id
stringlengths
7
11
seq
listlengths
1
347
keywords
listlengths
1
8
A157980_aug
[ 3, 11, 83, 6563, 43046747, 1853020188851911, 3.4336838202925124e+30, 1.1790184577738583e+61, 1.3900845237714473e+122 ]
null
A029159_aug
[ 4, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 14, 15, 16, 17, 19, 20, 21, 23, 25, 26, 28, 30, 32, 34, 36, 39, 41, 43, 46, 49, 51, 54, 58, 60, 64, 67, 71, 74, 78, 82, 86, 90, 94, 99, 103, 108, 113, 118, 123, 128 ]
null
A289890_aug
[ 9, 100, 890, 9100, 99900, 901000, 10089000, 88910000, 1010990000, 9900100000, 98998900000, 990091000000, 10010999000000, 99999010000000, 999890890000000, 9999999100000000, 99989109900000000, 1000010001000000000, 9998889989000000000 ]
null
A136865_aug
[ 0, -1, 6, -4, 66, -31, 69, -38, 662, -39, 931, -66, 934, -73, 976, -94, 977, -6023, 978, -6032, 1039, -8661, 1040, -8930, 1067, -8933, 1074, -8996, 1101, -9389, 1311, -9399, 4708, -65292, 4709, -65301, 4799, -65308, 5191, -65519, 31481, -65520, 31490, -68210, 31760, -68237, 31763, -68244, 31826, -68271, 32228, -68472, 32498, -72402, 34598 ]
null
A362749_aug
[ 1, 2, 3, 1, 4, 1, 1, 1, 8, 2, 4, 1, 1, 3, 4, 2, 2, 1, 2, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 5, 4, 2, 3, 2, 1, 4, 4, 1, 1, 2 ]
null
A078302_aug
[ 5, 3, 9, 1 ]
null
A004732_aug
[ 4, 4, 8, 4, 32, 20, 64, 28, 512, 84, 1024, 132, 4096, 1716, 8192, 2860, 131072, 9724, 262144, 16796, 1048576, 117572, 2097152, 208012, 16777216, 742900, 33554432, 1337220, 134217728, 38779380, 268435456, 70715340, 8589934592 ]
null
A259691_aug
[ 1, 2, 5, 1, 12, 52, 20, 203, 104, 1, 1116, 42, 4140, 3196, 56, 21147, 18944, 455, 1 ]
null
A176002_aug
[ 1, 7, 41, 217, 825, 1848, 3186, 4563, 6118, 8098, 10152, 13002, 15895, 18956, 22219, 25791, 29768, 33797, 38041, 42446, 48545, 55093, 62296, 69644, 76994, 84566, 92140, 101168, 111825, 123801, 136016, 148890, 162137, 175525, 188957, 203494, 218307, 233422, 248834, 264343 ]
null
A168751
[ 1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566406250, 1549720764160156200, 38743019104003910000, 968575477600097700000 ]
[ "nonn", "easy" ]
A347358_aug
[ 3, 1, 29, 5, 31, 7, 41, 37, 47, 43, 89, 83, 107, 101, 103, 97, 113, 109, 179, 173, 191, 181, 197, 193, 211, 293, 223, 199, 311, 307, 317, 313, 331 ]
null
A153182_aug
[ 2, 3, 5, 1, -1, 9, 9, -7, -3, 11, 9, 1, -7, 9, 17, -15, -9, 17, 13, 1, -7, 17, 9, -23, -7, 11, 25, 1, -15, 25, 17, -23, -19, 17, 17, 1, -9, 9, 25, -31, -7, 33, 17, 1, -23, 25, 17, -39, -23, 19, 29, 1, -7, 25, 33, -31, -15, 17, 9, 1, -31, 25, 33, -39, -25, 33 ]
null
A107529_aug
[ -1, -2244, -887944, -138356812, -11611049232, -613117108692, -22401565939096, -604236908351836, -12614080176060960, -211304637639230180, -2922548785348161000, -34155084597146145000, -343782301079271600000, -3.0283146001503203e+21, -2.366526555890924e+22, -1.6598788260406327e+23 ]
null
A177333_aug
[ 2, 2, 2, 2, 5, 5, 2, 2, 7, 7, 3, 3, 2, 2, 2, 2, 5, 5, 4, 3, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 2, 2, 3, 3, 3, 3, 2, 2, 4, 4, 2, 2, 2, 2, 3, 3, 4, 4, 2, 2, 2, 2, 4, 4, 2, 2, 3, 3, 7, 7, 2, 2, 2, 2, 3, 3, 3, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 3, 4, 2, 2, 4, 4, 5, 3, 2, 2, 4, 4, 2, 2, 2, 2, 3, 3, 2, 2, 4 ]
null
A326742_aug
[ 39, 87, 108, 168, 285, 339, 369, 399, 429, 459, 489, 519, 549, 579, 609, 639, 696, 714, 738, 765, 849, 897, 939, 951, 975, 1023, 1143, 1239, 1266, 1278, 1539, 1557, 1575, 1629, 1644, 1839, 2139, 2439, 2454, 2517, 2739, 2745, 2907, 3087, 3108, 3168, 3285, 3387, 3408, 3468, 3585 ]
null
A229012_aug
[ 3, 2, 4, 2, 2, 7, 14, 5, 2, 15, 23, 6, 31, 46, 7, 2, 101, 34, 57, 130, 8, 2, 186, 47, 332, 359, 2, 105, 62, 9, 794, 307, 830, 1145, 2, 193, 79, 10, 1527, 470, 3527, 3002, 353, 2054, 11, 2, 681, 98, 6635, 2666, 10735, 10860, 653, 5108, 12, 2, 946, 119, 13040, 4335, 27379 ]
null
A345041_aug
[ 0, 1, 27, 3670, 10621303, 607748159931, 868304751259834900, 7.2322259721325e+25, 1.411349468696136e+35, 2.150685295370978e+46, 2.1313139470892733e+59 ]
null
A098057_aug
[ 15, 8, 48, 27, 147, 84, 451, 257, 1413, 796, 4544, 2526, 14978, 8226, 50434, 27417, 172865, 93183, 601263, 321857, 2116968, 1126644, 7530200, 3987960, 27019301, 14249649 ]
null
A304992_aug
[ 0, -1, 6, 17, 97, 209, 968, 1937, 7036, 15257, 44814, 93179, 262390, 518549, 1311014, 2657327, 6189159, 12124097, 27239759, 52063667, 111630479, 211503287, 432900235, 806091179, 1610854426, 2940167267, 5691072910, 10289144975, 19402974146, 34523231687 ]
null
A059070_aug
[ -1, -44, -45, -20, -10, 0, -1, -13756, -30480, -32365, -21760, -10300, -3568, -970, -160, -40, 0, -1, -6699824, -23123880, -38358540, -40563765, -30573900, -17399178, -7723640, -2729295, -776520, -180100, -33372, -5355, -540, -90, 0, -1 ]
null
A203308_aug
[ -3, -3, 16, 9104, 153675644, 153926018668796, 1.3624548214772202e+22, 1.483120293632865e+32, 2.629250144284629e+44, 9.695031112583946e+58 ]
null
A339849_aug
[ 1, 0, 1, 0, 4, 3, 4, -9, 4, 3, 4, -40, 40, -4, -3, -4, 144, -405, 144, -4, -3, -4, 494, -3357, 3747, -104, 394, 393, 394, -1282, 25217, -78883, 25217, -1282, 394, 393, 394, -5246, 178275, -1297011, 1995173, 519887, 703408, 697768, 697769, 697768, 716748, -552936, 20289866, -80476347, 20289866, -552936, 716748, 697768, 697769 ]
null
A350930
[ 1, 1, -5, -42, -1810, -48098, -2737409, -114381074 ]
[ "sign", "hard", "more" ]
A134234_aug
[ 0, 1, 2, 1, 1, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1 ]
null
A114041_aug
[ -3, -6, -9, -8, -6, -8, -7, -4, -3, -4, -8, -4, -8, -4, -7, -9, -4, -4, -8, -9, -5, -8, -4, -8, -7, -7, 0, -2, -9, -5, -9, -4, -8, -1, -8, -7, -4, -3, -2, -7, -8, -7, -2, 0, -9, -7, -9, -6, -5, -6, -8, -5, -8, -7, -3, -7, -5, -5, -8, -7, -2, -2, -6, -6, 0, -4, -5, -3, -4, -5, -8, -6, 0, -3, -2, 0, -9, -6, -4, -8, -4, -8, -5, -2, -1, -2, -8, -4, -5, -3, -3, -9, -5, -2, -3, -7, -1, -8, -2 ]
null
A277896_aug
[ 0, 0, 4, 0, 9, 8, 25, 0, 12, 18, 49, 16, 121, 50, 20, 0, 169, 24, 289, 27, 28, 98, 361, 32, 45, 242, 36, 75, 529, 40, 841, 0, 44, 338, 63, 48, 961, 578, 52, 54, 1369, 56, 1681, 147, 60, 722, 1849, 64, 175, 90, 68, 363, 2209, 72, 99, 150, 76, 1058, 2809, 80, 3481, 1682, 84, 0, 117, 88, 3721, 507, 92, 126, 4489, 96, 5041, 1922, 100, 867, 275 ]
null
A056404_aug
[ 1, 1, 3, 9, 17, 111, 156, 1099, 3072, 21789, 42334, 528487, 859501, 8546878, 31968376, 159715435, 398048505, 5303677376, 8835749346, 99411964817, 331215913868, 1987084087016, 4515860983384, 62095480510303 ]
null
A102881_aug
[ 9, 9, 10, 14, 12, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8 ]
null
A320990_aug
[ 0, 5, 45, 370, 21210, 10691615, 349658543495, 5866117884595980000, 3.224932219788065e+30, 2.974474965669113e+49, 1.5082379902377172e+80 ]
null
A070524_aug
[ 0, -7, -341, -55987, -46873, -11111111111, -9726655034461, -14709241, -19676527011956855000, -4.166090266796104e+22, -8177824843189, -3.576863477148967e+29 ]
null
A175356_aug
[ 1, 5, 4, 6, 3, 0, 0, 0, 5, 2, 5, 5, 2, 2, 3, 0, 0, 3, 2, 2, 0, 2, 4, 3, 6, 3, 4, 4, 3, 3, 6, 6, 3, 3, 0, 5, 2, 0, 2, 4 ]
null
A273075_aug
[ 1, 23, 123, 437, 1052, 2217, 4120, 7093, 11384, 17357, 25464, 36305, 50340, 67997, 89764, 116605, 148759, 187103, 232128, 284975, 346308 ]
null
A140951_aug
[ 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ]
null
A234871_aug
[ 1, 5, 65, 1110, 21620, 455126, 10085845, 231814440, 5475346305, 132090011900, 3240886705386, 80621405042750, 2028732009726240, 51548408940061460, 1320738410528418000, 34083616545621830000, 885134579074202200000, 2.3114512490211286e+22, 6.066008607003126e+23 ]
null
A057953_aug
[ 1, -2, 0, -5, -2, -8, -4, -11, -8, -15, -11, -21, -17, -25, -19, -29, -24, -33, -29, -42, -35, -44, -40, -54, -47, -55, -49, -63, -57, -70, -67, -80, -72, -83, -72, -87, -81, -90, -81, -98, -93, -107, -102, -117, -107, -116, -110, -129, -122, -136, -128, -146, -138, -154, -144, -163, -156, -167, -161, -185, -180, -188, -178, -194, -186, -203, -197, -217, -208, -230, -223, -244, -237, -250, -236, -253, -243, -259, -251, -274, -264, -276, -271, -295 ]
null
A167842_aug
[ 303, 2361, 37029, 103629, 162969, 169629, 1962969, 3703629, 22963701, 1037029629, 2962962969, 96370370367, 103703629629, 1962970370367 ]
null
A004939_aug
[ 0, 7, 14, 21, 27, 34, 41, 48, 55, 62, 69, 75, 82, 89, 96, 103, 110, 117, 123, 130, 137, 144, 151, 158, 164, 171, 178, 185, 192, 199, 206, 212, 219, 226, 233, 240, 247, 254, 260, 267, 274, 281, 288, 295, 302, 308 ]
null
A351664_aug
[ 1653, 3741, 5205, 7953, 8376, 8517, 9276, 10104, 11208, 11976, 12621, 13128, 15369, 16572, 18177, 19545, 20028, 20673, 21468, 25017, 25224, 26229 ]
null
A352679_aug
[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1 ]
null
A096445_aug
[ 1, 1, 2, 2, 2, 4, 4, 4, 6, 4, 6, 8, 6, 8, 8, 8, 8, 12, 10, 8, 16, 12, 12, 16, 10, 12, 18, 16, 14, 16, 16, 16, 24, 16, 16, 24, 18, 20, 24, 16, 20, 32, 22, 24, 24, 24, 24, 32, 28, 20, 32, 24, 26, 36, 24, 32, 40, 28, 30, 32, 30, 32, 48, 32, 24 ]
null
A266497_aug
[ 2, 10, 36, 114, 338, 964, 2680, 7312, 19652, 52152, 136888, 355846, 917108, 2345394, 5956064, 15028430, 37696714, 94042548, 233425260, 576667792, 1418381322, 3474325438, 8477474424, 20610026538, 49933837294, 120585705156, 290304868676, 696846855532, 1668039665550 ]
null
A261339_aug
[ 94999, 40879, 3, 249119, 35699, 5459, 371099, 1, 1037819, 858359, 19, 1374959, 162059, 71, 3136679, 3, 2331499, 14819, 19, 13559, 962279, 19, 19, 10859, 479, 5459, 145319, 4159, 37399, 583439, 590159, 105719, 10859, 1, 162059 ]
null
A005255_aug
[ 0, 1, 2, 4, 7, 13, 24, 46, 88, 172, 337, 667, 1321, 2629, 5234, 10444, 20842, 41638, 83188, 166288, 332404, 664636, 1328935, 2657533, 5314399, 10628131, 21254941, 42508561, 85014493, 170026357, 340047480, 680089726, 1360169008, 2720327572 ]
null
A077223_aug
[ 2, 1, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 2, 1, 0, 3, 0, 3, 2, 1, 2, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 0, 3, 2, 1, 0, 3, 0, 1, 2, 3, 2, 1, 0, 3, 2, 1, 2, 1, 0, 1, 0, 3, 2, 3, 2, 3, 0, 1, 0, 3 ]
null
A358171_aug
[ 4, 4, 4, 5, 4, 6, 4, 7, 5, 8, 4, 10, 4, 12, 6, 11, 4, 9, 4, 16, 8, 20, 4, 18, 5, 36, 7, 28, 4, 14, 4, 19, 12, 68, 6, 17, 4, 132, 20, 32, 4, 24, 4, 52, 10, 260, 4, 34, 5, 13, 36, 100, 4, 15, 8, 60, 68, 516, 4, 30, 4, 1028, 16, 35, 12, 44, 4, 196, 132, 22, 4, 33, 4 ]
null
A087891_aug
[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 1, 0, 0, 1, 2, 0, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 1, 1, 0, 0, 0, 2, 2, 0, 1, 0, 1, 2, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 2, 0, 0 ]
null
A230619_aug
[ 0, 0, 0, 509978, 128706852, 35145166536, 8937075346246, 2294186499807542, 587879941920096100, 150672100573449550000, 3.861866788067132e+22, 9.898104313860041e+24, 2.5369356350600764e+27 ]
null
A002542_aug
[ 2, 56, 16256, 1073709056, 4611686016279904000, 8.507059173023462e+37, 2.894802230932905e+76 ]
null
A361504_aug
[ 13, 14, 42, 12, 11, 24, 347, 19, 3466, 15, 16, 17, 49012, 25, 18, 31, 32, 20, 528231, 21, 717126, 38, 22, 44, 23, 35, 63056215, 47, 45, 26, 1375559400, 27, 7038527851, 28, 29, 55 ]
null
A256266_aug
[ 0, 6, 8, 4, 8, 6, 8, 4, 2, 4, 0, 0, 4, 2, 4, 0, 6, 6, 0, 8, 0, 6, 6, 0, 8, 0, 6, 6, 0, 8, 0, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8, 6, 8, 4, 4, 8 ]
null
A386210_aug
[ 9, 2, 611, 64, 101011, 7230, 29071029, 1616840, 12651053525, 579105874, 7725759334447, 300690186312, 6310055339511207, 213427512112286, 6655158897686650000, 198849700754364030, 8.817879279123178e+21, 235791417133696800000, 3.471477693610654e+23 ]
null
A179284_aug
[ 10, 1021, 2122, 12123, 23234, 133335, 1133446, 2134557, 3234558, 4334659, 5434770, 6535781, 17545792, 28646793, 39757804, 139767905, 240779006, 341880117, 451981228, 562091339, 673092340, 784202451, 1784203452 ]
null
A303872_aug
[ 2, -1, -1, 4, 1, 12, 16, -24, 80, -10, -12, -32, -192, 160, -84, 1, -448, 560, 112, -1, 1792, -1120, 18, -256, 4032, -672, 512, -4608 ]
null
A194623_aug
[ 4, 1, -4, -2, 3, 1, 2, -4, 0, 0, -1, 2, -5, 0, 2, 1, 3, -6, 8, -3, 1, -6, 8, -6, 0, 5, -1, -5, 0, 7, -1, -5, 2, 3, -4, 5, -5, 3, -5, 5, -4, -2, 8, -4, -3, 6, -8, 9, -6, 4, -5, 2, 0, -1, 3, -3, -3, 8, -4, 2, 0, -2, 5, -7, 7, -4, 0, -1, -3, 1, -1, -1, 4, 5, -4, -1, -4, 9, -7, 7, -6, 3, -1, -2, 1, -3, 0, 3, -4, 8, -8, 1, 1, -1, 6, 2, -7, 4, -5 ]
null
A111359_aug
[ 3, 6, 9, 10, 13, 42, 73, 184, 511, 690, 3275, 18918, 20574, 21340, 44140, 116669, 543214, 567016, 637321, 688792, 878649, 2582446, 27067133, 152149612, 180031091, 180397517, 290516940, 303713151, 749973242, 1138167152, 1149871982, 1340024880, 1992196101 ]
null
A255125_aug
[ 0, 1, 1, 1, 3, 1, 13, 6, 47, 26, 140, 81, 482, 253, 1875, 949, 7088, 3666, 26100, 13614, 96246, 50082, 356123, 185131, 1316197, 684758, 4868019, 2530257, 18096921, 9378335, 67669905, 34974646, 253565649, 130998912, 947992195, 490501587, 3533571444, 1830664188 ]
null
A076461_aug
[ 21, -563, 5314, -26462, 93463, -264305, 640284, -1383268, 2736473, -5047727, 8796246, -14621898, 23357979, -36066477, 54076848, -79027280, 112909469, -158115883, 217490538, -294382262, 392701471, -516979433, 672431044, -865020092, 1101528033, -1389625255, 1737945854, -2156164898 ]
null
A058879_aug
[ -1, -1, -1, -1, -1, -3, -1, -1, -4, -7, -1, -1, -4, -9, -18, -1, -1, -5, -10, -28, -44, -1, -1, -5, -13, -32, -71, -117, -1, -1, -6, -14, -45, -89, -202, -299, -1, -1, -6, -17, -52, -130, -264, -542, -793, -1, -1, -7, -19, -69, -163, -413, -751, -1507, -2095, -1, -1, -7, -22, -79, -224, -544, -1221, -2179, -4114, -5607 ]
null
A003481_aug
[ 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0 ]
null
A164298_aug
[ 28, 9, 320, 94, 3728, 1092, 43456, 12728, 506560, 148368, 5904896, 1729504, 68832512, 20160576, 802370560, 235008896, 9353116672, 2739464448, 109027917824, 31933537792, 1270922547200, 372244595712, 14814958895104, 4339200997376, 50581433585664 ]
null
A170097_aug
[ 1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664060, 12699033492898898000, 495262306223057000000, 1.9315229942699222e+22 ]
null
A162208_aug
[ 5, 1, 30, 14, 85, 54, 155, 120, 205, 185, 205, 212, 155, 185, 85, 120, 30, 54, 5, 14, 1 ]
null
A249948_aug
[ -3, 4, -1, 3, -3, 0, -3, 3, 0, -3, 3, -3, 0, 0, -3, 4, -1, -3, 3, 4, 3, 0, -3, 0, -3, 3, 0, -3, 3, -1, 3, -3, 0, 0, -3, 3, 4, -3, -1, 4, 3, -3, -1, 3, -3, 0, -3, 3, -3, 0, 0, -3, 4, -1, -3, 0, -3, 0, 3, -3, 0, -3, 0, -3, -1, 4, -3, 3, -1, -3, 4, 3, -3, -1, 4, -3, 0, 0, -3, 4, -1, 3, -3, 4, 3, -3, 0, 0 ]
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A212628_aug
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