Index to Sequences of Fractions (or Rational Numbers)

in the On-Line Encyclopedia of Integer Sequences

Sequences of fractions (or rational numbers) appear in the OEIS as a pair of sequences,
giving the numerators and denominators separately.

Here is a bare-bones list that that gives the A-numbers of the numerator and denominator sequences.

This Index is described in more detail in the Comments at the end of this file.

This Index is under construction.

0, 0, 1, 0, 1/2, 1, 0, 1/3, 1/2, 2/3, 1, 0, 1/4, 1/3, 1/2, 2/3, 3/4, 1, 0, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, ... = A006842/A006843 0, 1/2, -1/12, 1/24, -19/720, 3/160, -863/60480, 275/24192, -33953/3628800, 8183/1036800, -3250433/479001600, 4671/788480, -13695779093/2615348736000, 2224234463/475517952000, ... = A002206/A002207 0, 1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800, 0, 1/6227020800, 0, -1/1307674368000, ... = A033999/A009445 0, 1, 0, -1/3, 0, 2/15, 0, -17/315, 0, 62/2835, 0, -1382/155925, 0, 21844/6081075, 0, -929569/638512875, 0, 6404582/10854718875, 0, -443861162/1856156927625, ... = A002430/A036279 0, 1, 0, 1/3, 0, 2/15, 0, 17/315, 0, 62/2835, 0, 1382/155925, 0, 21844/6081075, 0, 929569/638512875, 0, ... = A002430/A036279 0, 1, 0, 1/6, 0, 3/40, 0, 5/112, 0, 35/1152, 0, 63/2816, 0, 231/13312, 0, 143/10240, 0, 6435/557056, 0, 12155/1245184, 0, 46189/5505024, 0, ... = A055786/A002595 0/1, 1/1, 0/1, 1/2, 1/1, 0/1, 1/3, 1/2, 2/3, 1/1, 0/1, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 1/1, 0/1, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, ... = A049455/A049456 0/1, 1/1, 0/1, 1/2, 1/1, 0/1, 1/3, 1/2, 2/3, 1/1, 0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1, 0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1, ... = A006842/A006843 0, 1/2, 1/2, 1/6, 2/3, 1/6, 1/8, 3/8, 3/8, 1/8, 7/90, 16/45, 2/15, 16/45, 7/90, 19/288, 25/96, 25/144, 25/144, 25/96, 19/288, 41/840, 9/35, 9/280, 34/105, 9/280, 9/35, 41/840, ... = A100640/A100641 = A100642/A002176 (the latter is not in lowest terms) 0, 1, 1/2, 1/3, 2/3, 1/4, 2/5, 3/5, 3/4, 1/5, 2/7, 3/8, 3/7, 4/7, 5/8, 5/7, 4/5, ... = A007305/A007306 0, 1/2, 1/6, 1/8, 7/90, 19/288, 41/840, 751/17280, 989/28350, 2857/89600, 16067/598752, 434293/17418240, 1364651/63063000, 8181904909/402361344000, ... = A100640/A100641 = A002177/A002176 (the latter is not in lowest terms) 0, 1, 1/2, 2/3, 5/8, 19/30, 91/144, 177/280, 3641/5760, 28673/45360, 28319/44800, 2523223/3991680, 27526069/43545600, 109339663/172972800, 4239014627/6706022400, ... = A103816/A053556 0, 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12, 12/13, 13/14, 14/15, 15/16, 16/17, 17/18, ... = A001477/A000027 0, 1/2, 3/2, 9/4, 3, 7/2, 4, 14/3, 61/12, 16/3, 35/6, 19/3,... = A099319/A099320 0, 1, 3, 17/3, 53/6, 62/5, 163/10, 717/35, 3489/140, ... = A093418/A096620 0, 1, 3, 22/7, 333/106, 355/113, 103993/33102, ... = A002485/A002486 0, 1/2, 5/6, 5/6, 31/30, 31/30, 247/210, 247/210, 247/210, 247/210, 2927/2310, 2927/2310, 40361/30030, 40361/30030, 40361/30030, ... = A106830/A034386 1, -2/3, 7/15, -12/35, 83/315, -146/693, 523/3003, -952/6435, 14051/109395, -26206/230945, 32867/323323, -62260/676039, 1423159/16900975, -2723234/35102025, 10461043/145422675, -20155888/300540195, 623034403/9917826435, ... = A034430/A001147 1, -1/3, -1/45, -2/945, -1/4725, -2/93555, -1382/638512875, -4/18243225, -3617/162820783125, -87734/38979295480125, -349222/1531329465290625, ... = A002431/A036278 1, -1/2, 1/5, -1/20, -1/350, 1/140, 1/1050, -1/300, -37/57750, 111/38500, 177/250250, -177/45500, -2753/2388750, 2753/367500, ... = A003163/A003164 1, -1/2, 1/24, -1/720, 1/40320, -1/3628800, 1/479001600, -1/87178291200, ... = A033999/A010050 1, -1/3, 1/5, -1/7, 1/9, -1/11, 1/13, -1/15, 1/17, -1/19, 1/21, -1/23, 1/25, -1/27, 1/29, -1/31, 1/33, -1/35, ... = A033999/A005408 1, -1/6, 1/120, -1/5040, 1/362880, -1/39916800, 1/6227020800, -1/1307674368000, ... = A033999/A009445 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, 0, -691/2730, 0, 7/6, 0, -3617/510, 0, 43867/798, 0, -174611/330, ... = A027641/A027642 1, -1/2, 1, 0, -1, 1, 1/4, 0, -3/2, 1, 0, 1, 0, -2, 1, -1/2, 0, 5/2, 0, -5/2, 1, 0, -3, 0, 5, 0, -3, 1, 17/8, 0, -21/2, 0, 35/4, 0, -7/2, 1, 0, 17, 0, -28, 0, 14, 0, -4, 1, ... = A060096/A060097 1, -1/2, 1, 1/6, -1, 1, 0, 1/2, -3/2, 1, -1/30, 0, 1, -2, 1, 0, -1/6, 0, 5/3, -5/2, 1, 1/42, 0, -1/2, 0, 5/2, -3, 1, ... = A053382/A053383 (refelected) 1, -1, 5/6, -1/2, 1/10, 1/6, -5/42, -1/6, 7/30, 3/10, -15/22, -5/6, 7601/2730, 691/210, -91/6, -35/2, 3617/34, 3617/30, -745739/798, -43867/42, ... = A100615/A100616. 1, -1/12, 7/240, -31/1344, 127/3840, -2555/33792, 1414477/5591040, -57337/49152, 118518239/16711680, ... = A001896/A033469 1, -1/3, 7/15, -31/21, 127/15, -2555/33, 1414477/1365, -57337/3, 118518239/255, -5749691557/399, 91546277357/165, -1792042792463/69, 1982765468311237/1365, -286994504449393/3, 3187598676787461083/435, ... = A001896/A001897 1, -1/2, 11/24, -7/16, 2447/5760, -959/2304, 238043/580608, -67223/165888, 559440199/1393459200, -123377159/309657600, ... = A055505/A055535 1, 0, -1/3, 0, -1/45, 0, -2/945, 0, -1/4725, 0, -2/93555, 0, -1382/638512875, 0, -4/18243225, 0, -3617/162820783125, 0, ... = A002431/A036278 1, 0, -1/2, 0, 1/24, 0, -1/720, 0, 1/40320, 0, -1/3628800, 0, 1/479001600, 0, -1/87178291200, ... = A033999/A010050 1/3, 0, 1/45, 0, 2/945, 0, 1/4725, 0, 2/93555, 0, 1382/638512875, 0, 4/18243225, 0, 3617/162820783125, 0, ... = A002431/A036278 1, 0, 1/2, 0, 5/24, 0, 61/720, 0, 277/8064, 0, 50521/3628800, 0, 540553/95800320, 0, 199360981/87178291200, ... = A046976/A046977 1, 0, 1/2, 1/3, 3/8, 11/30, 53/144, 103/280, 2119/5760, 16687/45360, 16481/44800, 1468457/3991680, 16019531/43545600, 63633137/172972800, 2467007773/6706022400, ... = A053557/A053556 1, 1/2, -1/12, 1/24, -19/720, 3/160, -863/60480, 275/24192, -33953/3628800, 8183/1036800, -3250433/479001600, 4671/788480, -13695779093/2615348736000, 2224234463/475517952000, ... = A002206/A002207 1, 1/2, -1/6, 1/4, -19/30, 9/4, -863/84, 1375/24, -33953/90,... = A006232/A006233 1, 1, -1/2, 1, -1, 1/6, 1, -3/2, 1/2, 0, 1, -2, 1, 0, -1/30, 1, -5/2, 5/3, 0, -1/6, 0, 1, -3, 5/2, 0, -1/2, 0, 1/42, ... = A053382/A053383 1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6, -3617/510, 43867/798, -174611/330, ... = A000367/A002445 1, 1, 1, 1, -432000/691, 1, -3456000/3617, -9504000/43867, ... = A085092/A001067 1, 1, 1/2, 1/4, 1/8, 0, 1/16, 3/64, -29/128, 25/128, 263/256, -1481/512, -5493/1024, 80505/2048, ... = A030274/A030275 1, 1, 1/2, 1/6, 1/24, 1/120, 1/720, 1/5040, 1/40320, 1/362880, 1/3628800, 1/39916800, ... = 1/A000142 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16 ... = 1/A000027 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024, 1/2048, 1/4096, 1/8192, 1/16384, ... 1/A000079 1, 1/3, 1/5, 1/7, 1/9, 1/11, 1/13, 1/15, 1/17, 1/19, 1/21, 1/23, 1/25, 1/27, 1/29, 1/31, 1/33, ... = 1/A005408 1, 1/3, 1/9, 1/27, 1/81, 1/243, 1/729, 1/2187, 1/6561, 1/19683, 1/59049, 1/177147, 1/531441, ... = 1/A000244 1, 1/4, 1/16, 1/64, 1/256, 1/1024, 1/4096, 1/16384, 1/65536, 1/262144, 1/1048576, 1/4194304, ... = 1/A000302 1, 1/4, 1/9, 1/16, 1/25, 1/36, 1/49, 1/64, 1/81, 1/100, 1/121, 1/144, 1/169, 1/196, 1/225, 1/256, ... = 1/A000290 1/2, 1/3, 1/5, 1/7, 1/11, 1/13, 1/17, 1/19, 1/23, 1/29, 1/31, 1/37, 1/41, 1/43, 1/47, 1/53, 1/59, 1/61, ... = 1/A000040 1/2, 1/4, 1/6, 1/8, 1/10, 1/12, 1/14, 1/16, 1/18, 1/20, 1/22, 1/24, 1/26, 1/28, 1/30, 1/32, 1/34, 1/36, 1/38, ... = 1/A005843 1/6, 1/90, 1/945, 1/9450, 1/93555, 691/638512875, 2/18243225, 3617/325641566250, 43867/38979295480125, ... = A046988/A002432 1, 1/2, 1/3, 1/3, 3/10, 3/10, 29/105, 29/105, 17/70, 17/70, 193/1155, 193/1155, -123/1430, -123/1430, -2687/2145, -2687/2145, -202863/24310, -202863/24310, -307072861/4849845, ... = A100651/A100652 1, 1, 1/2, 1/3, 5/24, 2/15, 61/720, 17/315, 277/8064, 62/2835, 50521/3628800, 1382/155925, 540553/95800320, ... = A099612/A099617 1, 1/2, 1/3, 2/3, 1/5, 2/5, 3/5, 1/7, 2/7, 3/7, 5/7, 1/8, 1/4, 3/8, 5/8, 7/8, 1/11, 2/11, ... = A066657/A066658 1/3, 1/45, 2/945, 1/4725, 2/93555, 1382/638512875, 4/18243225, 3617/162820783125, 87734/38979295480125, 349222/1531329465290625, ... = A002431/A036278 1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1, ... = A038566/A020653 1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, ... = A038568/A038569 1, 1/3, 2/15, 17/315, 62/2835, 1382/155925, 21844/6081075, 929569/638512875, 6404582/10854718875, ... = A002430/A036729 1, 1, 3/2, 4/3, 17/12, 13/10, 77/60, 128/105, 167/140, 73/63, 319/280, 1294/1155, 30697/27720, 28211/25740, 8707/8008, 9728/9009, 17587/16380, 18181/17017, ... = A100560/A100561 1, 1/2, 3/8, 5/16, 35/128, 63/256, 231/1024, 429/2048, 6435/32768, 12155/65536, 46189/262144, ... = A001790/A046161 1, 1/6, 3/40, 5/112, 35/1152, 63/2816, 231/13312, 143/10240, 6435/557056, 12155/1245184, 46189/5505024, ... = A055786/A002595 1, 1/2, 5/12, 3/8, 251/720, 95/288, 19087/60480, 5257/17280, 1070017/3628800, ... = A002208/A002209 1, 1/2, 5/12, 3/8, 251/720, 95/288, 19087/60480, 5257/17280, 1070017/3628800, 25713/89600, 26842253/95800320, 4777223/17418240, 703604254357/2615348736000, 106364763817/402361344000, ... = A002208/A002209 1, 1/2, 5/6, 7/12, 47/60, 37/60, 319/420, 533/840, 1879/2520, 1627/2520, 20417/27720, 18107/27720, ... = A058313/A058312 1, 1/2, 5/6, 9/4, 251/30, 475/12, 19087/84, 36799/24, 1070017/90, ... = A002657/A002790 1, 1/2, 5/24, 61/720, 277/8064, 50521/3628800, 540553/95800320, 199360981/87178291200, ... = A046976/A046977 1/4, 1/32, 5/1536, 61/184320, 277/8257536, 50521/14863564800, 540553/1569592442880, 199360981/5713316492083200, ... = A046976/A053005 1/2, 2/3, 3/8, 16/45, 25/96, 9/35, 3577/17280, 2944/14175, 15741/89600, 26575/149688, 4495513/29030400, 12504/79625, 56280729661/402361344000, 44436679/312741000, ... = A100643/A100644 = A002178/A002176 (the latter not being in lowest terms) 1, 2, 5/3, 7/4, 19/11, 26/15, 71/41, 97/56, 265/153, 362/209, 989/571, 1351/780, 3691/2131, ... = A002531/A002530 1/2, 2/5, 5/12, 7/17, 33/80, 106/257, 563/1365, 1232/2987, 1795/4352, 8412/20395, ... = A085394/A085395 1, 2, 5/2, 8/3, 8/3, 13/5, 151/60, 256/105, 83/35, 146/63, 1433/630, 2588/1155, 15341/6930, 28211/12870, 52235/24024, 19456/9009, 19345/9009, ... = A046825/A046826 1, 2, 5/2, 17/6, 91/30, 379/120, 5047/1560, 35849/10920, 614893/185640, 6800951/2042040, 607326679/181741560, ... = A059248/A035105 1, 2, 5/2, 29/10, 941/290, 969581/272890, 1014556267661/264588959090, 1099331737522548368039021/268440386798659418988490, ... = A073833/A073834 1, 2, 9/4, 20/9, 155/72, 21/10, 7441/3600, 3224/1575, 5697/2800, 3575/1764, 28523/14112, 27183/13475, 70357417/34927200, 4661447/2316600, ... = A100516/A100517 1, 2, 13/6, 32/15, 73/35, 647/315, 28211/13860, 6080/3003, 18181/9009, 1542158/765765, 2786599/1385670, 29229544/14549535, 134354573/66927861, ... = A100512/A100513. 1, 2, 17/8, 56/27, 1759/864, 1009/500, 86831/43200, 2322304/1157625, 85922/42875, 1144667/571536, 16019198113/8001504000, 123357293/61631955, ... = A100518/A100519 1, 2, 41/20, 85/42, 9287/4620, 10034/5005, 4089347/2042040, 3529889/1763580, 119042647/59491432, 191288533/95611230, 1553111566613/776363187600, ... = A100514/A100515 1, 3/2, 2, 13/6, 12/5, 49/20, 93/37, 5/2, 127/51, ... = A095132/A095131 1/6, 3/8, 2/15, 25/144, 9/280, 49/640, -464/14175, 27/2240, -16175/199584, -3237113/87091200, -105387/875875, -1737125143/22353408000, -770720657/5003856000, -25881785/229605376, ... = A100645/A100646 = A002179/A002176 (the latter not being in lowest terms) 1, 3/2, 4/3, 4/3, 41/30, 41/30, 47/35, 47/35, 289/210, 289/210, 1502/1155, 1502/1155, 15551/10010, 15551/10010, 5809/15015, 5809/15015, 3818123/510510, 3818123/510510, ... = A100649/A100650 1, 3/2, 4/3, 7/4, 6/5, 2, 8/7, 15/8, 13/9, 9/5, 12/11, 7/3, 14/13, 12/7, 8/5, 31/16, 18/17, 13/6, 20/19, 21/10, 32/21, 18/11, 24/23, 5/2, 31/25, ... = A017665/A017666 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, 8119/5741, 19601/13860, 47321/33461, 114243/80782, ... = A001333/A000129 1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520, 7381/2520, 83711/27720, 86021/27720, ... = A001008/A002805 1, 3/2, 21/8, 77/16, 1155/128, 4389/256, 33649/1024, 129789/2048, 4023459/32768 ... = A067002/A046161 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = A079268/A079269 1/10, 3/10, 567/130, 43659/170, 392931/10, ... = A002306/A047817 1, 4/3, 2, 4, 8, 64/3, 64, 256, ... = A007361/A007362 1/2, 5/12, 3/8, 251/720, 233/720, ... = erroneous version of A002208/A002209 1, 5/4, 10/9, 21/16, 26/25, 25/18, 50/49, 85/64, 91/81, 13/10, 122/121, 35/24, 170/169, 125/98, 52/45, 341/256, 290/289, 455/324, 362/361, 273/200, 500/441, ... = A017667/A017668 1, 5/3, 23/15, 45/29, 925/597, 7285/4701, ... = A053518/A053519 1/2, 5/6, 31/30, 247/210, 2927/2310, 40361/30030, 716167/510510, 14117683/9699690, 334406399/223092870, 9920878441/6469693230, ... = A024451/A002110 1/2, 7/12, 37/60, 533/840, 1627/2520, 18107/27720, 237371/360360, 95549/144144, 1632341/2450448, 155685007/232792560, 156188887/232792560, 3602044091/5354228880, ... = A082687/A082688 1, 7/4, 137/72, 2341/1200, 38629/19600, 1257937/635040, 50881679/25613280, 164078209/82450368, 18480100619/9275666400, 1187779852639/595703908800, ... = A100520/A100521 1, 9/8, 28/27, 73/64, 126/125, 7/6, 344/343, 585/512, 757/729, 567/500, 1332/1331, 511/432, 2198/2197, 387/343, 392/375, 4681/4096, 4914/4913, 757/648, ... = A017669/A017670 1/8, 16/45, 25/144, 34/105, 2989/17280, 5248/14175, 1209/5600, 5675/12474, 560593/1935360, 893128/1576575, 11148172711/28740096000, 109420087/156370500, ... = A100647/A100648 1, 17/16, 82/81, 273/256, 626/625, 697/648, 2402/2401, 4369/4096, 6643/6561, 5321/5000, 14642/14641, 3731/3456, 28562/28561, 20417/19208, 51332/50625, ... = A017671/A017672 2, 2, 4/3, 16/13, 256/217, 65536/57073, 4294967296/3811958497, 18446744073709551616/16605534578235736513, ... = A001146/A100441 2, 4/3, 16/9, 64/45, 384/225, 2304/1575, 18432/11025, 147456/99225, 1474560/893025, 14745600/9823275, 176947200/108056025, ... = A001900/A000246 2, 5/2, 12/5, 113/47, 351/146, 3623/1507, 3974/1653, 19519/8119, 355316/147795, 374835/155914, ... = A060807/A060808