sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A002501
|
a(n) = 7^n - 3*4^n + 2*3^n.
|
[
"1",
"19",
"205",
"1795",
"14221",
"106819",
"778765",
"5581315",
"39606541",
"279447619",
"1965098125",
"13792018435",
"96690872461",
"677427332419",
"4744368982285",
"33220131761155",
"232579232659981",
"1628208214321219",
"11398072876175245",
"79788974736297475",
"558532690864457101"
] |
[
"nonn",
"easy"
] | 48 | 1 | 2 |
[
"A001047",
"A002501",
"A002502",
"A005333",
"A093732",
"A093733",
"A262307"
] |
[
"M5078",
"N2197"
] |
N. J. A. Sloane
| 2023-10-17T01:04:27 |
oeisdata/seq/A002/A002501.seq
|
edab15e64249a52f33bbe736b498c741
|
A002502
|
Number of connected relations.
|
[
"1",
"65",
"1795",
"36317",
"636331",
"10365005",
"162470155",
"2495037197",
"37898120011",
"572284920845",
"8614868501515",
"129467758660877",
"1943971108806091",
"29175170378428685",
"437752102106036875",
"6567275797761209357"
] |
[
"nonn",
"nice",
"easy"
] | 32 | 1 | 2 |
[
"A001047",
"A002501",
"A002502",
"A005333",
"A093732",
"A093733",
"A262307"
] |
[
"M5336",
"N2323"
] |
N. J. A. Sloane
| 2022-01-29T01:05:52 |
oeisdata/seq/A002/A002502.seq
|
dfb56826db116097b54499f5cde600ed
|
A002503
|
Numbers k such that binomial(2*k,k) is divisible by (k+1)^2.
|
[
"5",
"14",
"27",
"41",
"44",
"65",
"76",
"90",
"109",
"125",
"139",
"152",
"155",
"169",
"186",
"189",
"203",
"208",
"209",
"219",
"227",
"230",
"237",
"265",
"275",
"298",
"307",
"311",
"314",
"321",
"324",
"329",
"344",
"377",
"413",
"419",
"428",
"434",
"439",
"441",
"449",
"458",
"459",
"467",
"475"
] |
[
"nonn",
"easy",
"nice"
] | 42 | 1 | 1 |
[
"A000108",
"A000396",
"A002503",
"A065344",
"A065349",
"A065350",
"A067348",
"A135627"
] |
[
"M3840",
"N1573"
] |
N. J. A. Sloane, Mira Bernstein
| 2021-03-28T07:01:58 |
oeisdata/seq/A002/A002503.seq
|
b36220c7c111c3ff456f7a90e6c46493
|
A002504
|
Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407).
|
[
"2",
"3",
"4",
"5",
"7",
"10",
"11",
"12",
"14",
"15",
"18",
"24",
"25",
"26",
"28",
"29",
"31",
"33",
"35",
"38",
"39",
"42",
"43",
"46",
"49",
"50",
"53",
"56",
"59",
"63",
"64",
"67",
"68",
"75",
"81",
"82",
"87",
"89",
"91",
"92",
"94",
"96",
"106",
"109",
"120",
"124",
"126",
"129",
"130",
"137",
"141",
"143",
"148",
"154",
"157",
"158",
"159",
"165",
"166",
"171",
"172"
] |
[
"nonn"
] | 63 | 1 | 1 |
[
"A002407",
"A002504",
"A111251",
"A121259"
] |
[
"M0522",
"N0188"
] |
N. J. A. Sloane
| 2024-02-22T13:34:13 |
oeisdata/seq/A002/A002504.seq
|
0b183d701e0cdda6a9a8a6b0c1992c57
|
A002505
|
Nearest integer to the n-th Gram point.
|
[
"18",
"23",
"28",
"32",
"35",
"39",
"42",
"46",
"49",
"52",
"55",
"58",
"60",
"63",
"66",
"68",
"71",
"74",
"76",
"79",
"81",
"84",
"86",
"88",
"91",
"93",
"95",
"98",
"100",
"102",
"104",
"107",
"109",
"111",
"113",
"115",
"118",
"120",
"122",
"124",
"126"
] |
[
"nonn"
] | 73 | 0 | 1 |
[
"A002505",
"A114857",
"A114858",
"A273061"
] |
[
"M5052",
"N2185"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002505.seq
|
e7dc0d38ab85454613fce126be9ae959
|
A002506
|
Denominators of coefficients of expansion of Bessel function J_2(x).
|
[
"8",
"96",
"3072",
"184320",
"17694720",
"2477260800",
"475634073600",
"119859786547200",
"38355131695104000",
"15188632151261184000",
"7290543432605368320000",
"4170190843450270679040000",
"2802368246798581896314880000"
] |
[
"nonn"
] | 17 | 0 | 1 |
[
"A002454",
"A002474",
"A002506",
"A014401",
"J0",
"J1",
"J3"
] | null |
N. J. A. Sloane
| 2023-10-17T05:43:35 |
oeisdata/seq/A002/A002506.seq
|
e27bb5d5fb52d4c6dd630817e1cc93dc
|
A002507
|
Expansion of a modular function for Gamma_0(6).
|
[
"1",
"2",
"-5",
"-24",
"-23",
"76",
"249",
"168",
"-599",
"-1670",
"-1026",
"3272",
"8529",
"5232",
"-14062",
"-35976",
"-22337",
"51516",
"131617",
"82568",
"-169376",
"-432636",
"-273332",
"513584",
"1309800",
"830372",
"-1456569",
"-3709672",
"-2354215",
"3904696",
"9931407",
"6301120",
"-9983208",
"-25339626",
"-16057040",
"24504584",
"62033318"
] |
[
"sign",
"easy"
] | 30 | -3 | 2 |
[
"A002507",
"A002508",
"A105559",
"A128632",
"A128633"
] |
[
"M1542",
"N0602"
] |
N. J. A. Sloane
| 2021-12-20T20:25:56 |
oeisdata/seq/A002/A002507.seq
|
e6419c4ec4eacc37d96fe148b9044a5c
|
A002508
|
Expansion of a modular function for Gamma_0(6).
|
[
"1",
"-2",
"9",
"-4",
"28",
"18",
"118",
"80",
"504",
"466",
"1631",
"2160",
"5466",
"7498",
"17658",
"25088",
"51944",
"78660",
"149099",
"226544",
"412920",
"627830",
"1090006",
"1671840",
"2796805",
"4263984",
"6969690",
"10555224",
"16836620",
"25396506",
"39699240",
"59409184",
"91460952",
"135795598",
"205951071",
"303740496",
"454672142"
] |
[
"sign",
"easy"
] | 26 | 3 | 2 |
[
"A002507",
"A002508",
"A002509"
] |
[
"M1910",
"N0754"
] |
N. J. A. Sloane
| 2018-04-09T08:24:51 |
oeisdata/seq/A002/A002508.seq
|
a7a4eb753be9d88faeeeceb6f72fc8be
|
A002509
|
Expansion of a modular function for Gamma_0(14).
|
[
"1",
"-1",
"4",
"-5",
"15",
"-19",
"45",
"-52",
"118",
"-137",
"281",
"-316",
"625",
"-695",
"1331",
"-1444",
"2696",
"-2907",
"5308",
"-5640",
"10122",
"-10650",
"18845",
"-19628",
"34241",
"-35378",
"61036",
"-62524",
"106783",
"-108593",
"183799",
"-185646",
"311625",
"-312800",
"521232",
"-520044",
"860728",
"-854151",
"1404871",
"-1386868",
"2267960",
"-2228161"
] |
[
"sign",
"easy"
] | 25 | 4 | 3 | null |
[
"M3256",
"N1314"
] |
N. J. A. Sloane
| 2018-04-09T11:00:44 |
oeisdata/seq/A002/A002509.seq
|
0f19fbff0e65090a00d8947a5938ebe5
|
A002510
|
Expansion of a modular function for Gamma_0(15).
|
[
"1",
"1",
"2",
"8",
"10",
"24",
"53",
"74",
"153",
"280",
"436",
"793",
"1322",
"2085",
"3510",
"5648",
"8796",
"14042",
"21921",
"33490",
"51796",
"78843",
"118108",
"178029",
"265225",
"390852",
"576946",
"843694",
"1224329",
"1775450",
"2556360",
"3658111",
"5224159",
"7418887",
"10481780",
"14773012",
"20723154",
"28941023"
] |
[
"nonn",
"easy"
] | 32 | 6 | 3 | null |
[
"M1825",
"N0725"
] |
N. J. A. Sloane
| 2021-12-20T20:25:28 |
oeisdata/seq/A002/A002510.seq
|
dc287bdebd827147b4fe8aecf3ba0355
|
A002511
|
Expansion of a modular function for Gamma_0(21).
|
[
"1",
"1",
"2",
"6",
"8",
"13",
"29",
"44",
"66",
"122",
"184",
"269",
"448",
"668",
"972",
"1505",
"2205",
"3153",
"4677",
"6717",
"9480",
"13656",
"19245",
"26793",
"37714",
"52301",
"71894",
"99392",
"135969",
"184637",
"251492",
"339793",
"456432",
"613837",
"820388",
"1091154",
"1451243",
"1920637",
"2531468"
] |
[
"nonn",
"easy"
] | 32 | 6 | 3 | null |
[
"M1566",
"N0610"
] |
N. J. A. Sloane
| 2018-04-09T08:05:47 |
oeisdata/seq/A002/A002511.seq
|
dd79d2c197d6ef11d3ce9d11eca5283f
|
A002512
|
Expansion of chi(x)^10 / phi(x)^4 in powers of x where phi(), chi() are Ramanujan theta functions.
|
[
"1",
"2",
"5",
"10",
"22",
"40",
"75",
"130",
"230",
"382",
"636",
"1022",
"1645",
"2570",
"4002",
"6110",
"9297",
"13910",
"20715",
"30462",
"44597",
"64584",
"93085",
"132990",
"189164",
"266992",
"375192",
"523800",
"728285",
"1006684",
"1386043",
"1898586",
"2591120",
"3519840",
"4764736",
"6423032"
] |
[
"nonn"
] | 32 | 0 | 2 |
[
"A000122",
"A000700",
"A002512",
"A010054",
"A121373"
] |
[
"M1380",
"N0539"
] |
N. J. A. Sloane, Simon Plouffe
| 2018-03-08T02:50:45 |
oeisdata/seq/A002/A002512.seq
|
4bf0b769fcd7ff79e314e3d732bdd05c
|
A002513
|
Number of "cubic partitions" of n: expansion of Product_{k>0} 1/((1-x^(2k))^2*(1-x^(2k-1))) in powers of x.
|
[
"1",
"1",
"3",
"4",
"9",
"12",
"23",
"31",
"54",
"73",
"118",
"159",
"246",
"329",
"489",
"651",
"940",
"1242",
"1751",
"2298",
"3177",
"4142",
"5630",
"7293",
"9776",
"12584",
"16659",
"21320",
"27922",
"35532",
"46092",
"58342",
"75039",
"94503",
"120615",
"151173",
"191611",
"239060",
"301086",
"374026",
"468342",
"579408",
"721638",
"889287"
] |
[
"nonn",
"easy",
"nice"
] | 125 | 0 | 3 |
[
"A000122",
"A001934",
"A002513",
"A015128",
"A089799",
"A215947",
"A273225",
"A319455"
] |
[
"M2354",
"N0930",
"N0931"
] |
N. J. A. Sloane, Simon Plouffe
| 2024-02-07T09:01:35 |
oeisdata/seq/A002/A002513.seq
|
52e5a03663c49f8f2b1a0089125c61e5
|
A002514
|
Coefficients in the asymptotic expansions of modified Hankel functions h_1(z) and h_2(z), rounded to nearest integer.
|
[
"0",
"0",
"0",
"0",
"1",
"3",
"15",
"79",
"474",
"3207",
"24087",
"198923",
"1791902",
"17484377",
"183707380",
"2067904033",
"24827519376",
"316694549817",
"4277112686513",
"60971132411393",
"914869422343564",
"14413525170009350",
"237888443951757586",
"4104608160094692304"
] |
[
"nonn"
] | 25 | 1 | 6 | null |
[
"M2992",
"N1212"
] |
N. J. A. Sloane
| 2015-10-19T01:27:30 |
oeisdata/seq/A002/A002514.seq
|
b3e3a38e99be944285c8aa91971b6201
|
A002515
|
Lucasian primes: p == 3 (mod 4) with 2*p+1 prime.
|
[
"3",
"11",
"23",
"83",
"131",
"179",
"191",
"239",
"251",
"359",
"419",
"431",
"443",
"491",
"659",
"683",
"719",
"743",
"911",
"1019",
"1031",
"1103",
"1223",
"1439",
"1451",
"1499",
"1511",
"1559",
"1583",
"1811",
"1931",
"2003",
"2039",
"2063",
"2339",
"2351",
"2399",
"2459",
"2543",
"2699",
"2819",
"2903",
"2939",
"2963",
"3023",
"3299"
] |
[
"nonn",
"easy"
] | 59 | 1 | 1 |
[
"A002145",
"A002515",
"A005384"
] |
[
"M2884",
"N2039"
] |
N. J. A. Sloane
| 2025-04-03T14:59:50 |
oeisdata/seq/A002/A002515.seq
|
750c9ea84f98789f716a5aa4f94dfdbf
|
A002516
|
Earliest sequence with a(a(n)) = 2n.
|
[
"0",
"3",
"6",
"2",
"12",
"7",
"4",
"10",
"24",
"11",
"14",
"18",
"8",
"15",
"20",
"26",
"48",
"19",
"22",
"34",
"28",
"23",
"36",
"42",
"16",
"27",
"30",
"50",
"40",
"31",
"52",
"58",
"96",
"35",
"38",
"66",
"44",
"39",
"68",
"74",
"56",
"43",
"46",
"82",
"72",
"47",
"84",
"90",
"32",
"51",
"54",
"98",
"60",
"55",
"100",
"106",
"80",
"59",
"62",
"114",
"104",
"63",
"116",
"122",
"192",
"67",
"70",
"130"
] |
[
"nonn",
"nice"
] | 52 | 0 | 2 |
[
"A002516",
"A002517",
"A004767",
"A007379",
"A017089",
"A091067"
] | null |
Colin Mallows
| 2021-09-20T04:38:27 |
oeisdata/seq/A002/A002516.seq
|
ee5a4d748d7e0bded83409600d9ec1ae
|
A002517
|
Earliest sequence with a(a(n))=3n.
|
[
"0",
"2",
"3",
"6",
"5",
"12",
"9",
"8",
"21",
"18",
"11",
"30",
"15",
"14",
"39",
"36",
"17",
"48",
"27",
"20",
"57",
"24",
"23",
"66",
"63",
"26",
"75",
"54",
"29",
"84",
"33",
"32",
"93",
"90",
"35",
"102",
"45",
"38",
"111",
"42",
"41",
"120",
"117",
"44",
"129",
"108",
"47",
"138",
"51",
"50",
"147",
"144",
"53",
"156",
"81",
"56",
"165",
"60",
"59",
"174",
"171",
"62",
"183",
"72",
"65",
"192"
] |
[
"nonn",
"nice",
"easy"
] | 17 | 0 | 2 |
[
"A002516",
"A002517",
"A005843",
"A007379",
"A007494",
"A016789",
"A017197"
] | null |
Colin Mallows
| 2016-08-28T18:23:33 |
oeisdata/seq/A002/A002517.seq
|
c716ec50b890e890a1218c73ad589646
|
A002518
|
Earliest sequence with a(a(n))=5n.
|
[
"0",
"2",
"5",
"4",
"15",
"10",
"7",
"30",
"9",
"40",
"25",
"12",
"55",
"14",
"65",
"20",
"17",
"80",
"19",
"90",
"75",
"22",
"105",
"24",
"115",
"50",
"27",
"130",
"29",
"140",
"35",
"32",
"155",
"34",
"165",
"150",
"37",
"180",
"39",
"190",
"45",
"42",
"205",
"44",
"215",
"200",
"47",
"230",
"49",
"240",
"125",
"52",
"255",
"54",
"265",
"60",
"57",
"280",
"59",
"290",
"275",
"62",
"305"
] |
[
"nonn",
"nice"
] | 15 | 0 | 2 |
[
"A002516",
"A002517",
"A002518",
"A007379"
] | null |
Colin Mallows
| 2016-08-28T18:23:33 |
oeisdata/seq/A002/A002518.seq
|
8359e9e4498d9816e1e492e08d333723
|
A002519
|
Theta series of 28-dimensional unimodular lattice with no roots and a parity vector of norm 4.
|
[
"1",
"0",
"0",
"1728",
"106472",
"1734912",
"19335168",
"141575552",
"805208040",
"3725209088",
"14647517184",
"50579062848",
"156715230240",
"443680116992",
"1162915024896",
"2851005884544",
"6596700471272",
"14509559545344",
"30507866603520"
] |
[
"nonn"
] | 24 | 0 | 4 |
[
"A002519",
"A002520"
] | null |
N. J. A. Sloane
| 2023-10-17T05:44:05 |
oeisdata/seq/A002/A002519.seq
|
4ce13d3bea8715a61a8696c8621ea26b
|
A002520
|
Theta series of 28-dimensional unimodular lattice with no roots and with no parity vector of norm 4.
|
[
"1",
"0",
"0",
"2240",
"98280",
"1790208",
"19138560",
"141920640",
"805208040",
"3723722240",
"14651449344",
"50573436480",
"156717687840",
"443691198720",
"1162883174400",
"2851049534592",
"6596666916840",
"14509544394240",
"30507984568320"
] |
[
"nonn",
"nice",
"easy"
] | 17 | 0 | 4 |
[
"A002519",
"A002520"
] | null |
N. J. A. Sloane
| 2022-01-29T01:04:45 |
oeisdata/seq/A002/A002520.seq
|
85ef50bd1b3af29306416d759d735e4b
|
A002521
|
Weight distribution of [ 28,14,9 ] ternary self-dual code.
|
[
"1",
"0",
"0",
"2184",
"78624",
"768096",
"2159976",
"1555632",
"216216",
"2240"
] |
[
"nonn",
"fini",
"full"
] | 11 | 0 | 4 | null | null |
N. J. A. Sloane
| 2023-10-16T23:43:47 |
oeisdata/seq/A002/A002521.seq
|
35ed9611857db3fe03ed6ecab498df1d
|
A002522
|
a(n) = n^2 + 1.
|
[
"1",
"2",
"5",
"10",
"17",
"26",
"37",
"50",
"65",
"82",
"101",
"122",
"145",
"170",
"197",
"226",
"257",
"290",
"325",
"362",
"401",
"442",
"485",
"530",
"577",
"626",
"677",
"730",
"785",
"842",
"901",
"962",
"1025",
"1090",
"1157",
"1226",
"1297",
"1370",
"1445",
"1522",
"1601",
"1682",
"1765",
"1850",
"1937",
"2026",
"2117",
"2210",
"2305",
"2402",
"2501"
] |
[
"nonn",
"easy",
"changed"
] | 431 | 0 | 2 |
[
"A000027",
"A000124",
"A000125",
"A000127",
"A002496",
"A002522",
"A005408",
"A005843",
"A006261",
"A016813",
"A020725",
"A027383",
"A028872",
"A031396",
"A051890",
"A055096",
"A058331",
"A059100",
"A059592",
"A061547",
"A062318",
"A080856",
"A086514",
"A087475",
"A094626",
"A101220",
"A114949",
"A117619",
"A117950",
"A117951",
"A124808",
"A132411",
"A132414",
"A161701",
"A161704",
"A161706",
"A161707",
"A161708",
"A161710",
"A161713",
"A161715",
"A188377",
"A198300",
"A198306",
"A198307",
"A198308",
"A198309",
"A198310",
"A254858",
"A302612",
"A302644",
"A302645",
"A302646"
] | null |
N. J. A. Sloane
| 2025-07-10T10:44:43 |
oeisdata/seq/A002/A002522.seq
|
52d7a786e51edaf25339e291881f9df9
|
A002523
|
a(n) = n^4 + 1.
|
[
"1",
"2",
"17",
"82",
"257",
"626",
"1297",
"2402",
"4097",
"6562",
"10001",
"14642",
"20737",
"28562",
"38417",
"50626",
"65537",
"83522",
"104977",
"130322",
"160001",
"194482",
"234257",
"279842",
"331777",
"390626",
"456977",
"531442",
"614657",
"707282",
"810001",
"923522",
"1048577",
"1185922",
"1336337",
"1500626",
"1679617"
] |
[
"nonn",
"easy"
] | 77 | 0 | 2 |
[
"A000404",
"A002523",
"A005117",
"A111925"
] | null |
N. J. A. Sloane
| 2024-01-26T04:41:03 |
oeisdata/seq/A002/A002523.seq
|
29b12b748da26681a90bf3370dd071f8
|
A002524
|
Number of permutations of length n within distance 2 of a fixed permutation.
|
[
"1",
"1",
"2",
"6",
"14",
"31",
"73",
"172",
"400",
"932",
"2177",
"5081",
"11854",
"27662",
"64554",
"150639",
"351521",
"820296",
"1914208",
"4466904",
"10423761",
"24324417",
"56762346",
"132458006",
"309097942",
"721296815",
"1683185225",
"3927803988",
"9165743600",
"21388759708",
"49911830577",
"116471963129"
] |
[
"nonn",
"easy"
] | 95 | 0 | 3 |
[
"A002524",
"A306209"
] |
[
"M1600",
"N0626"
] |
N. J. A. Sloane
| 2025-01-05T19:51:32 |
oeisdata/seq/A002/A002524.seq
|
37d7a34bd3526326e15c557ba9c7e2d2
|
A002525
|
Number of permutations according to distance.
|
[
"0",
"1",
"2",
"4",
"10",
"24",
"55",
"128",
"300",
"700",
"1632",
"3809",
"8890",
"20744",
"48406",
"112960",
"263599",
"615120",
"1435416",
"3349624",
"7816528",
"18240289",
"42564706",
"99327052",
"231785058",
"540883000",
"1262179815",
"2945365040",
"6873169028",
"16038912628"
] |
[
"nonn"
] | 55 | 0 | 3 |
[
"A002524",
"A002525"
] |
[
"M1203",
"N0463"
] |
N. J. A. Sloane
| 2022-01-22T16:26:42 |
oeisdata/seq/A002/A002525.seq
|
d3f1c974ea78dedf5bcc502d145b6ac7
|
A002526
|
Number of permutations of length n within distance 3 of a fixed permutation.
|
[
"1",
"1",
"2",
"6",
"24",
"78",
"230",
"675",
"2069",
"6404",
"19708",
"60216",
"183988",
"563172",
"1725349",
"5284109",
"16177694",
"49526506",
"151635752",
"464286962",
"1421566698",
"4352505527",
"13326304313",
"40802053896",
"124926806216",
"382497958000",
"1171122069784",
"3585709284968",
"10978628154457"
] |
[
"nonn",
"easy",
"nice"
] | 65 | 0 | 3 |
[
"A002524",
"A002526",
"A002527",
"A002528",
"A002529",
"A188379",
"A188491",
"A188492",
"A188493",
"A188494",
"A188495",
"A188496",
"A188497",
"A188498",
"A306209"
] |
[
"M1671",
"N0657"
] |
N. J. A. Sloane
| 2025-01-05T19:51:32 |
oeisdata/seq/A002/A002526.seq
|
94684f5f2b941a92b5b8dbedd12c1647
|
A002527
|
Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(1) <= 3.
|
[
"0",
"1",
"2",
"6",
"18",
"60",
"184",
"560",
"1695",
"5200",
"15956",
"48916",
"149664",
"458048",
"1402360",
"4294417",
"13149210",
"40259178",
"123260854",
"377395940",
"1155508592",
"3537919648",
"10832298239",
"33165996032",
"101546731816",
"310913195800",
"951945967120",
"2914642812096",
"8923975209168"
] |
[
"nonn"
] | 52 | 0 | 3 | null |
[
"M1626",
"N0637"
] |
N. J. A. Sloane
| 2023-10-28T14:19:23 |
oeisdata/seq/A002/A002527.seq
|
870c8ea90b93436c21c5c1e1c2856c66
|
A002528
|
a(n) = A188491(n+1) - A188494(n) - A002526(n).
|
[
"0",
"0",
"2",
"4",
"12",
"32",
"108",
"336",
"1036",
"3120",
"9540",
"29244",
"89768",
"274788",
"840936",
"2573972",
"7881922",
"24135000",
"73897320",
"226249264",
"692714696",
"2120941424",
"6493883944",
"19882820480",
"60876609464",
"186390208744",
"570684661408",
"1747307671896",
"5349860697088"
] |
[
"nonn",
"easy"
] | 37 | 0 | 3 | null |
[
"M1256",
"N0480"
] |
N. J. A. Sloane
| 2024-12-27T22:37:52 |
oeisdata/seq/A002/A002528.seq
|
4b32d198b6fad2a7209a0c5e133d5df6
|
A002529
|
a(n) = A002527(n+1) - A002527(n) - A002526(n).
|
[
"0",
"0",
"2",
"6",
"18",
"46",
"146",
"460",
"1436",
"4352",
"13252",
"40532",
"124396",
"381140",
"1166708",
"3570684",
"10932274",
"33475170",
"102499334",
"313825690",
"960844358",
"2941873064",
"9007393480",
"27578681888",
"84439657768",
"258534813320",
"791574775192",
"2423623112104",
"7420586212184",
"22720153701768",
"69563959091138"
] |
[
"nonn",
"easy"
] | 40 | 0 | 3 | null |
[
"M1620",
"N0633"
] |
N. J. A. Sloane
| 2025-02-21T12:34:27 |
oeisdata/seq/A002/A002529.seq
|
7e10340c8144d92bd5a85ecadd7ec5a0
|
A002530
|
a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.
|
[
"0",
"1",
"1",
"3",
"4",
"11",
"15",
"41",
"56",
"153",
"209",
"571",
"780",
"2131",
"2911",
"7953",
"10864",
"29681",
"40545",
"110771",
"151316",
"413403",
"564719",
"1542841",
"2107560",
"5757961",
"7865521",
"21489003",
"29354524",
"80198051",
"109552575",
"299303201",
"408855776",
"1117014753",
"1525870529",
"4168755811"
] |
[
"nonn",
"easy",
"frac",
"core",
"nice"
] | 206 | 0 | 4 |
[
"A000129",
"A001076",
"A001353",
"A001835",
"A002530",
"A002531",
"A003297",
"A005668",
"A041007",
"A041009",
"A041011",
"A041015",
"A041017",
"A042935",
"A042937",
"A048788",
"A049310",
"A108412",
"A152063"
] |
[
"M2363",
"N0934"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002530.seq
|
a31b37dcbf564dfb9bb4b1d02567104a
|
A002531
|
a(2*n) = a(2*n-1) + a(2*n-2), a(2*n+1) = 2*a(2*n) + a(2*n-1); a(0) = a(1) = 1.
|
[
"1",
"1",
"2",
"5",
"7",
"19",
"26",
"71",
"97",
"265",
"362",
"989",
"1351",
"3691",
"5042",
"13775",
"18817",
"51409",
"70226",
"191861",
"262087",
"716035",
"978122",
"2672279",
"3650401",
"9973081",
"13623482",
"37220045",
"50843527",
"138907099",
"189750626",
"518408351",
"708158977",
"1934726305"
] |
[
"nonn",
"frac",
"easy",
"core",
"nice"
] | 148 | 0 | 3 |
[
"A001075",
"A001834",
"A002316",
"A002530",
"A002531",
"A026150",
"A048788",
"A053120",
"A083332",
"A199710"
] |
[
"M1340",
"N0513"
] |
N. J. A. Sloane
| 2024-09-25T10:29:13 |
oeisdata/seq/A002/A002531.seq
|
dcd8a753a4813fb699c01a2cbc7b1fa5
|
A002532
|
a(n) = 2*a(n-1) + 5*a(n-2), a(0) = 0, a(1) = 1.
|
[
"0",
"1",
"2",
"9",
"28",
"101",
"342",
"1189",
"4088",
"14121",
"48682",
"167969",
"579348",
"1998541",
"6893822",
"23780349",
"82029808",
"282961361",
"976071762",
"3366950329",
"11614259468",
"40063270581",
"138197838502",
"476712029909",
"1644413252328",
"5672386654201",
"19566839570042",
"67495612411089"
] |
[
"nonn",
"easy",
"changed"
] | 84 | 0 | 3 |
[
"A000129",
"A001333",
"A002532",
"A002533",
"A002605",
"A015518",
"A015519",
"A015581",
"A026150",
"A046717",
"A063727",
"A083098",
"A083099",
"A083100",
"A084057"
] |
[
"M1923",
"N0758"
] |
N. J. A. Sloane
| 2025-07-13T11:06:36 |
oeisdata/seq/A002/A002532.seq
|
5fb393f91601060144dffff6a13a9841
|
A002533
|
a(n) = 2*a(n-1) + 5*a(n-2), with a(0) = a(1) = 1.
|
[
"1",
"1",
"7",
"19",
"73",
"241",
"847",
"2899",
"10033",
"34561",
"119287",
"411379",
"1419193",
"4895281",
"16886527",
"58249459",
"200931553",
"693110401",
"2390878567",
"8247309139",
"28449011113",
"98134567921",
"338514191407",
"1167701222419",
"4027973401873",
"13894452915841",
"47928772841047",
"165329810261299"
] |
[
"nonn",
"easy"
] | 87 | 0 | 3 |
[
"A000129",
"A001333",
"A002532",
"A002533",
"A002605",
"A015518",
"A015519",
"A026150",
"A046717",
"A063727",
"A083098",
"A083099",
"A083100",
"A084057"
] |
[
"M4369",
"N1834"
] |
N. J. A. Sloane
| 2025-01-12T12:40:41 |
oeisdata/seq/A002/A002533.seq
|
3665d8f6c6e3090d321f03b87f5d32b8
|
A002534
|
a(n) = 2*a(n-1) + 9*a(n-2), with a(0) = 0, a(1) = 1.
|
[
"0",
"1",
"2",
"13",
"44",
"205",
"806",
"3457",
"14168",
"59449",
"246410",
"1027861",
"4273412",
"17797573",
"74055854",
"308289865",
"1283082416",
"5340773617",
"22229288978",
"92525540509",
"385114681820",
"1602959228221",
"6671950592822",
"27770534239633",
"115588623814664"
] |
[
"nonn",
"easy"
] | 68 | 0 | 3 |
[
"A002534",
"A015445",
"A099012"
] |
[
"M2058",
"N0814"
] |
N. J. A. Sloane
| 2025-06-01T05:55:36 |
oeisdata/seq/A002/A002534.seq
|
2c3aaa658427f78134201adbdb3fdb4b
|
A002535
|
a(n) = 2*a(n-1) + 9*a(n-2), with a(0)=a(1)=1.
|
[
"1",
"1",
"11",
"31",
"161",
"601",
"2651",
"10711",
"45281",
"186961",
"781451",
"3245551",
"13524161",
"56258281",
"234234011",
"974792551",
"4057691201",
"16888515361",
"70296251531",
"292589141311",
"1217844546401",
"5068991364601",
"21098583646811",
"87818089575031",
"365523431971361",
"1521409670118001",
"6332530227978251"
] |
[
"nonn",
"easy"
] | 60 | 0 | 3 |
[
"A002534",
"A002535",
"A011557",
"A084132",
"A098158",
"A111015"
] |
[
"M4786",
"N2043"
] |
N. J. A. Sloane
| 2023-01-29T06:01:58 |
oeisdata/seq/A002/A002535.seq
|
1dee9211fb1ff98f7f3f4dddb0824e01
|
A002536
|
a(n) = 8*a(n-2) - 9*a(n-4).
|
[
"0",
"1",
"1",
"5",
"8",
"31",
"55",
"203",
"368",
"1345",
"2449",
"8933",
"16280",
"59359",
"108199",
"394475",
"719072",
"2621569",
"4778785",
"17422277",
"31758632",
"115784095",
"211059991",
"769472267",
"1402652240",
"5113721281",
"9321678001",
"33984519845",
"61949553848",
"225852667231"
] |
[
"nonn",
"easy"
] | 48 | 0 | 4 | null |
[
"M3783",
"N1540"
] |
N. J. A. Sloane
| 2023-10-17T05:44:17 |
oeisdata/seq/A002/A002536.seq
|
cddec4499698f939d63c086b855c9da7
|
A002537
|
a(2n) = a(2n-1) + 3a(2n-2), a(2n+1) = 2a(2n) + 3a(2n-1).
|
[
"1",
"1",
"4",
"11",
"23",
"79",
"148",
"533",
"977",
"3553",
"6484",
"23627",
"43079",
"157039",
"286276",
"1043669",
"1902497",
"6936001",
"12643492",
"46094987",
"84025463",
"306335887",
"558412276",
"2035832213",
"3711069041",
"13529634721",
"24662841844",
"89914587851"
] |
[
"nonn"
] | 37 | 0 | 3 | null |
[
"M3409",
"N1379"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A002/A002537.seq
|
8e46d20c3f2f801a2091ccaa7a8f4cf2
|
A002538
|
Second-order Eulerian numbers <<n+1,n-1>>.
|
[
"1",
"8",
"58",
"444",
"3708",
"33984",
"341136",
"3733920",
"44339040",
"568356480",
"7827719040",
"115336085760",
"1810992556800",
"30196376985600",
"532953524275200",
"9927928075161600",
"194677319705702400",
"4008789120817152000",
"86495828444928000000",
"1951566265951948800000",
"45958933902500720640000"
] |
[
"nonn",
"nice"
] | 133 | 1 | 2 |
[
"A002538",
"A008517",
"A112007",
"A121579"
] |
[
"M4548",
"N1932"
] |
N. J. A. Sloane, Simon Plouffe, Mira Bernstein, Robert G. Wilson v
| 2024-12-27T08:48:31 |
oeisdata/seq/A002/A002538.seq
|
37ba957812ba759cd5353e513e2a987a
|
A002539
|
Eulerian numbers of the second kind: <<n+3, n>>.
|
[
"1",
"22",
"328",
"4400",
"58140",
"785304",
"11026296",
"162186912",
"2507481216",
"40788301824",
"697929436800",
"12550904017920",
"236908271543040",
"4687098165573120",
"97049168010017280",
"2099830209402931200",
"47405948832458496000",
"1115089078488795648000",
"27290469545695931904000",
"694002594415741341696000"
] |
[
"nonn",
"nice",
"easy"
] | 61 | 0 | 2 |
[
"A002539",
"A008517",
"A112007"
] |
[
"M5126",
"N2221"
] |
N. J. A. Sloane , Simon Plouffe, Robert G. Wilson v, Mira Bernstein
| 2018-08-11T02:55:20 |
oeisdata/seq/A002/A002539.seq
|
873f6cf10dbccf5ad18b331f7591bb0c
|
A002540
|
Increasing gaps between prime-powers.
|
[
"1",
"5",
"13",
"19",
"32",
"53",
"89",
"139",
"199",
"293",
"887",
"1129",
"1331",
"5591",
"8467",
"9551",
"15683",
"19609",
"31397",
"155921",
"360653",
"370261",
"492113",
"1349533",
"1357201",
"2010733",
"4652353",
"17051707",
"20831323",
"47326693",
"122164747",
"189695659",
"191912783",
"387096133",
"436273009",
"1294268491"
] |
[
"nonn",
"nice"
] | 55 | 1 | 2 |
[
"A000961",
"A002386",
"A002540",
"A057820",
"A094158",
"A121493"
] |
[
"M1431",
"N0565"
] |
N. J. A. Sloane
| 2024-10-18T08:58:38 |
oeisdata/seq/A002/A002540.seq
|
3ae2c979deeea30fbbf3ed5712cdf844
|
A002541
|
a(n) = Sum_{k=1..n-1} floor((n-k)/k).
|
[
"0",
"1",
"2",
"4",
"5",
"8",
"9",
"12",
"14",
"17",
"18",
"23",
"24",
"27",
"30",
"34",
"35",
"40",
"41",
"46",
"49",
"52",
"53",
"60",
"62",
"65",
"68",
"73",
"74",
"81",
"82",
"87",
"90",
"93",
"96",
"104",
"105",
"108",
"111",
"118",
"119",
"126",
"127",
"132",
"137",
"140",
"141",
"150",
"152",
"157",
"160",
"165",
"166",
"173",
"176",
"183",
"186",
"189",
"190",
"201",
"202",
"205"
] |
[
"nonn",
"easy",
"nice"
] | 101 | 1 | 3 |
[
"A000005",
"A002541",
"A003238",
"A003988",
"A004199",
"A006218",
"A020639",
"A027749",
"A032741",
"A070776",
"A126656",
"A320224",
"A320225",
"A320226"
] |
[
"M0970",
"N0362"
] |
N. J. A. Sloane
| 2024-07-31T09:21:54 |
oeisdata/seq/A002/A002541.seq
|
9b9c969b1baa4886bd6285b38022d5c9
|
A002542
|
Number of two-valued complete Post functions of n variables.
|
[
"0",
"2",
"56",
"16256",
"1073709056",
"4611686016279904256",
"85070591730234615856620279821087277056",
"28948022309329048855892746252171976963147354982949671778132708698262398304256"
] |
[
"nonn"
] | 37 | 1 | 2 |
[
"A002542",
"A002543"
] |
[
"M2174",
"N0869"
] |
N. J. A. Sloane
| 2022-09-08T08:44:31 |
oeisdata/seq/A002/A002542.seq
|
374768420a31d44ac34273b9da338f11
|
A002543
|
Complete Post functions of n variables.
|
[
"0",
"2",
"16",
"980",
"9332768"
] |
[
"nonn",
"more"
] | 30 | 1 | 2 |
[
"A002542",
"A002543",
"A002857"
] |
[
"M2098",
"N0830"
] |
N. J. A. Sloane
| 2023-10-16T23:47:32 |
oeisdata/seq/A002/A002543.seq
|
cffe2f4c10ac2cfbb18d9523bd3812dc
|
A002544
|
a(n) = binomial(2*n+1,n)*(n+1)^2.
|
[
"1",
"12",
"90",
"560",
"3150",
"16632",
"84084",
"411840",
"1969110",
"9237800",
"42678636",
"194699232",
"878850700",
"3931426800",
"17450721000",
"76938289920",
"337206098790",
"1470171918600",
"6379820115900",
"27569305764000",
"118685861314020",
"509191949220240",
"2177742427450200",
"9287309860732800"
] |
[
"nonn",
"easy",
"nice"
] | 125 | 0 | 2 |
[
"A002457",
"A002544",
"A002674",
"A002736",
"A085373",
"A202543",
"A331430"
] |
[
"M4855",
"N2075"
] |
N. J. A. Sloane, Simon Plouffe
| 2022-10-18T19:10:58 |
oeisdata/seq/A002/A002544.seq
|
a7b38ee9037ebe97ffe43e36c441e6c7
|
A002545
|
Numerator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
|
[
"1",
"3",
"7",
"15",
"29",
"469",
"29531",
"1303",
"16103",
"190553",
"128977",
"9061",
"30946717",
"39646461",
"58433327",
"344499373",
"784809203",
"169704792667",
"665690574539",
"5667696059",
"337284946763",
"7964656853269",
"46951444927823",
"284451446729",
"1597747168263479",
"816088653136373"
] |
[
"nonn",
"frac"
] | 42 | 3 | 2 |
[
"A002545",
"A002546"
] |
[
"M2651",
"N1058"
] |
N. J. A. Sloane
| 2018-11-17T20:45:11 |
oeisdata/seq/A002/A002545.seq
|
bace7b883cdec811576e9d84b94063aa
|
A002546
|
Denominator of Sum_{i+j+k=n; i,j,k > 0} 1/(i*j*k).
|
[
"1",
"2",
"4",
"8",
"15",
"240",
"15120",
"672",
"8400",
"100800",
"69300",
"4950",
"17199000",
"22422400",
"33633600",
"201801600",
"467812800",
"102918816000",
"410646075840",
"3555377280",
"215100325440",
"5162407810560",
"30920671782000",
"190281057120",
"1085315579548200",
"562756226432400",
"22969641895200"
] |
[
"nonn",
"frac"
] | 29 | 1 | 2 |
[
"A002545",
"A002546"
] |
[
"M1110",
"N0424"
] |
N. J. A. Sloane
| 2018-11-17T21:31:11 |
oeisdata/seq/A002/A002546.seq
|
72871e792f283202737fc72071984deb
|
A002547
|
Numerator of the n-th harmonic number H(n) divided by (n+1); a(n) = A001008(n) / ((n+1)*A002805(n)).
|
[
"1",
"1",
"11",
"5",
"137",
"7",
"363",
"761",
"7129",
"671",
"83711",
"6617",
"1145993",
"1171733",
"1195757",
"143327",
"42142223",
"751279",
"275295799",
"55835135",
"18858053",
"830139",
"444316699",
"269564591",
"34052522467",
"34395742267",
"312536252003",
"10876020307",
"9227046511387",
"300151059037"
] |
[
"nonn",
"frac"
] | 87 | 1 | 3 |
[
"A001008",
"A002547",
"A002548",
"A002805"
] |
[
"M4765",
"N2036"
] |
N. J. A. Sloane
| 2025-06-02T13:25:48 |
oeisdata/seq/A002/A002547.seq
|
16712dfa8785aeccbca84322a6169b8c
|
A002548
|
Denominators of coefficients for numerical differentiation.
|
[
"1",
"1",
"12",
"6",
"180",
"10",
"560",
"1260",
"12600",
"1260",
"166320",
"13860",
"2522520",
"2702700",
"2882880",
"360360",
"110270160",
"2042040",
"775975200",
"162954792",
"56904848",
"2586584",
"1427794368",
"892371480",
"116008292400",
"120470149800",
"1124388064800"
] |
[
"nonn",
"frac"
] | 57 | 2 | 3 |
[
"A002547",
"A002548",
"A093762"
] |
[
"M4822",
"N2063"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002548.seq
|
7ec594ac727e01304bdeb3ede4bf8fc7
|
A002549
|
Numerators of coefficients of log(1+x)/sqrt(1+x).
|
[
"1",
"1",
"23",
"11",
"563",
"1627",
"88069",
"1423",
"1593269",
"7759469",
"31730711",
"46522243",
"3788707301",
"2888008157",
"340028535787",
"41743955887",
"10823198495797",
"2738032559863",
"409741429887649",
"25876414060339",
"17141894231615609"
] |
[
"nonn",
"frac"
] | 34 | 1 | 3 |
[
"A002428",
"A002549",
"A002550"
] |
[
"M5128",
"N2223"
] |
N. J. A. Sloane
| 2015-07-18T13:15:38 |
oeisdata/seq/A002/A002549.seq
|
fb7741b39a67d712de7904e00ffe6470
|
A002550
|
Denominators of coefficients of log(1+x)/sqrt(1+x).
|
[
"1",
"1",
"24",
"12",
"640",
"1920",
"107520",
"1792",
"2064384",
"10321920",
"43253760",
"64880640",
"5398069248",
"4198498304",
"503819796480",
"62977474560",
"16610786017280",
"4271344975872",
"649244436332544",
"41618233098240",
"27967452642017280"
] |
[
"nonn",
"frac"
] | 24 | 1 | 3 |
[
"A002549",
"A002550"
] |
[
"M5139",
"N2229"
] |
N. J. A. Sloane
| 2023-10-16T23:49:00 |
oeisdata/seq/A002/A002550.seq
|
55715f16e4a19b1c53b911dfe90f1344
|
A002551
|
Numerators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).
|
[
"0",
"1",
"-3",
"43",
"-95",
"12139",
"-25333",
"81227",
"-498233",
"121563469",
"-246183839",
"32808117961",
"-13219717433",
"3226018634857",
"-8835766426243",
"390013167515221",
"-260612031438103",
"36514732926665911",
"-73104960503491573",
"9265088297941326563",
"-389193444786378151123"
] |
[
"sign",
"frac"
] | 29 | 1 | 3 |
[
"A002551",
"A002552"
] |
[
"M3151",
"N1276"
] |
N. J. A. Sloane
| 2023-10-16T23:50:02 |
oeisdata/seq/A002/A002551.seq
|
c4d191237f11d0018980312ef4ad9a2a
|
A002552
|
Denominators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).
|
[
"1",
"1",
"2",
"24",
"48",
"5760",
"11520",
"35840",
"215040",
"51609600",
"103219200",
"13624934400",
"5449973760",
"1322526965760",
"3606891724800",
"158703235891200",
"105802157260800",
"14800210341396480",
"29600420682792960",
"3749386619820441600"
] |
[
"nonn",
"frac"
] | 23 | 1 | 3 |
[
"A002551",
"A002552"
] |
[
"M2133",
"N0846"
] |
N. J. A. Sloane
| 2023-10-16T23:50:51 |
oeisdata/seq/A002/A002552.seq
|
55c1579697e964ced02fc1c43980b7a1
|
A002553
|
Coefficients for numerical differentiation.
|
[
"1",
"24",
"640",
"7168",
"294912",
"2883584",
"54525952",
"167772160",
"36507222016",
"326417514496",
"5772436045824",
"50577534877696",
"1759218604441600",
"15199648742375424",
"261208778387488768",
"2233785415175766016",
"101457092405402533888"
] |
[
"nonn"
] | 31 | 0 | 2 |
[
"A001818",
"A002553",
"A002555"
] |
[
"M5166",
"N2243"
] |
N. J. A. Sloane
| 2015-07-18T13:17:00 |
oeisdata/seq/A002/A002553.seq
|
56c3ee748b7814d37274b4c2c56b3989
|
A002554
|
Numerators of coefficients for numerical differentiation.
|
[
"1",
"-5",
"259",
"-3229",
"117469",
"-7156487",
"2430898831",
"-60997921",
"141433003757",
"-25587296781661",
"51270597630767",
"-6791120985104747",
"3400039831130408821",
"-15317460638921852507",
"25789165074168004597399",
"-1550286106708510672406629",
"24823277118070193095631689"
] |
[
"sign",
"frac"
] | 41 | 1 | 2 |
[
"A001824",
"A002554",
"A002555"
] |
[
"M4034",
"N1676"
] |
N. J. A. Sloane
| 2023-10-15T09:27:53 |
oeisdata/seq/A002/A002554.seq
|
68f47418b93e16c55a5f368115022920
|
A002555
|
Denominators of coefficients for numerical differentiation.
|
[
"1",
"24",
"5760",
"322560",
"51609600",
"13624934400",
"19837904486400",
"2116043145216",
"20720294477955072",
"15747423803245854720",
"131978409017679544320",
"72852081777759108464640",
"151532330097738945606451200",
"2828603495157793651320422400",
"19687080326298243813190139904000"
] |
[
"nonn",
"frac"
] | 32 | 1 | 2 |
[
"A001824",
"A002554",
"A002555"
] |
[
"M5177",
"N2249"
] |
N. J. A. Sloane
| 2019-02-27T14:03:01 |
oeisdata/seq/A002/A002555.seq
|
e0888601b0cdb2e65aa16bda714b66f5
|
A002556
|
Odd squarefree numbers with an odd number of prime factors that have no prime factors greater than 31.
|
[
"3",
"5",
"7",
"11",
"13",
"17",
"19",
"23",
"29",
"31",
"105",
"165",
"195",
"231",
"255",
"273",
"285",
"345",
"357",
"385",
"399",
"429",
"435",
"455",
"465",
"483",
"561",
"595",
"609",
"627",
"651",
"663",
"665",
"715",
"741",
"759",
"805",
"897",
"935",
"957",
"969",
"1001",
"1015",
"1023",
"1045",
"1085",
"1105",
"1131",
"1173",
"1209",
"1235",
"1265"
] |
[
"nonn",
"fini",
"full"
] | 40 | 1 | 1 |
[
"A002556",
"A002557",
"A056912",
"A067019"
] |
[
"M2412",
"N0955"
] |
N. J. A. Sloane, Oct 07 2015
| 2022-09-08T08:44:31 |
oeisdata/seq/A002/A002556.seq
|
590c3d24350366429eb21c86ed62ae47
|
A002557
|
Odd squarefree numbers with an even number of prime factors that have no prime factors greater than 31.
|
[
"1",
"15",
"21",
"33",
"35",
"39",
"51",
"55",
"57",
"65",
"69",
"77",
"85",
"87",
"91",
"93",
"95",
"115",
"119",
"133",
"143",
"145",
"155",
"161",
"187",
"203",
"209",
"217",
"221",
"247",
"253",
"299",
"319",
"323",
"341",
"377",
"391",
"403",
"437",
"493",
"527",
"551",
"589",
"667",
"713",
"899",
"1155",
"1365",
"1785",
"1995",
"2145",
"2415",
"2805",
"3003"
] |
[
"nonn",
"full",
"fini"
] | 43 | 1 | 2 |
[
"A002556",
"A002557",
"A046337",
"A056913",
"A059897"
] |
[
"M4959",
"N2126"
] |
N. J. A. Sloane
| 2025-05-03T15:28:28 |
oeisdata/seq/A002/A002557.seq
|
32b956323178d8711e825784d2919f61
|
A002558
|
Coefficients of a Dirichlet series.
|
[
"1",
"-1",
"4",
"-3",
"-4",
"-4",
"8",
"11",
"4",
"4",
"12",
"-48",
"-12",
"-8",
"-16",
"25",
"-16",
"-4",
"20",
"0",
"32",
"-12",
"24",
"248",
"-4",
"12",
"4",
"-208",
"-28",
"16",
"32",
"-41",
"48",
"16",
"-32",
"-400",
"-36",
"-20",
"-48",
"88",
"-40",
"-32",
"44",
"-544",
"-16",
"-24",
"48",
"732",
"8",
"4"
] |
[
"sign"
] | 21 | 1 | 3 | null |
[
"M3211",
"N1300"
] |
N. J. A. Sloane
| 2023-10-16T23:51:59 |
oeisdata/seq/A002/A002558.seq
|
7a6abcc1c917b7b324203a2d3742cc15
|
A002559
|
Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.
|
[
"1",
"2",
"5",
"13",
"29",
"34",
"89",
"169",
"194",
"233",
"433",
"610",
"985",
"1325",
"1597",
"2897",
"4181",
"5741",
"6466",
"7561",
"9077",
"10946",
"14701",
"28657",
"33461",
"37666",
"43261",
"51641",
"62210",
"75025",
"96557",
"135137",
"195025",
"196418",
"294685",
"426389",
"499393",
"514229",
"646018",
"925765",
"1136689",
"1278818"
] |
[
"nonn",
"nice",
"easy"
] | 218 | 1 | 2 |
[
"A000045",
"A001653",
"A002559",
"A004280",
"A158381",
"A158384",
"A178444",
"A256395"
] |
[
"M1432",
"N0566"
] |
N. J. A. Sloane and J. H. Conway
| 2025-01-05T19:51:32 |
oeisdata/seq/A002/A002559.seq
|
0941322a31ac4c7075ba5d74a306caf2
|
A002560
|
Number of polygonal graphs.
|
[
"1",
"1",
"4",
"2",
"7",
"5",
"15",
"6",
"37",
"13",
"36",
"32",
"37",
"34",
"73",
"58",
"183",
"150",
"262",
"186",
"1009",
"420",
"707",
"703",
"760",
"1180",
"4639"
] |
[
"nonn",
"more"
] | 28 | 4 | 3 | null |
[
"M3203",
"N1295"
] |
N. J. A. Sloane
| 2023-10-16T23:52:38 |
oeisdata/seq/A002/A002560.seq
|
a0b6b9b9b3b5ec2a359bdaa10f526c48
|
A002561
|
a(n) = n^5 + 1.
|
[
"0",
"1",
"2",
"33",
"244",
"1025",
"3126",
"7777",
"16808",
"32769",
"59050",
"100001",
"161052",
"248833",
"371294",
"537825",
"759376",
"1048577",
"1419858",
"1889569",
"2476100",
"3200001",
"4084102",
"5153633",
"6436344",
"7962625",
"9765626",
"11881377",
"14348908",
"17210369",
"20511150",
"24300001",
"28629152",
"33554433"
] |
[
"nonn",
"easy"
] | 64 | -1 | 3 |
[
"A000584",
"A002561"
] | null |
N. J. A. Sloane
| 2024-02-26T20:11:20 |
oeisdata/seq/A002/A002561.seq
|
476af1a52bf465a1cfe7643313e99f8c
|
A002562
|
Number of ways of placing n nonattacking queens on n X n board (symmetric solutions count only once).
|
[
"1",
"0",
"0",
"1",
"2",
"1",
"6",
"12",
"46",
"92",
"341",
"1787",
"9233",
"45752",
"285053",
"1846955",
"11977939",
"83263591",
"621012754",
"4878666808",
"39333324973",
"336376244042",
"3029242658210",
"28439272956934",
"275986683743434",
"2789712466510289",
"29363495934315694"
] |
[
"nonn",
"nice"
] | 78 | 1 | 5 |
[
"A000170",
"A002562",
"A032522",
"A033148"
] |
[
"M0180",
"N0068"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002562.seq
|
d5461d61c4fb72664a7df25ee0ceeb59
|
A002563
|
Number of nonisomorphic solutions to minimal dominating set on queens' graph Q(n).
|
[
"1",
"1",
"1",
"3",
"37",
"1",
"13",
"638",
"21",
"1",
"1",
"1",
"41",
"588",
"25872",
"43",
"22",
"2"
] |
[
"nonn",
"more"
] | 25 | 1 | 4 |
[
"A002563",
"A002564",
"A075458"
] |
[
"M3142",
"N1273"
] |
N. J. A. Sloane
| 2021-09-02T14:08:51 |
oeisdata/seq/A002/A002563.seq
|
47b98c85ef5b7be3464e846e10d38319
|
A002564
|
Number of different ways one can attack all squares on an n X n chessboard using the minimum number of queens.
|
[
"1",
"4",
"1",
"12",
"186",
"4",
"86",
"4860",
"114",
"8",
"2",
"8",
"288",
"4632",
"205832",
"2968",
"124",
"16",
"84"
] |
[
"nonn",
"more"
] | 102 | 1 | 2 |
[
"A002563",
"A002564",
"A002568",
"A075458",
"A182333",
"A286883"
] |
[
"M3199",
"N1293"
] |
N. J. A. Sloane
| 2025-05-09T23:11:19 |
oeisdata/seq/A002/A002564.seq
|
9200c6dfddcdf49d55e15464a112a688
|
A002565
|
Number of non-isomorphic ways to attack all squares on an n X n chessboard using the smallest possible number of queens with each queen attacking at least one other.
|
[
"0",
"2",
"5",
"3",
"15",
"150",
"5",
"56",
"3",
"39",
"681"
] |
[
"nonn",
"more"
] | 29 | 1 | 2 |
[
"A002565",
"A002566"
] |
[
"M1313",
"N0502"
] |
N. J. A. Sloane
| 2017-12-25T11:58:13 |
oeisdata/seq/A002/A002565.seq
|
df727107221062e07b8d7dd469485778
|
A002566
|
Number of ways to attack all squares on an n X n chessboard using the smallest possible number of queens with each queen attacking at least one other.
|
[
"0",
"6",
"20",
"12",
"70",
"960",
"22",
"352",
"10",
"216",
"4814",
"72"
] |
[
"nonn",
"hard",
"more"
] | 42 | 1 | 2 |
[
"A002565",
"A002566"
] |
[
"M4130",
"N1713"
] |
N. J. A. Sloane
| 2025-06-12T21:38:31 |
oeisdata/seq/A002/A002566.seq
|
fefb7dd0a23f20f417f2ae5221f1f12b
|
A002567
|
Number of nonisomorphic solutions to minimal independent dominating set on queens' graph Q(n).
|
[
"1",
"1",
"1",
"2",
"2",
"17",
"1",
"91",
"16",
"1",
"1",
"105",
"4",
"55",
"1314",
"16",
"2",
"28"
] |
[
"nonn",
"more"
] | 24 | 1 | 4 |
[
"A002567",
"A002568",
"A075324"
] |
[
"M0389",
"N0147"
] |
N. J. A. Sloane
| 2023-10-16T23:53:35 |
oeisdata/seq/A002/A002567.seq
|
a70601a9fef4f113c155ccdaa977a85f
|
A002568
|
Number of different ways one can attack all squares on an n X n chessboard with the smallest number of non-attacking queens needed.
|
[
"1",
"4",
"1",
"16",
"16",
"120",
"8",
"728",
"92",
"8",
"2",
"840",
"24",
"436",
"10188",
"128",
"12",
"224",
"8424",
"312",
"72",
"192",
"8784",
"368",
"56",
"224",
"14500",
"280",
"10880",
"240"
] |
[
"nonn",
"hard",
"more"
] | 38 | 1 | 2 |
[
"A002564",
"A002567",
"A002568",
"A103315",
"A122749"
] |
[
"M3200",
"N1294"
] |
N. J. A. Sloane
| 2024-10-04T10:04:12 |
oeisdata/seq/A002/A002568.seq
|
3385530a1110c3518c24e103d9a87822
|
A002569
|
Max_{k=0..n} { Number of partitions of n into exactly k parts }.
|
[
"1",
"1",
"1",
"1",
"2",
"2",
"3",
"4",
"5",
"7",
"9",
"11",
"15",
"18",
"23",
"30",
"37",
"47",
"58",
"71",
"90",
"110",
"136",
"164",
"201",
"248",
"300",
"364",
"436",
"525",
"638",
"764",
"919",
"1090",
"1297",
"1549",
"1845",
"2194",
"2592",
"3060",
"3590",
"4242",
"5013",
"5888",
"6912",
"8070",
"9418",
"11004",
"12866",
"15021",
"17475",
"20298",
"23501",
"27169"
] |
[
"nonn"
] | 68 | 0 | 5 |
[
"A000041",
"A002569",
"A008284",
"A026819",
"A046155"
] |
[
"M0283",
"N0101"
] |
N. J. A. Sloane
| 2017-10-22T22:08:25 |
oeisdata/seq/A002/A002569.seq
|
493a7e46a7dc33d36078870c47cffae7
|
A002570
|
From a definite integral.
|
[
"1",
"1",
"6",
"11",
"36",
"85",
"235",
"600",
"1590",
"4140",
"10866",
"28416",
"74431",
"194821",
"510096",
"1335395",
"3496170",
"9153025",
"23963005",
"62735880",
"164244756",
"429998256",
"1125750156",
"2947252056",
"7716006181",
"20200766305",
"52886292930",
"138458112275",
"362488044120"
] |
[
"nonn"
] | 43 | 1 | 3 | null |
[
"M4090",
"N1698"
] |
N. J. A. Sloane
| 2024-07-31T04:10:07 |
oeisdata/seq/A002/A002570.seq
|
18fa109671063feb6c239b05079e3be2
|
A002571
|
From a definite integral.
|
[
"1",
"5",
"10",
"30",
"74",
"199",
"515",
"1355",
"3540",
"9276",
"24276",
"63565",
"166405",
"435665",
"1140574",
"2986074",
"7817630",
"20466835",
"53582855",
"140281751",
"367262376",
"961505400",
"2517253800",
"6590256025",
"17253514249",
"45170286749",
"118257345970"
] |
[
"nonn"
] | 58 | 1 | 2 |
[
"A000045",
"A000204",
"A001654",
"A002571",
"A006206",
"A064831",
"A077916",
"A180662"
] |
[
"M3802",
"N1553"
] |
N. J. A. Sloane
| 2023-08-05T13:09:26 |
oeisdata/seq/A002/A002571.seq
|
3e1f83e8e2d63a73a0a39a5c9541038c
|
A002572
|
Number of partitions of 1 into n powers of 1/2; or (according to one definition of "binary") the number of binary rooted trees.
|
[
"1",
"1",
"1",
"2",
"3",
"5",
"9",
"16",
"28",
"50",
"89",
"159",
"285",
"510",
"914",
"1639",
"2938",
"5269",
"9451",
"16952",
"30410",
"54555",
"97871",
"175586",
"315016",
"565168",
"1013976",
"1819198",
"3263875",
"5855833",
"10506175",
"18849555",
"33818794",
"60675786",
"108861148",
"195312750",
"350419594",
"628704034",
"1127987211",
"2023774607",
"3630948907"
] |
[
"core",
"nonn",
"nice",
"easy"
] | 127 | 1 | 4 |
[
"A002572",
"A002573",
"A002574",
"A007178",
"A047913",
"A049284",
"A049285",
"A102375",
"A294775"
] |
[
"M0710",
"N0261"
] |
N. J. A. Sloane
| 2025-07-01T08:53:47 |
oeisdata/seq/A002/A002572.seq
|
cfdad48fce16e966e9ebced1ace249e4
|
A002573
|
Restricted partitions.
|
[
"0",
"1",
"1",
"2",
"4",
"7",
"12",
"22",
"39",
"70",
"126",
"225",
"404",
"725",
"1299",
"2331",
"4182",
"7501",
"13458",
"24145",
"43316",
"77715",
"139430",
"250152",
"448808",
"805222",
"1444677",
"2591958",
"4650342",
"8343380",
"14969239",
"26856992",
"48185362",
"86451602",
"155106844",
"278284440",
"499283177",
"895787396",
"1607174300",
"2883507098"
] |
[
"nonn",
"easy"
] | 32 | 1 | 4 |
[
"A002572",
"A002573",
"A002574",
"A047913",
"A049284",
"A049285",
"A176431"
] |
[
"M1062",
"N0399"
] |
N. J. A. Sloane
| 2021-12-20T20:22:22 |
oeisdata/seq/A002/A002573.seq
|
13680bf5a9e9c06eb1a9b7a540de4ede
|
A002574
|
Restricted partitions.
|
[
"0",
"0",
"1",
"1",
"2",
"4",
"7",
"13",
"24",
"42",
"76",
"137",
"245",
"441",
"792",
"1420",
"2550",
"4576",
"8209",
"14732",
"26433",
"47424",
"85092",
"152670",
"273914",
"491453",
"881744",
"1581985",
"2838333",
"5092398",
"9136528",
"16392311",
"29410243",
"52766343",
"94670652",
"169853138",
"304741614",
"546751437",
"980952673",
"1759973660"
] |
[
"nonn",
"easy"
] | 32 | 1 | 5 |
[
"A002572",
"A002573",
"A002574",
"A047913",
"A049284",
"A049285"
] |
[
"M1070",
"N0404"
] |
N. J. A. Sloane
| 2023-10-17T05:26:00 |
oeisdata/seq/A002/A002574.seq
|
8455a00139af3f4ffec0fe0847c40440
|
A002575
|
Coefficients of Bell's formula for making change.
|
[
"1",
"3",
"9",
"35",
"201",
"1827",
"27337",
"692003",
"30251721",
"2320518947",
"316359580361",
"77477180493603",
"34394869942983369",
"27893897106768940835",
"41603705003444309596873",
"114788185359199234852802339",
"588880400923055731115178072777"
] |
[
"nonn"
] | 25 | 2 | 2 |
[
"A002575",
"A002576",
"A002577",
"A125792",
"A262554"
] |
[
"M2820",
"N1134"
] |
N. J. A. Sloane
| 2023-03-22T21:57:38 |
oeisdata/seq/A002/A002575.seq
|
e2b34dc9a58e07e5e5862d59a6cd5189
|
A002576
|
Coefficients of Bell's formula for making change.
|
[
"2",
"16",
"130",
"1424",
"23682",
"637328",
"28867714",
"2260015504",
"311718542466",
"76844461332880",
"34239915581996162",
"27825107366882974096",
"41547917209230771715202",
"114704977949192346233608592",
"588650824552337332645472468098"
] |
[
"nonn"
] | 19 | 3 | 1 |
[
"A002575",
"A002576",
"A002577",
"A262554"
] |
[
"M2091",
"N0826"
] |
N. J. A. Sloane
| 2023-10-16T23:58:10 |
oeisdata/seq/A002/A002576.seq
|
c2e1f79409fbc5da81c8b3db5d5247db
|
A002577
|
Number of partitions of 2^n into powers of 2.
|
[
"1",
"2",
"4",
"10",
"36",
"202",
"1828",
"27338",
"692004",
"30251722",
"2320518948",
"316359580362",
"77477180493604",
"34394869942983370",
"27893897106768940836",
"41603705003444309596874",
"114788185359199234852802340",
"588880400923055731115178072778",
"5642645813427132737155703265972004"
] |
[
"nonn",
"easy",
"nice"
] | 87 | 0 | 2 |
[
"A000079",
"A000123",
"A000290",
"A000447",
"A002575",
"A002576",
"A002577",
"A018818",
"A078121",
"A078125",
"A078537",
"A125790",
"A145513",
"A145515",
"A152977"
] |
[
"M1239",
"N0473"
] |
N. J. A. Sloane
| 2024-07-31T09:02:17 |
oeisdata/seq/A002/A002577.seq
|
61643426add5a6a88cca59c7a6c9f4ba
|
A002578
|
Number of integral points in a certain sequence of open quadrilaterals.
|
[
"0",
"0",
"1",
"3",
"6",
"9",
"13",
"18",
"24",
"31",
"39",
"47",
"56",
"66",
"77",
"89",
"102",
"115",
"129",
"144",
"160",
"177",
"195",
"213",
"232",
"252",
"273",
"295",
"318",
"341",
"365",
"390",
"416",
"443",
"471",
"499",
"528",
"558",
"589",
"621",
"654",
"687",
"721",
"756",
"792",
"829",
"867",
"905",
"944",
"984",
"1025",
"1067",
"1110"
] |
[
"nonn",
"easy"
] | 38 | 1 | 4 |
[
"A002578",
"A002579"
] |
[
"M2529",
"N0997"
] |
N. J. A. Sloane
| 2024-05-02T09:47:05 |
oeisdata/seq/A002/A002578.seq
|
833286773d405133f83b47036b3a398d
|
A002579
|
Number of integral points in a certain sequence of closed quadrilaterals.
|
[
"3",
"5",
"8",
"12",
"17",
"23",
"30",
"37",
"45",
"54",
"64",
"75",
"87",
"99",
"112",
"126",
"141",
"157",
"174",
"191",
"209",
"228",
"248",
"269",
"291",
"313",
"336",
"360",
"385",
"411",
"438",
"465",
"493",
"522",
"552",
"583",
"615",
"647",
"680",
"714",
"749",
"785",
"822",
"859",
"897",
"936",
"976",
"1017",
"1059",
"1101",
"1144"
] |
[
"nonn",
"easy"
] | 30 | 1 | 1 |
[
"A002578",
"A002579"
] |
[
"M2440",
"N0967"
] |
N. J. A. Sloane
| 2024-05-02T04:31:59 |
oeisdata/seq/A002/A002579.seq
|
b5c0cd5334e1cdc7dc6aebfe8e0a4eb4
|
A002580
|
Decimal expansion of cube root of 2.
|
[
"1",
"2",
"5",
"9",
"9",
"2",
"1",
"0",
"4",
"9",
"8",
"9",
"4",
"8",
"7",
"3",
"1",
"6",
"4",
"7",
"6",
"7",
"2",
"1",
"0",
"6",
"0",
"7",
"2",
"7",
"8",
"2",
"2",
"8",
"3",
"5",
"0",
"5",
"7",
"0",
"2",
"5",
"1",
"4",
"6",
"4",
"7",
"0",
"1",
"5",
"0",
"7",
"9",
"8",
"0",
"0",
"8",
"1",
"9",
"7",
"5",
"1",
"1",
"2",
"1",
"5",
"5",
"2",
"9",
"9",
"6",
"7",
"6",
"5",
"1",
"3",
"9",
"5",
"9",
"4",
"8",
"3",
"7",
"2",
"9",
"3",
"9",
"6",
"5",
"6",
"2",
"4",
"3",
"6",
"2",
"5",
"5",
"0",
"9",
"4",
"1",
"5",
"4",
"3",
"1",
"0",
"2",
"5"
] |
[
"nonn",
"easy",
"cons"
] | 115 | 1 | 2 |
[
"A002580",
"A002581",
"A002945",
"A005480",
"A005481",
"A005482",
"A005486",
"A010581",
"A010582",
"A092039",
"A092041",
"A139340",
"A246644",
"A253583",
"A270714"
] |
[
"M1354",
"N0521"
] |
N. J. A. Sloane
| 2025-03-16T08:17:26 |
oeisdata/seq/A002/A002580.seq
|
b097f85b54763636d27607366f0db794
|
A002581
|
Decimal expansion of cube root of 3.
|
[
"1",
"4",
"4",
"2",
"2",
"4",
"9",
"5",
"7",
"0",
"3",
"0",
"7",
"4",
"0",
"8",
"3",
"8",
"2",
"3",
"2",
"1",
"6",
"3",
"8",
"3",
"1",
"0",
"7",
"8",
"0",
"1",
"0",
"9",
"5",
"8",
"8",
"3",
"9",
"1",
"8",
"6",
"9",
"2",
"5",
"3",
"4",
"9",
"9",
"3",
"5",
"0",
"5",
"7",
"7",
"5",
"4",
"6",
"4",
"1",
"6",
"1",
"9",
"4",
"5",
"4",
"1",
"6",
"8",
"7",
"5",
"9",
"6",
"8",
"2",
"9",
"9",
"9",
"7",
"3",
"3",
"9",
"8",
"5",
"4",
"7",
"5",
"5",
"4",
"7",
"9",
"7",
"0",
"5",
"6",
"4",
"5",
"2",
"5",
"6",
"6",
"8",
"6",
"8",
"3",
"5",
"0",
"8"
] |
[
"nonn",
"cons"
] | 64 | 1 | 2 |
[
"A002581",
"A002946"
] |
[
"M3220",
"N1304"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002581.seq
|
67c113dcaf596f29353a68f1194db28b
|
A002582
|
Largest prime factor of n! - 1.
|
[
"1",
"5",
"23",
"17",
"719",
"5039",
"1753",
"2999",
"125131",
"7853",
"479001599",
"3593203",
"87178291199",
"1510259",
"6880233439",
"256443711677",
"478749547",
"78143369",
"19499250680671",
"4826713612027",
"170006681813",
"498390560021687969",
"991459181683",
"114776274341482621993"
] |
[
"nonn",
"nice"
] | 51 | 2 | 2 |
[
"A002582",
"A002583",
"A033312",
"A054415",
"A056110"
] |
[
"M3925",
"N1613"
] |
N. J. A. Sloane
| 2022-09-08T08:44:31 |
oeisdata/seq/A002/A002582.seq
|
fad84370187b97b3054e5fb634abdef4
|
A002583
|
Largest prime factor of n! + 1.
|
[
"2",
"2",
"3",
"7",
"5",
"11",
"103",
"71",
"661",
"269",
"329891",
"39916801",
"2834329",
"75024347",
"3790360487",
"46271341",
"1059511",
"1000357",
"123610951",
"1713311273363831",
"117876683047",
"2703875815783",
"93799610095769647",
"148139754736864591",
"765041185860961084291",
"38681321803817920159601"
] |
[
"nonn",
"nice"
] | 58 | 0 | 1 |
[
"A002582",
"A002583",
"A002981",
"A038507",
"A051301",
"A056111",
"A096225"
] |
[
"M0294",
"N0312"
] |
N. J. A. Sloane
| 2022-09-08T08:44:31 |
oeisdata/seq/A002/A002583.seq
|
ced5172fdc4f1976266231c2e4948def
|
A002584
|
Largest prime factor of product of first n primes - 1, or 1 if no such prime exists.
|
[
"1",
"5",
"29",
"19",
"2309",
"30029",
"8369",
"929",
"46027",
"81894851",
"876817",
"38669",
"304250263527209",
"92608862041",
"59799107",
"1143707681",
"69664915493",
"1146665184811",
"17975352936245519",
"2140320249725509"
] |
[
"nonn",
"nice"
] | 55 | 1 | 2 |
[
"A002110",
"A002584",
"A002585",
"A006530",
"A057588"
] |
[
"M3952",
"N1628"
] |
N. J. A. Sloane
| 2020-02-13T11:57:10 |
oeisdata/seq/A002/A002584.seq
|
4fcdc0cfc08cda408f8866cb496bd6eb
|
A002585
|
Largest prime factor of 1 + (product of first n primes).
|
[
"3",
"7",
"31",
"211",
"2311",
"509",
"277",
"27953",
"703763",
"34231",
"200560490131",
"676421",
"11072701",
"78339888213593",
"13808181181",
"18564761860301",
"19026377261",
"525956867082542470777",
"143581524529603",
"2892214489673",
"16156160491570418147806951",
"96888414202798247",
"1004988035964897329167431269"
] |
[
"nonn",
"nice"
] | 69 | 1 | 1 |
[
"A002110",
"A002584",
"A002585",
"A006530",
"A006862",
"A051342"
] |
[
"M2697",
"N1081"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002585.seq
|
07990a743f7f635a7d7d5495bbc9563b
|
A002586
|
Smallest prime factor of 2^n + 1.
|
[
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"257",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"65537",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"97",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"641",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"257",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"193",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"257",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"274177",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"97",
"3",
"5",
"3",
"17",
"3",
"5",
"3",
"65537",
"3",
"5",
"3",
"17",
"3",
"5"
] |
[
"nonn",
"nice"
] | 78 | 1 | 1 |
[
"A000215",
"A001269",
"A002586",
"A002587",
"A019434",
"A050922",
"A093179"
] |
[
"M2385",
"N0947"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A002/A002586.seq
|
29dc9af3804d10307ba2f6b90c994246
|
A002587
|
Largest prime factor of 2^n + 1.
|
[
"2",
"3",
"5",
"3",
"17",
"11",
"13",
"43",
"257",
"19",
"41",
"683",
"241",
"2731",
"113",
"331",
"65537",
"43691",
"109",
"174763",
"61681",
"5419",
"2113",
"2796203",
"673",
"4051",
"1613",
"87211",
"15790321",
"3033169",
"1321",
"715827883",
"6700417",
"20857",
"26317",
"86171",
"38737",
"25781083",
"525313"
] |
[
"nonn"
] | 114 | 0 | 1 |
[
"A000051",
"A002586",
"A002587",
"A006530",
"A274903"
] |
[
"M2386",
"N0948"
] |
N. J. A. Sloane
| 2025-07-02T16:01:54 |
oeisdata/seq/A002/A002587.seq
|
9c8ccb09dce15ca5f22568d80a2b74eb
|
A002588
|
a(n) = largest noncomposite factor of 2^(2n+1) - 1.
|
[
"1",
"7",
"31",
"127",
"73",
"89",
"8191",
"151",
"131071",
"524287",
"337",
"178481",
"1801",
"262657",
"2089",
"2147483647",
"599479",
"122921",
"616318177",
"121369",
"164511353",
"2099863",
"23311",
"13264529",
"4432676798593",
"131071",
"20394401",
"201961",
"1212847",
"3203431780337"
] |
[
"nonn"
] | 55 | 0 | 2 |
[
"A002184",
"A002588",
"A005420",
"A147590"
] |
[
"M4401",
"N1856"
] |
N. J. A. Sloane
| 2022-09-08T08:44:31 |
oeisdata/seq/A002/A002588.seq
|
6755ee2b42efe4b671377d4c14ac4938
|
A002589
|
Largest primitive factor of 2^(2n+1) + 1.
|
[
"3",
"1",
"11",
"43",
"19",
"683",
"2731",
"331",
"43691",
"174763",
"5419",
"2796203",
"4051",
"87211",
"3033169",
"715827883",
"20857",
"86171",
"25781083",
"22366891",
"8831418697",
"2932031007403",
"18837001",
"165768537521",
"4363953127297",
"6529",
"28059810762433",
"48912491",
"160465489"
] |
[
"nonn"
] | 44 | 0 | 1 | null |
[
"M2234",
"N0886"
] |
N. J. A. Sloane
| 2025-02-25T23:22:13 |
oeisdata/seq/A002/A002589.seq
|
19cd2f37ba17037321ea9ef0b4f683c7
|
A002590
|
Largest prime factor of 16^n + 1.
|
[
"2",
"17",
"257",
"241",
"65537",
"61681",
"673",
"15790321",
"6700417",
"38737",
"4278255361",
"2931542417",
"22253377",
"308761441",
"54410972897",
"4562284561",
"67280421310721",
"2879347902817",
"487824887233",
"24517014940753",
"44479210368001",
"88959882481"
] |
[
"nonn"
] | 71 | 0 | 1 | null |
[
"M5046",
"N2180"
] |
N. J. A. Sloane
| 2025-03-15T13:49:44 |
oeisdata/seq/A002/A002590.seq
|
85c28cda9ec8836392e27fcdd510f3cd
|
A002591
|
Largest prime factor of 3^(2n+1) - 1.
|
[
"2",
"13",
"11",
"1093",
"757",
"3851",
"797161",
"4561",
"34511",
"363889",
"368089",
"1001523179",
"391151",
"8209",
"20381027",
"4404047",
"2413941289",
"2664097031",
"17189128703",
"797161",
"86950696619",
"380808546861411923",
"927001",
"96656723",
"131713",
"99810171997"
] |
[
"nonn"
] | 47 | 0 | 1 |
[
"A002591",
"A057958",
"A059885",
"A074477",
"A085028",
"A133801",
"A235366",
"A274909"
] |
[
"M4886",
"N2095"
] |
N. J. A. Sloane
| 2022-10-19T09:16:24 |
oeisdata/seq/A002/A002591.seq
|
e4dd6c4d4c550c3c4857c819ae659666
|
A002592
|
Largest prime factor of 9^n + 1.
|
[
"2",
"5",
"41",
"73",
"193",
"1181",
"6481",
"16493",
"21523361",
"530713",
"42521761",
"570461",
"769",
"4795973261",
"647753",
"47763361",
"926510094425921",
"1743831169",
"282429005041",
"25480398173",
"128653413121",
"109688713",
"56625998353",
"70601370627701"
] |
[
"nonn"
] | 46 | 0 | 1 |
[
"A002592",
"A006530",
"A062396",
"A274903",
"A274909"
] |
[
"M3994",
"N1655"
] |
N. J. A. Sloane
| 2022-09-08T08:44:31 |
oeisdata/seq/A002/A002592.seq
|
ad612af9be672e4c0f12cb9596901d47
|
A002593
|
a(n) = n^2*(2*n^2 - 1); also Sum_{k=0..n-1} (2k+1)^3.
|
[
"0",
"1",
"28",
"153",
"496",
"1225",
"2556",
"4753",
"8128",
"13041",
"19900",
"29161",
"41328",
"56953",
"76636",
"101025",
"130816",
"166753",
"209628",
"260281",
"319600",
"388521",
"468028",
"559153",
"662976",
"780625",
"913276",
"1062153",
"1228528",
"1413721",
"1619100",
"1846081"
] |
[
"nonn",
"nice",
"easy"
] | 162 | 0 | 3 |
[
"A000290",
"A000384",
"A000447",
"A000583",
"A002309",
"A002593",
"A253724",
"A253725",
"A260810"
] |
[
"M5199",
"N2262"
] |
N. J. A. Sloane
| 2025-05-24T16:20:06 |
oeisdata/seq/A002/A002593.seq
|
5e6d03f5d621bd709f213a1cffe98590
|
A002594
|
a(n) = n^2*(16*n^4-20*n^2+7)/3.
|
[
"1",
"244",
"3369",
"20176",
"79225",
"240276",
"611569",
"1370944",
"2790801",
"5266900",
"9351001",
"15787344",
"25552969",
"39901876",
"60413025",
"89042176",
"128177569",
"180699444",
"250043401",
"340267600",
"456123801",
"603132244",
"787660369",
"1017005376",
"1299480625",
"1644505876",
"2062701369",
"2565985744",
"3167677801",
"3882602100",
"4727198401",
"5719634944",
"6879925569",
"8230050676"
] |
[
"nonn",
"easy",
"changed"
] | 45 | 1 | 2 |
[
"A000539",
"A002594",
"A016757"
] |
[
"M5421",
"N2354"
] |
N. J. A. Sloane
| 2025-07-08T00:16:50 |
oeisdata/seq/A002/A002594.seq
|
41b2ccd53f591864ad614177bbc46cc7
|
A002595
|
Denominators of Taylor series expansion of arcsin(x). Also arises from arccos(x), arccsc(x), arcsec(x), arcsinh(x).
|
[
"1",
"6",
"40",
"112",
"1152",
"2816",
"13312",
"10240",
"557056",
"1245184",
"5505024",
"12058624",
"104857600",
"226492416",
"973078528",
"2080374784",
"23622320128",
"30064771072",
"635655159808",
"446676598784",
"11269994184704",
"23639499997184",
"6597069766656"
] |
[
"nonn",
"frac",
"nice",
"easy"
] | 47 | 0 | 2 |
[
"A000165",
"A001147",
"A002595",
"A055786",
"A143582",
"A162443",
"G1"
] |
[
"M4233",
"N1768"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002595.seq
|
b3d21f48d18ad7a33f2158a8ffecea43
|
A002596
|
Numerators in expansion of sqrt(1+x). Absolute values give numerators in expansion of sqrt(1-x).
|
[
"1",
"1",
"-1",
"1",
"-5",
"7",
"-21",
"33",
"-429",
"715",
"-2431",
"4199",
"-29393",
"52003",
"-185725",
"334305",
"-9694845",
"17678835",
"-64822395",
"119409675",
"-883631595",
"1641030105",
"-6116566755",
"11435320455",
"-171529806825",
"322476036831",
"-1215486600363",
"2295919134019"
] |
[
"easy",
"nice",
"frac",
"sign"
] | 97 | 0 | 5 |
[
"A000108",
"A000265",
"A001795",
"A001803",
"A002596",
"A046161",
"A098597",
"A161198",
"A161200",
"A161202"
] |
[
"M3768",
"N1538"
] |
N. J. A. Sloane
| 2025-02-16T08:32:26 |
oeisdata/seq/A002/A002596.seq
|
d9d6ddd57f9586413ae0e172a9b87649
|
A002597
|
Number of partitions into one kind of 1's, two kinds of 2's, and three kinds of 3's.
|
[
"1",
"1",
"3",
"6",
"9",
"15",
"25",
"34",
"51",
"73",
"97",
"132",
"178",
"226",
"294",
"376",
"466",
"582",
"722",
"872",
"1062",
"1282",
"1522",
"1812",
"2147",
"2507",
"2937",
"3422",
"3947",
"4557",
"5243",
"5978",
"6825",
"7763",
"8771",
"9912",
"11172",
"12516",
"14028",
"15680",
"17444",
"19404",
"21540",
"23808",
"26316",
"29028",
"31908"
] |
[
"nonn"
] | 44 | 0 | 3 |
[
"A002597",
"A064349"
] |
[
"M2533",
"N1000"
] |
N. J. A. Sloane
| 2023-06-25T15:52:42 |
oeisdata/seq/A002/A002597.seq
|
1f738f9c0c7a52262532ef5a467ab080
|
A002598
|
A generalized partition function.
|
[
"1",
"6",
"9",
"13",
"19",
"37",
"58",
"97",
"143",
"227",
"328",
"492",
"688",
"992",
"1364",
"1903",
"2551",
"3473",
"4586",
"6097",
"7911",
"10333",
"13226",
"16988",
"21454",
"27172",
"33938",
"42437",
"52423",
"64833",
"79354",
"97130",
"117824",
"142930",
"172018",
"206925",
"247179",
"295105",
"350154",
"415124",
"489414",
"576540"
] |
[
"nonn",
"easy"
] | 30 | 1 | 2 |
[
"A002598",
"A064349"
] |
[
"M4077",
"N1693"
] |
N. J. A. Sloane
| 2023-10-17T06:11:55 |
oeisdata/seq/A002/A002598.seq
|
ea364c67cf9136673d9080675a8948d1
|
A002599
|
A generalized partition function.
|
[
"1",
"6",
"15",
"19",
"24",
"42",
"73",
"127",
"208",
"337",
"528",
"827",
"1263",
"1902",
"2819",
"4133",
"5986",
"8578",
"12146",
"17057",
"23711",
"32708",
"44726",
"60713",
"81800",
"109468",
"145526",
"192288",
"252521",
"329792",
"428316",
"553478",
"711596",
"910563",
"1159790",
"1470798",
"1857286",
"2335838"
] |
[
"nonn"
] | 28 | 1 | 2 | null |
[
"M4106",
"N1703"
] |
N. J. A. Sloane
| 2023-10-17T07:41:20 |
oeisdata/seq/A002/A002599.seq
|
4565efb1f4a83b7396b23335b45e1f25
|
A002600
|
A generalized partition function.
|
[
"1",
"10",
"25",
"37",
"42",
"48",
"79",
"145",
"244",
"415",
"672",
"1100",
"1722",
"2727",
"4193",
"6428",
"9658",
"14478",
"21313",
"31304",
"45329",
"65311",
"93074",
"132026",
"185413",
"259242",
"359395",
"495839",
"679175",
"926064",
"1254360",
"1691753",
"2268267",
"3028345",
"4021954",
"5320139",
"7003154"
] |
[
"nonn"
] | 27 | 1 | 2 | null |
[
"M4686",
"N2002"
] |
N. J. A. Sloane
| 2023-10-17T08:18:51 |
oeisdata/seq/A002/A002600.seq
|
451e7169981d5f22a10c3dfdbe86c90a
|
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