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OEIS分数阶指数

从奥伊斯维基
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OEIS中分数(或有理数)序列的索引

说明

  • 序列片段(或)有理数出现在奥伊斯®作为联系一对整数序列,分别给出分子和分母。
  • 这个页面包含一个简单的列表,它给出了A数分子分母最重要的有理数序列的序列。
  • 根据下列规则(按基本顺序与将主数据库排序成词典顺序时使用的那些相同),条目按字典顺序排列:
    • (i)忽略符号,
    • (ii)忽略任何0、+1或-1的初始项(剩下的首要项是第一非平凡项
    • (iii)将所得的分数序列排序成词典顺序。
    • 全序列A000 0 12已被人工插入来标记其第一非平凡项小于大于1的序列之间的边界。
  • OEIS包含超过3400个条目关键字“压裂”,意味着超过1700个序列的分数。这里还有很多需要补充的地方。如果你愿意帮忙,请大家帮忙!
  • 有关更多信息(包括如何添加其他条目)请参阅评论在这个文件的末尾。
  • 也见主OEIS指标.


分数表

第一非平凡项<=1/3

  • 1/192,1/21504,1/190080,27/573440,127/218880,34603/40480,278617/2106,264156210586399/53329920,…=A08615/A08616(哈达玛质量)
  • 1, 1/48, 77/7680, 17017/1105920, 52055003/1061683200, 1509595087/5662310400, 3603403472669/1630745395200, 10151817126357907/391378894848000,…=A226256/A226257
  • 1, 1 / 12, 1 / 288,-139/51840,-571/2488320,163879/209018880,5246819/75246796800,-534703531/902961561600,…=A000 1163/A000 1164(斯特灵近似)
  • 1,-1/12,7/240,-31/1344,127/3840,-2555/33792,1414477/5591040,-57337/49152,118518239/16711680,…=A00 1896/A0334(伯努利(2n,1/2))
  • 1/10,3/10,567/130,43659/170,392931/10,…=A000 2306/A047 817(Hurwitz数HYN)
  • 1/9,10/81,100/729,1000/6561,10000/59049,…=A1000/A1000
  • 1/8,1/12,11/96,17/72,619/960,709/324,…=A226258/A226259
  • 1, 1/8, 35/384, 385/3072, 25025/98304, 1616615/2359296, 260275015/113246208, 929553625/100663296, 835668708875/19327352832,…=A225697/A225698
  • 1/8、16/45、25/144、34/105、2989/17280、5248/14175、1209/5600、5675/12474、560593/1935360、893128/1576575、11148172711/28740096000、109420087/156370500、…=A10064/A10064(笛卡尔C(n,3))
  • 1,-1/7,1/49,-1/343,1/2401,-1/16807,1/117649,-1/823543,1/5764801,-1/40353607,1/282475249,-1/1977326743,…=A033 99/A000 0420(级数为1)^ n/7 ^ n,其中n=0…INF,收敛到7/8;实际上,可以用与x的幂相关的分母序列展开它。A000 1018A000 1019A011557…),当应用于无穷级数(-1)^ n/x^ n时,它将收敛到x/(x+1))。
  • 0, 1, 0,-1/6,0, 1/120, 0,-1/5040,0, 1/362880, 0,-1/39916800,0, 1/6227020800, 0,-1/1307674368000,…=A033 99/A000 9445(辛(X))
  • 1, 0, 1/6, 0, 7/360, 0, 31/15120, 0, 127/604800, 0, 73/3421440, 0, 1414477/653837184000, 0, 8191/37362124800, 0, 16931177/762187345920000,…=A036280/A03681(X/SIN X)
  • 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、…=A055 786A/A00 2595
  • 1,-1/6,1/120,-1/5040,1/362880,-1/39916800,1/6227020800,-1/1307674368000,…=A033 99/A000 9445(辛(X))
  • 1/6,1/90,1/945,1/9450,1/93555,691/638512875,2/18243225,3617/325641566250,43867/38979295480125,…=A046988/A000 2432
  • 1, 1/6, 7/360, 31/15120, 127/604800, 73/3421440, 1414477/653837184000, 8191/37362124800,…=A036280/A03681(X/SIN X)
  • 1,-1/6,1/36,-1/216,1/1296,-1/7776,1/46656,-1/279936,1/1679616,-1/10077696,1/60466176,-1/362797056,…=A033 99/A000 0400(级数为1)^ n/6 ^ n,其中n=0…INF,收敛到6/7)
  • 1, 1 / 6,- 1/30,1/42,-1/30,5/66,-691/2730,7/6,-3617/510,43867/798,-174611/330,…=A000 0367/A000 2445(伯努利数B{{2n})
  • 1, 1/6, 3/40, 5/112, 35/1152, 63/2816, 231/13312, 143/10240, 6435/557056, 12155/1245184, 46189/5505024,…=A055 786A/A00 2595
  • 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,--,…=A100645/A10064=A000 2179/A000 2176(后者不是最低值)(笛卡尔数C(n,2))
  • 1, 1, 1/5, 1/61, 1/1385, 1/50521, 1/2702765, 1/199360981, 1/19391512145, 1/2404879675441,…= 1A000 0364
  • 1,-1/5,1/25,-1/125,1/625,-1/3125,1/15625,-1/78125,1/390625,-1/1953125,1/9765625,-1/48828125,…=A033 99/A000 0351(级数为1)^ n/5 ^ n,其中n=0…INF,收敛到5/6)
  • 5/24,5/16,1105/1152,565/128,82825/3072,19675/96,1282031525/688128,80727925/4096,…=A226260/A226261
  • 1/4,1/32,5/1536,61/184320,277/8257536,50521/14863564800,540553/1569592442880,199360981/5713316492083200,…=A046966/A05300
  • 1, 1/4, 1/16, 1/64, 1/256, 1/1024, 1/4096, 1/16384, 1/65536, 1/262144, 1/1048576, 1/4194304,…= 1A000 0302(1/4 ^ n)
  • 1,-1/4,1/16,-1/64,1/256,-1/1024,1/4096,-1/16384,1/65536,-1/262144,1/1048576,-1/4194304,…=A033 99/A000 0302(级数为1)^ n/4 ^ n,其中n=0…INF,收敛到4/5)
  • 1, 1/4, 1/9, 1/16, 1/25, 1/36, 1/49, 1/64, 1/81, 1/100, 1/121, 1/144, 1/144, 1/////,…= 1A000 0290(1/n ^ 2)
  • 1/4,2/5,1/5,1/2,1/10,1/10,2/11,1/10,1/4,1/4,1/10,4/13,1/10,…=A91093A/A29
  • 16/64,26/65,19/95,49/98,11/110,12/120,22/121,13/130,33/132,34/136,…=A91093A/A29
  • 1/4,5/12,13/24,47/72,271/360,301/360,2287/2520,491/504,1045/1008,367/336,1919/1680,1999/1680,22829/18480,…=A250133/A96358
  • 1, 1/4, 3/2, 3/16, 15/8, 5/32, 35/16, 35/256, 315/128, 63/512, 693/256, 231/2048,…=A163590/A240988((N-1)!!* 2 ^((1 +(-1)^ n)/ 2))^((-1)^ n),从n=1开始)
  • 1, 0,-1/3,0,-1/45,0,-2/945,0,-1/4725,0,-2/93555,0,-1382/638512875,1382/638512875,--,γ,--,,…=A000 2431/A03627(COT(X))
  • 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,--,…=A000 2430/A03627(谭(X))
  • 1,-1/3,-1/45,-2/945,-1/4725,-2/93555,-1382/638512875,-4/18243225,-3617/162820783125,-87734/38979295480125,-349222/1531329465290625,…=A000 2431/A03627(COT(X))
  • 1, 1/3, 1/9, 1/27, 1/81, 1/243, 1/729, 1/2187, 1/6561, 1/19683, 1/59049, 1/177147, 1/盎司…= 1A000 0244(1/3 ^ n)
  • 1,-1/3,1/9,-1/27,1/81,-1/243,1/729,-1/2187,1/6561,-1/19683,1/59049,-1/177147,1/177147,…=A033 99/A000 0244(级数为1)^ n/3 ^ n,其中n=0…INF,收敛到3/4)
  • 1, 1/3, 2/15, 17/315, 62/2835, 1382/155925, 21844/6081075, 929569/638512875, 6404582/10854718875,…=A000 2430/A03627(谭(X))
  • 1, 1/3, 1/6, 1/10, 1/15, 1/21, 1/28, 1/36, 1/45, 1/55, 1/66, 1/78,…= 1A000 0217(1/三角数)
  • 1,-1/3,1/5,-1/7,1/9,-1/11,1/13,-1/15,1/17,-1/19,1/21,-1/23,1/23,--,γ,-,-,,-,-,…=A033 99/A000 5408((+- 1)/(2n+1))
  • 1, 1/3, 1/5, 1/7, 1/9, 1/11, 1/13, 1/15, 1/17, 1/19, 1/21, 1/23, 1/23, 1///////,…= 1A000 5408(1/(2n+1))
  • 1,-1/3,7/15,-31/21,127/15,-2555/33,1414477/1365,-57337/3,118518239/255,-5749691557/399,91546277357/165,-1792042792463/69,1792042792463/69,--,γ,…=A00 1896/A00 1897(余数)

范围内的第一非平凡项(1/3,1/2)

  • - 691/2730,691/2730,7/6,-7/6,-3617/510,3617/510,…=A051716/A051717(伯努利孪生数)
  • 1, 0,-1/2,0, 1/24, 0,-1/720,0, 1/40320, 0,-1/3628800,0, 1/479001600, 0,-1/87178291200,…=A033 99/A010050(COX(X))
  • 1, 0, 1/2, 0, 5/24, 0, 61/720, 0, 277/8064, 0, 50521/3628800, 0, 540553/95800320, 0, 199360981/87178291200,…=A046966/A04697(秒(X))
  • 1,-1/2,1/24,-1/720,1/40320,-1/3628800,1/479001600,-1/87178291200,…=A033 99/A010050(COX(X))
  • 1,- 1/2,1/12,0,-1/720,0, 1 / 30240, 0,-1/1209600,0, 1 / 47900160, 0,-691/1307674368000,0, 1 / 74724249600, 0,-γ,γ,…=A1200/A227 829
  • 0, 1 / 2,-1/12,1/24,-19/720,3/160,-863/60480,275/24192,-33953/3628800,8183/1036800,-3250433/479001600,4671/788480,-4671/788480,γ,…=A00 2206/A00 2207(对数数)
  • 1, 1 / 2,-1/8,1/16,-5/128,7/256,-21/1024,33/2048,-429/32768,715/65536,…=A00 2596/A046161(qRT(1 +x))
  • 1,- 1/2,1/6,0,-1/30,0, 1 / 42, 0,-1/30,0, 5 / 66, 0,-691/2730,0, 7 / 6, 0,--,α/α,--,…=A02664/A027(伯努利数BYN)
  • 1, 1, 1/2, 1/6, 1/24, 1/120, 1/720, 1/5040, 1/40320, 1/362880, 1/3628800, 1/39916800,…= 1A000 0142(1/n!)
  • 0/1,1/1,1/2,1/6,1/12,7/60,1/20,11/420,13/840,11/2520,11/2520,23/27720,23/27720,γ,…=A212111/A212112
  • 0, 1/2, 1/6, 1/8, 7/90, 19/288, 41/840, 751/17280, 989/28350, 2857/89600, 16067/598752, 434293/17418240, 1364651/17418240, 1364651//,…=A100640/A10064=A000 2177/A000 2176(后者不是最低的)
  • 1, 1 / 2,- 1/6,1/4,-19/30,9/4,-863/84,1375/24,-33953/90,…=A000 623/A000 623(柯西数)
  • 0, 1, 1/2, 1/6, 5/12, 13/60, 1/20, 27/140, 19/280, 451/2520, 199/2520, 4709/27720〕。=A21692/A21693A(分数雷曼)
  • 1,-1/2,1/5,-1/20,-1/350,1/140,1/1050,-1/300,-37/57750,111/38500,177/250250,-177/45500,-177/45500,γ,…=A000 3163/A000 3164(Van der Pol数)
  • 1, 1, 1/2, 1/5, 1/14, 1/42, 1/132, 1/429, 1/1430, 1/4862, 1/16796, 1/58786, 1/208012, 1/208012, 1//,…= 1A000 0108(1 /加泰罗尼亚)
  • 1, 1, 1、1/2、1/5、1/16、1/61、1/272、1/1385、1/7936、1/50521、1/353792、1/2702765、1/22368256、…= 1A000 0111(1/欧拉)
  • 1, 1/2, 5/24, 61/720, 277/8064, 50521/3628800, 540553/95800320, 199360981/87178291200,…=A046966/A04697(秒(X))
  • 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,…=A03074/A030255
  • 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024, 1/2048, 1/2048, 1///,…= 1A000 0 79(1/2 ^ n)
  • 1,-1/2,1/4,-1/8,1/16,-1/32,1/64,-1/128,1/256,-1/512,1/1024,-1/2048,1/2048,--,γ,…=A033 99/A000 0 79(级数为1)^ n/2 ^ n,其中n=0…INF,收敛到2/3)
  • 1/2,1/4,1/6,1/8,1/10,1/12,1/14,1/16,1/18,1/20,1/22,1/24,1/24,γ,γ,γ,γ,γ,…= 1A000 5843(1/(2n))
  • 1,-1/2,-1/3,-1/6,-1/30,1/30,1/42,-1/42,-1/30,1/30,5/66,-5/66,-5/66,γ,γ,-,…=A051716/A051717
  • 1, 1, 1/2, 1/3, 1/6, 7/60, 19/360, 3/70, 5/336, 13/756, 199/75600, 1663/207900,-10819/9979200,10819/9979200,…=A226932/A226933
  • 1, 1, 1/2, 1/3, 5/24, 2/15, 61/720, 17/315, 277/8064, 62/2835, 50521/3628800, 1382/155925, 540553/95800320,…=A09612/A09617
  • 1/2,1/3,1/5,1/7,1/11,1/13,1/17,1/19,1/23,1/29,1/31,1/37,1/37,γ,γ,γ,γ,…= 1A000 000
  • 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/12, 1/////…= 1A000 00 27
  • 1,-1/2,1/3,-1/4,1/5,-1/6,1/7,-1/8,1/9,-1/10,1/11,-1/12,1/12,--,γ,--…=A033 99/A000 00 27(Ln(1+x)的MaLururin级数的项,其中x=1;因此,级数(-1)^ n/(n+1),其中n=0…INF,收敛到Ln(2))
  • 1, 1/2, 1/3, 1/3, 3/10, 3/10, 29/105, 29/105, 17/70, 17/70, 193/1155, 193/1155、-1155、-、、、、、、、、、…=A100651/A100652
  • 1, 0, 1/2, 1/3, 3/8, 11/30, 53/144, 103/280, 2119/5760, 16687/45360, 16481/44800, 1468457/3991680, 16019531/43545600, 63633137/43545600, 63633137//,…=A053557/A053556
  • 1, 1/2, 1/3, 2/3, 1/5, 2/5, 3/5, 1/7, 2/7, 3/7, 5/7, 1/8, 1/8, 1/////////,…=A066 667/A066 665
  • 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, 4/////,…=A000 7305/A000 7306
  • 1/2,1/3,2/3,1/4,3/4,2/5,3/5,1/5,4/5,3/7,4/7,2/7,2/7,γ,γ,γ,γ,γ,γ,…=A020651/A08692
  • 1, 1/2, 3/8, 5/16, 35/128, 63/256, 231/1024, 429/2048, 6435/32768, 12155/65536, 46189/262144,…=A000 1790/A046161
  • 1/2,2/5,5/12,7/17,33/80,106/257,563/1365,1232/2987,1795/4352,8412/20395,…=A085/A085 395
  • 1/2,5/12,3/8,251/720,233/720,…=错误版本A00 2208/A00 2209
  • 1, 1/2, 5/12, 3/8, 251/720, 95/288, 19087/60480, 5257/17280, 1070017/3628800, 25713/89600, 26842253/95800320, 4777223/17418240, 703604254357/17418240, 703604254357//,…=A00 2208/A00 2209
  • 1,-1/2,11/24,-7/16,2447/5760,-959/2304,238043/580608,-67223/165888,559440199/1393459200,-123377159/309657600,…=A055 505/A055 535
  • 0, 1/2, 1/2, 1/6, 2/3, 1/6, 1/8, 3/8, 3/8, 1/8, 7/90, 16/45, 2/ω/y/y/y/y/y/y/y/y/y/y/y/y/y,…=A100640/A10064=A10064/A000 2176(后者不是最低的)
  • 1, 1/2, 1/2, 1/3, 2/3, 1/3, 2/3, 1/4, 3/4, 2/5, 3/5, 1/4, 3/4, 3/////////////////、…=A0938/A0938
  • 1, 1/2, 1/2, 11/24, 13/30, 77/180, 29/70, 459/1120,…=A226242/A226243(苏丹嫁妆)
  • 1, 1/2, 1/2, 2/3, 25/24, 9/5, 2401/720, 2048/315, 59049/4480, 15625/567, 214358881/3628800,…=A036502/A036503(n^(n-2)/n!)
  • - 1/2,-1/2,-19/8,-593/32,-23877/128,-4496245/2048,…=A226584A/A226585(Hubad模型)
  • 1/2、7/12、37/60、533/840、1627/2520、18107/27720、237371/360360、95549/144144、1632341/2450448、155685007/232792560、156188887/232792560、3602044091/5354228880、…=A0826870/A082688
  • 1/2,2/3,3/8,16/45,25/96,9/35,3577/17280,2944/14175,15741/89600,26575/149688,4495513/29030400,12504/79625,12504/79625,γ,…=A10064/A10064=A000 2178/A000 2176(后者没有最低限度)
  • 0, 1, 1/2, 2/3, 5/8, 19/30, 91/144, 177/280, 3641/5760, 28673/45360, 28319/44800, 2523223/3991680, 27526069/43545600, 109339663/43545600, 109339663//,…=A1038/A053556
  • 0, 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12, 12/12, 12/////////,…=A000 1477/A000 00 27
  • 1/2,2/3,4/5,8/9,16/17,32/33,64/65,128/129,256/257,512/513,1024/1025,2048/2049,4096/4097,…=A000 0 79/A000 0 51
  • 0, 1/2, 3/4, 7/8, 99/112, 9307/10528,…=A129660/A129661
  • 0, 1/2, 3/4, 7/8, 15/16, 31/32, 63/64, 127/128, 255/256, 511/512, 1023/1024, 2047/2048, 4095/2048, 4095///,…=A000 0225/A000 0 79
  • 1/2,5/6,1/2,31/30,1/2,41/42,1/2,31/30,1/2,61/66,1/2,3421/2730,3421/2730,γ,γ,…=A027 79/A027 760
  • 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
  • 0, 1/2, 5/6, 5/6, 31/30, 31/30, 247/210, 247/210, 247/210, 247/210, 2927/2310, 2927/2310, 40361/2310, 40361///,…=A1068/A034
  • 1/2,5/6,31/30,247/210,2927/2310,40361/30030,716167/510510,14117683/9699690,334406399/223092870,9920878441/6469693230,…=A024451/A1002110
  • 1, 1/2, 5/6, 9/4, 251/30, 475/12, 19087/84, 36799/24, 1070017/90,…=A00 2657/A000 790(柯西数)
  • 0, 1, 0,1/2,1, 0, 1 / 3, 1 / 2, 2 / 3, 1, 0,1/4,1/3,2/5,1/2,3/5,2/3,2/3,y/y/y/y/y/y/y/y/α,…=A04405/A04406
  • 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, 0,4, 1, 0,γ,γ,γ,γ,γ,γ,γ,…=A000 68 42/A000 68 43
  • 1,-1/2,1, 0,-1, 1, 1,4, 0,-3/2,1, 0, 1,0,-2, 1,-1/2,0, 5/2, 0,-2, 0,γ,-,-,-,-,-,,/,,,,,,,,,,,,,,,,,,,,…=A0600 96/A0600 97
  • 1,-1/2,1, 1,6,-1, 1, 0,1/2,-3/2,1,-1/30,0, 1,-2, 1, 0,-1/6,1/6 /y,-y,y/y-,-y,y/y,--,…=A05338/A05338(再选择)(伯努利多项式)
  • 0, 1/2, 1, 1/3, 2/3, 1/2, 2, 3/4, 3/5, 1/5, 1/2, 1, 1,2, 5, 1,4/7,1/8,1/8,γ,γ,γ,…=A000 7305/A047 67(Stern Brocot的另一个版本)
  • 0, 1/2, 1, 2/3, 3/2, 1/3, 2, 3/4, 5/3, 2/5, 5/2, 3/5, 4/3, 1/4, 3, 4/4, 3, 4///,…=A17491(n)/A000 248(n+1)(L-树)
  • 1, 1,- 1/2,1,- 1, 1 / 6, 1,-3/2,1/2,0, 1,-2, 1, 0,-1/30,1,-5/2,5/2,--,-,-,- -,-,-,-,-,,/…=A05338/A05338(伯努利多项式)
  • 1/2,1, 1, 1,13/10,1, 1, 3 / 2, 1, 1,16/11,1, 31 / 26, 10 / 7, 1, 1,24/17,4/3,1, 7 / 1, 7,γ,α/α/α/α/α,…=A225699/A225700
  • 1, 1/2, 11/8, 37/16, 563/128, 1695/256, 12255/1024, 36333/2048, 972867/32768,…=A24976/A046161
  • 0, 1/2, 3/2, 9/4, 3, 7/2, 4, 14/3, 61/12, 16/3, 35/6, 19/3,…=A09319/A09320(约为π(n))
  • 1/2、2, 1/4, 4/5, 5/2, 2/5, 5/4, 4, 1/6, 2/3, 9/4, 4/13, 13/14, 14/14, 14///…=A191379(n)/A191379(n+1)
  • 1, 1/2, 2, 1/3, 2/3, 3, 1/4, 3/2, 3/4, 4, 1/5, 2/5, 3/5, 4/5,…=A226314/A053531(列举有理数)
  • 0, 1, 1/2, 2, 1/3, 3/2, 2/3, 3, 1/4, 4/3, 3/5, 5/2, 2/5, 5/3, 3/4, 4, 1/4, 4, 1//,…=A000 248(n)/A000 248(n+1)(Stern Brocot)
  • 1, 1/2, 2, 1/3, 3, 1/4, 2/3, 3/2, 4, 1/5, 5, 1/6, 2/5, 3/4, 4/3, 5/2, 6,…=A038 566/A020653
  • 1, 1/2, 2, 1/3, 3, 2/3, 3/2, 1/4, 4, 3/4, 4/3,…=A038 568/A038 569(理据< ->整数)
  • 1, 1/2, 2, 2/3, 1/3, 3, 3/2, 3/5, 3/4, 1/4, 2/5, 5/2, 4, 4/3, 5/3,…=A162909/A16910(鸟树)
  • 1, 1/2, 2, 2/3, 3, 1/3, 3/2, 3/5, 5/2, 1/4, 4/3, 3/4, 4, 2/5, 5/3,…=A16911/A16912(滴滴树)

范围内的第一非平凡项(1/2,1)

  • 1,-2/3,7/15,-12/35,83/315,-146/693,523/3003,-952/6435,14051/109395,-26206/230945,32867/323323,-62260/676039,62260/676039,--,γ,--,,…=A034 430/A000 1147
  • 1, 2/3, 4/7, 8/15, 16/31, 32/63, 64/127, 128/255, 256/511, 512/1023, 1024/2047, 2048/4095, 4096/4095, 4096///,…=A000 0 79(n)/A000 0225(n-1)
  • 2/3,3/5,5/7,7/11,11/13,13/17,17/19,19/23,23/29,29/31,31/37,37/41,37/41,γ,γ,γ,γ,γ,…=A000 000(n)/A000 000(n+1)(素数(n)/素数(n+1))
  • 1, 3/4, 1/2, 3/8, 19/40, 53/120, 103/168, 4111/6720, 78293/120960,…=A040173/A040174(PROB)生成Syn)
  • 1,- 1, 5 / 6,-1/2,1/10,1/6,-5/42,-1/6,7/30,3/10,-15/22,-5/6,5/6,--,--,-,-,-,-,-,- -,- -,…=A100615/A100616.
  • 0, 1, 1、1, 1, 24/25, 1, 50/49, 1, 1、24/25、120/121、1, 170/169, 50/49, 24/25, 1, 288/289, 1, 362/361, 24/361, 24///////,…=A24988/A2429
  • 0, 1, 0、1, 7/8, 8/9, 15/17, 23/26, 38/43, 61/69, 343/388, 404/457, 747/845, 7127/8062, 29255/盎司…=A129688/A129699
  • 1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、1, 1, 1、…=A000 0 12= 1A000 0 12

范围内的第一个非平凡项(1, 3/2)

  • 1, 33/32, 8051/7776, 257875/248832,…=A09828/A069052
  • 1, 17/16, 82/81, 273/256, 626/625, 697/648, 2402/2401, 4369/4096, 6643/6561, 5321/5000, 14642/14641, 3731/3456, 28562/3456, 28562///,…=A01767/A017672
  • 1, 9/8, 28/27, 73/64, 126/125, 7/6, 344/343, 585/512, 757/729, 567/500, 1332/1331, 511/432, 2198/432, 2198/////////,…=A017699/A017670
  • 1, 5/4, 10/9, 21/16, 26/25, 25/18, 50/49, 85/64, 91/81, 13/10, 122/121, 35/24, 170/24, 170//////////////,…=A017667/A017668
  • 1, 5/4, 17/12, 37/24, 119/72, 631/360, 661/360, 4807/2520, 995/504, 2053/1008, 703/336, 3599/1680,…=A252511/A252512
  • 1, 3/2, 4/3, 4/3, 41/30, 41/30, 47/35, 47/35, 289/210, 289/210, 1502/1155, 1502/1155, 15551/1155, 15551/////////,…=A10064/A100650
  • 1, 1, 3/2, 4/3, 17/12, 13/10, 77/60, 128/105, 167/140, 73/63, 319/280, 1294/1155, 30697/27720, 28211/27720, 28211///////,…=A100560/A100561
  • 1, 3/2, 4/3, 7/4, 6/5, 2, 8/7, 15/8, 13/9, 9/5, 12/11, 7/3, 14/13, 12/13, 12///////////////////,…=A017665/A017666(n的除数的倒数之和)
  • 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, 8119/5741, 19601/13860, 47321/13860, 47321//,…=A131333/A000 0129(SqRT(2))
  • 3/2,5/3,7/5,11/7,13/11,17/13,19/17,23/19,29/23,31/29,37/31,41/37,41/37,γ,γ,γ,γ,γ,…=A000 000(n+1)/A000 000(n)(素数(n+1)/素数(n))
  • 1, 3/2, 7/4, 15/8, 31/16, 63/32, 127/64, 255/128, 511/256, 1023/512, 2047/1024, 4095/2048, 8191/2048, 8191///,…=A000 0225(n+1)/A000 0 79
  • 1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520, 7381/2520, 83711/27720, 86021/27720,…=A000 1008/A000 2805(调和数Hyn)
  • 1, 3/2, 2, 13/6, 12/5, 49/20, 93/37, 5/2, 127/51,…=A095132/A095131
  • 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510,…=A079268/A079269
  • 1, 3/2, 21/8, 77/16, 1155/128, 4389/256, 33649/1024, 129789/2048, 4023459/32768…=A069002/A046161
  • 0, 1,- 1, 3 / 2,-8/3,125/24,-54/5,16807/720,-16384/315,531441/4480,-156250/567,2357947691/3628800,…=A227 831/A09599(LambertW)

范围内的第一非平凡项(3/2,2)

  • 1, 5/3, 23/15, 45/29, 925/597, 7285/4701,…=A053518/A053519
  • 1, 7/4, 137/72, 2341/1200, 38629/19600, 1257937/635040, 50881679/25613280, 164078209/82450368, 18480100619/9275666400, 1187779852639/595703908800,…=A100520/A100521
  • 0,- 1, 0, 1,- 2,- 1/2,0, 1 / 2, 2,-3,-1,-1/3,0, 1 / 3, 1, 3,-1,--3/2,…=A196199/A000 47 37(理性的重复列表)
  • - 1, 0, 1,- 2,- 1/2,1/2,2,-3,-3/2,-2/3,-1/3,1/3,2/3,3/2,3/2,--,--,--,--,-,-,-,-,-,-,,,…=A113136/A113137(按高度排列的理性)
  • 1, 2, 1/2, 3, 1/3, 3/2, 2/3, 4, 1/4, 4/3,…=A020650/A020651(理性的另一个列举)
  • 0, 1, 2、1/2、3, 3/2, 1/3, 2/3, 4, 5/2, 4/3, 5/3, 1/4, 2/5, 3/4, 3/4, 3////////////,…=A229 72/A071766
  • 1, 1, 2、1, 3/2, 1, 3/2, 2, 6/5, 1, 5/4, 1, 3/2, 4/3, 1, 4/3, 3/2, 5/4, 8/7, 1、…=A224762/A224763(分数GijSWijt)
  • 1, 2,- 1, 3,- 1/2,0, 4,-1/3,1/2,5,-1/4,2/3,3/2,-2, 6,-1/5,1/5,γ,-,-,-,-,-,,…=A226131/A226130(有理数的斐波那契序)
  • 1, 2, 9/8, 176/2835, 23590375/167382319104,…=A0782424/A0782525(Birkhoff polytopes)
  • 2, 4/3, 8/7, 16/15, 32/31, 64/63, 128/127, 256/255, 512/511, 1024/1023, 2048/2047, 4096/4095, 8192/4095, 8192//,…=A000 0 79/A000 0225
  • 2, 4/3, 16/9, 64/45, 384/225, 2304/1575, 18432/11025, 147456/99225, 1474560/893025, 14745600/9823275, 176947200/108056025,…=A00 1900/A000 0246
  • 2, 3/2, 5/4, 9/8, 17/16, 33/32, 65/64, 129/128, 257/256, 513/512, 1025/1024, 2049/2048, 4097/2048, 4097///,…=A000 0 51/A000 0 79
  • 1, 2, 5/3, 7/4, 19/11, 26/15, 71/41, 97/56, 265/153, 362/209, 989/571, 1351/780, 3691/2131,…=A000 2531/A000 2530(SqRT(3))
  • 2, 2, 4/3, 16/13, 256/217, 65536/57073, 4294967296/3811958497,1844 67407370955 1616/166055 345 7823 57 36513,…=A000 1146/A10044
  • 1, 1, 1,2, 2, 3/2, 1, 3,3, 4/3, 2, 2,2, 3/2, 1, 4,4, 5/4, 5/3,…=A224764/A224765(n的分数指数)
  • 1, 2, 41/20, 85/42, 9287/4620, 10034/5005, 4089347/2042040, 3529889/1763580, 119042647/59491432, 191288533/95611230, 1553111566613/776363187600,…=A100514/A100515
  • 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, 9/4, 20/9, 155/72, 21/10, 7441/3600, 3224/1575, 5697/2800, 3575/1764, 28523/14112, 27183/13475, 70357417/34927200, 4661447/盎司…=A100516/A100517
  • 2, 2, 4/3, 16/13, 256/217, 65536/57073, 4294967296/3811958497,1844 67407370955 1616/166055 345 7823 57 36513,…=A000 1146/A10044
  • 2, 5/2, 12/5, 113/47, 351/146, 3623/1507, 3974/1653, 19519/8119, 355316/147795, 374835/155914,…=A060807/A060808
  • 1, 2, 5/2, 8/3, 8/3, 13/5, 151/60, 256/105, 83/35, 146/63, 1433/630, 2588/1155, 15341/6930, 28211/6930, 28211/////,…=A0462525/A0468 26
  • 1, 2, 5/2, 17/6, 91/30, 379/120, 5047/1560, 35849/10920, 614893/185640, 6800951/2042040, 607326679/181741560,…=A059248/A035105
  • 2, 5/2, 26/9, 103/32, 2194/625, 1223/324, 472730/117649, 556403/131072, 21323986/4782969,…=A909088/A036505
  • 1, 2, 5/2, 29/10, 941/290, 969581/272890, 1014556267661/264588959090,1099 33 33 172 22548 368039021/26844038 67 998 65 94 18988 490,…=A07833/A0738 34
  • 1, 2, 3、1/2、4, 1/3, 3/2, 5, 1/4, 4/3, 5/2, 2/3, 6,…=A22608/A226080(理性的另一个斐波那契排序)
  • 1, 2, 3、3/2、4, 5/2, 4/3, 5/3, 5, 7/2, 7/3, 8/3, 5/4, 7/5, 7/4, 8/盎司…=A071585/A071766(理据>1)
  • 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, 2721/1001, 23225/8544, 25946/9545, 49171/盎司…=A000 767/A000 767(e)
  • 1, 2, 3,15/4,35/8,77/16,1001/192,17017/3072,323323/55296,676039/110592,2800733/442368,86822723/13271040,…=A060753/A038 110
  • 2, 4, 20/3, 32/3, 256/15, 416/15, 4832/105, 8192/105, 42496/315, 74752/315, 1467392/3465, 2650112/3465, 62836736/45045, 115552256/45045, 115552256//,…=A10866/A229 726(重复)(和2 ^ k/k)
  • 2, 20/3, 256/15, 4832/105, 42496/315, 1467392/3465, 62836736/45045, 42790912/9009, 2535587840/153153, 170851041280/2909907,…=A229 727/A229 726(和2 ^ k/k)

第一非平凡项>2

  • 0, 1, 8/3, 29/6, 37/5, 103/10, 472/35, 2369/140, 2593/126,…=A115107/A09620(快速排序)
  • 1, 1, 3、3, 15, 1、63, 5, 21、1, 1023, 5/3, 4095, 1、17/3、17, 65535, 1、262143, 17/3, 65/3, 1, 4194303、17/5、…=A226305/A226306
  • 3, 22/7, 333/106, 355/113, 103993/33102,…=A000 2485/A000 248(PI)
  • 3, 9/2, 53/9, 231/32, 5319/625, 3167/324, 1296273/117649, 1604979/131072,…=A226931/A036505
  • 0, 1, 3,17/3,53/6,62/5,163/10,717/35,3489/140,…=A0931818/A09620
  • 1, 1, 1,1,432000/691,1,-3456000/3617,-9504000/43867,…=A085092/A000 1067



评论

  • 欢迎更新此索引,但请务必小心。请记住,这是一个科学数据库。请保存订购(在本页的顶部描述)。
  • 格式如下:每一个分数序列的一行,从*开始,接着是一个空间,然后最初的几个分数作为分子/分母,用逗号和空格分隔,接着是“…”=A000 000/A000 0 0 2“(说),哪里A000 000A000 0 0 2分别是分子和分母序列的A数。除非定义非常复杂,在结束时在括号中包含一个简短的描述。
  • 有几条线太短了。如果您愿意帮助,请添加更多的术语。
  • 插入的零点,有时是符号,在与A数.
  • 当您将一对分子和分母序列作为新序列提交给OEIS时,应该包括如下一行例子分子和分母序列的部分:
1,-1/3,-1/45,-2/945,-1/4725,-2/93555,-1382/638512875,-4/18243225,-3617/162820783125,-87734/38979295480125,-349222/1531329465290625,…=A000 2431/A03627
并在这里做一个对应的条目。
  • 分数被写成7/4(例如),而不是1(3/4)。混合分数
  • 分数通常在最低条件有任何共同因素被取消。
  • 这里提到的所有序列都应该具有关键词压裂在OEIS中。
  • 不要用名称对该索引进行更改(历史选项卡将显示谁做出了更改)。


  • 改变时请小心! 如果有疑问,请咨询其中之一主编在作出任何更改之前。