanske generalisera detta?

[Dave37]

Alltså jag är övertygad om att antalet sätt att skriva det på har med primtalsfaktorer att göra. Eller menar du att första numret alltid är ett högre än den nämnaren man valt? Alltså att 1/n = 1/(n+1) + 1/b? Sista numret följer också (1+n)(2+n), så en av lösningarna är alltid

 

1/n = 1/(n+1) + 1/((n+1)(2+n))

Redigerat 1 April 2013 av Dave37

[Mezox]

Ja det är det jag menar, men det ska nog vara n(n+1). Om detta alltid är sant så visar ju detta att det alltid finns ett annat sätt att representera det ensamma bråket (förutom då n=1 eftersom n(n+1) blir samma sak som n+1 i det fallet).

 

En annan grej att notera är att tal med många delare som t.ex. 12 och 60 har många olika sätt att skrivas på.

[Dave37]

Ah jo givetvis, 1/(n(n+1)), jag hoppade över 1/1 i min serie. Det är ju sant att det alltid finns två sätt att representera ett ensamt bråk på eftersom både n(n+1) och n+1 är naturliga tal om n är ett naturligt tal.

[WASD]

1/a = 1/b + 1/c
1/a = (c+b)/(cb)
1/a = 1/((cb)/(c+b)
a = (cb)/(c+b)
 
Vet inte vart jag vill komma riktigt. Men jag tror jag kom på ett sätt att göra min genereringar betydligt snabbare (Från n²/2 iterationer till n) ifall ni vill ha mer data.

 

-------------------

 

Upptäckte detta

1/479 kan fås av 1/480 + 1/229920.
479² + 479= 229920.
 
1/89 kan fås av 1/89 = 1/90 + 1/8010.
89² + 89 = 8010.

 

Detta verkar stämma för allt, inte bara primtal. Och när jag scrollar upp ser det ut som det är ni ni precis kommit fram till.

Redigerat 1 April 2013 av WASD

[Dave37]

Japp, frågan som kvarstår är vad reglerna för alla de andra talen är och hur den övergripande regeln är samt hur man tar reda på exakt hur många sätt ett givet bråk går att skriva på.