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
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A380004
|
Decimal expansion of obtuse vertex angles, in radians, in a pentagonal hexecontahedron face.
|
[
"2",
"0",
"6",
"1",
"8",
"7",
"3",
"0",
"3",
"4",
"3",
"2",
"4",
"4",
"0",
"7",
"3",
"5",
"5",
"8",
"6",
"6",
"0",
"9",
"8",
"1",
"7",
"6",
"0",
"8",
"9",
"3",
"1",
"5",
"9",
"9",
"2",
"9",
"2",
"1",
"0",
"5",
"0",
"6",
"9",
"0",
"8",
"8",
"1",
"7",
"9",
"8",
"1",
"4",
"7",
"1",
"5",
"3",
"9",
"7",
"5",
"0",
"9",
"8",
"5",
"0",
"0",
"0",
"3",
"1",
"5",
"5",
"5",
"3",
"0",
"6",
"9",
"1",
"6",
"7",
"9",
"7",
"3",
"5",
"7",
"8",
"9",
"3",
"7",
"1"
] |
[
"nonn",
"cons",
"easy"
] | 7 | 1 | 1 |
[
"A379888",
"A379889",
"A379890",
"A379892",
"A380002",
"A380003",
"A380004"
] | null |
Paolo Xausa, Jan 12 2025
| 2025-01-13T04:14:29 |
oeisdata/seq/A380/A380004.seq
|
e1c2155fc5801a56755e6c2ba671193b
|
A380005
|
Decimal expansion of (7/3)*log(log(12)) - exp(gamma)*log(log(12))^2, where gamma is the Euler-Mascheroni constant (A001620).
|
[
"6",
"4",
"8",
"2",
"1",
"3",
"6",
"4",
"9",
"4",
"2",
"1",
"7",
"9",
"9",
"7",
"6",
"2",
"7",
"2",
"0",
"0",
"9",
"4",
"2",
"5",
"6",
"4",
"3",
"5",
"3",
"2",
"9",
"0",
"1",
"8",
"9",
"9",
"3",
"0",
"4",
"4",
"7",
"9",
"9",
"1",
"1",
"0",
"1",
"5",
"4",
"3",
"1",
"5",
"7",
"5",
"4",
"8",
"0",
"0",
"1",
"4",
"6",
"7",
"0",
"6",
"3",
"4",
"4",
"5",
"9",
"7",
"1",
"5",
"4",
"2",
"4",
"5",
"1",
"0",
"2",
"4",
"4",
"9",
"5",
"4",
"3",
"1",
"7",
"6"
] |
[
"nonn",
"cons",
"easy"
] | 12 | 0 | 1 |
[
"A000203",
"A001620",
"A016635",
"A058209",
"A073004",
"A380005"
] | null |
Paolo Xausa, Jan 14 2025
| 2025-01-15T07:06:03 |
oeisdata/seq/A380/A380005.seq
|
95fe2158c3fcacd810047ce06edaa950
|
A380006
|
Irregular triangle read by rows: T(n,k) is the number of non-isomorphic p-subgroups in the symmetric group S_n, where p is the k-th noncomposite divisor of n!.
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"4",
"1",
"1",
"4",
"1",
"1",
"1",
"7",
"2",
"1",
"1",
"7",
"2",
"1",
"1",
"1",
"34",
"2",
"1",
"1",
"1",
"34",
"7",
"1",
"1",
"1",
"61",
"7",
"2",
"1",
"1",
"61",
"7",
"2",
"1",
"1",
"1",
"308",
"12",
"2",
"1",
"1"
] |
[
"nonn",
"tabf",
"more"
] | 16 | 1 | 8 |
[
"A000142",
"A008578",
"A036234",
"A380006"
] | null |
Miles Englezou, Jan 07 2025
| 2025-03-06T09:09:40 |
oeisdata/seq/A380/A380006.seq
|
cd85336a9987c1535702ff8239a1fe20
|
A380007
|
Hexagonal numbers that are sphenic numbers.
|
[
"66",
"190",
"231",
"435",
"561",
"861",
"946",
"1653",
"2278",
"3655",
"4371",
"5151",
"5995",
"6441",
"8911",
"9453",
"10011",
"10585",
"13366",
"15051",
"15753",
"16471",
"20301",
"21115",
"22366",
"22791",
"23653",
"26335",
"32131",
"33153",
"39621",
"40186",
"45451",
"50403",
"54946",
"62481",
"69751",
"72771",
"77421",
"80601",
"83845",
"93961",
"99235",
"102831"
] |
[
"nonn"
] | 19 | 1 | 1 |
[
"A000384",
"A007304",
"A129521",
"A380007"
] | null |
Massimo Kofler, Jan 08 2025
| 2025-01-08T17:24:39 |
oeisdata/seq/A380/A380007.seq
|
d260899a1049c7dd52dc3911c80d7188
|
A380008
|
Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are odious numbers (A000069).
|
[
"0",
"2",
"4",
"6",
"16",
"18",
"20",
"22",
"128",
"130",
"132",
"134",
"144",
"146",
"148",
"150",
"256",
"258",
"260",
"262",
"272",
"274",
"276",
"278",
"384",
"386",
"388",
"390",
"400",
"402",
"404",
"406",
"2048",
"2050",
"2052",
"2054",
"2064",
"2066",
"2068",
"2070",
"2176",
"2178",
"2180",
"2182",
"2192",
"2194",
"2196",
"2198",
"2304",
"2306",
"2308",
"2310",
"2320",
"2322",
"2324",
"2326",
"2432",
"2434",
"2436",
"2438",
"2448",
"2450",
"2452",
"2454"
] |
[
"base",
"easy",
"nonn"
] | 48 | 0 | 2 |
[
"A000069",
"A001285",
"A010059",
"A380008",
"A380009"
] | null |
Luis Rato, Jan 08 2025
| 2025-02-25T14:58:53 |
oeisdata/seq/A380/A380008.seq
|
bc289a97f238eaaf51921b001af54a48
|
A380009
|
Numbers t whose binary expansion Sum 2^e_i has exponents e_i which are evil numbers (A001969).
|
[
"0",
"1",
"8",
"9",
"32",
"33",
"40",
"41",
"64",
"65",
"72",
"73",
"96",
"97",
"104",
"105",
"512",
"513",
"520",
"521",
"544",
"545",
"552",
"553",
"576",
"577",
"584",
"585",
"608",
"609",
"616",
"617",
"1024",
"1025",
"1032",
"1033",
"1056",
"1057",
"1064",
"1065",
"1088",
"1089",
"1096",
"1097",
"1120",
"1121",
"1128",
"1129",
"1536",
"1537",
"1544",
"1545",
"1568",
"1569",
"1576",
"1577",
"1600",
"1601",
"1608",
"1609",
"1632",
"1633",
"1640",
"1641"
] |
[
"base",
"easy",
"nonn"
] | 48 | 0 | 3 |
[
"A000069",
"A001285",
"A001969",
"A010059",
"A380008",
"A380009"
] | null |
Luis Rato, Jan 09 2025
| 2025-02-06T13:51:45 |
oeisdata/seq/A380/A380009.seq
|
0a2fbad26ffde98758c745aca0af7f41
|
A380010
|
Beginning with 7, least prime such that concatenation of the first n terms is prime.
|
[
"7",
"3",
"3",
"3",
"31",
"23",
"13",
"3",
"167",
"13",
"137",
"3",
"73",
"383",
"499",
"431",
"13",
"101",
"61",
"47",
"67",
"101",
"13",
"83",
"1237",
"107",
"97",
"467",
"499",
"677",
"1423",
"353",
"73",
"431",
"331",
"683",
"487",
"2141",
"3",
"1753",
"1787",
"31",
"443",
"139",
"653",
"1327",
"17",
"919",
"173",
"2851",
"137",
"547",
"557",
"5167",
"347",
"7867",
"839",
"19",
"179",
"19"
] |
[
"base",
"nonn"
] | 19 | 1 | 1 |
[
"A111382",
"A111383",
"A113584",
"A379354",
"A379355",
"A379761",
"A380010",
"A380011"
] | null |
J.W.L. (Jan) Eerland, Jan 09 2025
| 2025-01-18T14:46:40 |
oeisdata/seq/A380/A380010.seq
|
66d426ab7c4599888cbb6caf4ef77a48
|
A380011
|
Beginning with 7, least prime such that the reversal concatenation of the first n terms is prime.
|
[
"7",
"3",
"3",
"13",
"3",
"2",
"13",
"47",
"43",
"47",
"37",
"41",
"109",
"41",
"139",
"149",
"109",
"263",
"73",
"563",
"163",
"41",
"19",
"797",
"61",
"107",
"31",
"821",
"43",
"149",
"37",
"953",
"211",
"89",
"547",
"353",
"337",
"167",
"67",
"239",
"1009",
"449",
"97",
"23",
"349",
"41",
"31",
"911",
"61",
"929",
"229",
"797",
"331",
"191",
"463",
"107",
"463",
"809",
"2887",
"971"
] |
[
"base",
"nonn"
] | 19 | 1 | 1 |
[
"A111382",
"A111383",
"A113584",
"A379354",
"A379355",
"A379761",
"A380010",
"A380011"
] | null |
J.W.L. (Jan) Eerland, Jan 09 2025
| 2025-01-18T14:45:51 |
oeisdata/seq/A380/A380011.seq
|
52aac45d55671c84d907083ff96c4955
|
A380012
|
Population of elementary triangular automaton rule 54 at generation n, starting from a lone 1 cell at generation 0.
|
[
"1",
"4",
"9",
"15",
"21",
"36",
"36",
"57",
"66",
"87",
"81",
"129",
"129",
"162",
"162",
"225",
"228",
"270",
"267",
"351",
"324",
"342",
"483",
"411",
"468",
"516",
"588",
"639",
"600",
"723",
"762",
"777",
"795",
"960",
"888",
"1071",
"972",
"1056",
"1323",
"1158",
"1242",
"1362",
"1362",
"1557",
"1449",
"1689",
"1677",
"1845",
"1710",
"1977",
"2007",
"2100",
"2166",
"2178",
"2499",
"2409",
"2430",
"2556"
] |
[
"nonn"
] | 26 | 0 | 2 |
[
"A380012",
"A380172",
"A380173"
] | null |
Paul Cousin, Jan 09 2025
| 2025-06-04T00:30:10 |
oeisdata/seq/A380/A380012.seq
|
eefe5afe9487dc032c45717fbad850a3
|
A380013
|
Continued fraction expansion of Sum_{i>=0} (-1)^i/(q(i)*q(i+1)) where q(0)=q(1)=1, q(2n+2)=q(2n+1)+q(2n), and q(2n+3)=q(2n+1)*(q(2n+2)+1).
|
[
"0",
"1",
"1",
"1",
"1",
"3",
"1",
"18",
"1",
"432",
"1",
"196992",
"1",
"38895676416",
"1",
"1512881323731695591424",
"1",
"2288809899755012359448064967916189926490112",
"1"
] |
[
"nonn",
"cofr"
] | 69 | 0 | 6 |
[
"A006280",
"A019426",
"A380013"
] | null |
Khalil Ayadi, Jan 09 2025
| 2025-02-12T16:54:19 |
oeisdata/seq/A380/A380013.seq
|
53d65fd8ea39e5c7e87061f478b07ca4
|
A380014
|
Expansion of e.g.f. 1/sqrt(exp(-2*x) - 2*x).
|
[
"1",
"2",
"10",
"88",
"1084",
"17176",
"332824",
"7623904",
"201540112",
"6038820640",
"202246657696",
"7486877795200",
"303561658686400",
"13378863292503424",
"636833910410881408",
"32559375816074384896",
"1779494669204225605888",
"103532173699456380625408",
"6388705590982575700625920"
] |
[
"nonn"
] | 9 | 0 | 2 |
[
"A072597",
"A380014",
"A380016",
"A380018"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-23T04:53:46 |
oeisdata/seq/A380/A380014.seq
|
a186cd73a95a05f9ed38f56da29e514d
|
A380015
|
Expansion of e.g.f. 1/sqrt(1 - 2*x*exp(x)).
|
[
"1",
"1",
"5",
"36",
"361",
"4640",
"72771",
"1347598",
"28778849",
"696288888",
"18823644595",
"562350743306",
"18397666000209",
"654164843763340",
"25118967828553067",
"1035914449832324070",
"45665488606439586241",
"2142825945301659242576",
"106641225471890568771747",
"5610282675990428302440130"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A006153",
"A380015",
"A380017",
"A380019"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-23T04:42:09 |
oeisdata/seq/A380/A380015.seq
|
db619f598adb8bda09a2a697d0fbbda9
|
A380016
|
Expansion of e.g.f. 1/(exp(-3*x) - 3*x)^(1/3).
|
[
"1",
"2",
"13",
"161",
"2833",
"64841",
"1827685",
"61192181",
"2372620801",
"104549934977",
"5160225776101",
"281994042839477",
"16902276273364465",
"1102519010117525105",
"77749077431938305541",
"5894145002422856684501",
"478015727336387513545345",
"41295912476641866286397825",
"3786025873450493919700627525"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A072597",
"A380014",
"A380016",
"A380018"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-09T08:00:45 |
oeisdata/seq/A380/A380016.seq
|
f74ede080b9b809067fda51b67b1a23f
|
A380017
|
Expansion of e.g.f. 1/(1 - 3*x*exp(x))^(1/3).
|
[
"1",
"1",
"6",
"55",
"716",
"12085",
"250726",
"6172915",
"175903400",
"5694587209",
"206438732810",
"8284550317351",
"364605758728828",
"17461047965591581",
"903964982917764782",
"50306323769422679995",
"2994799872257498255696",
"189906103853462927405329",
"12779300537432602189228306"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A006153",
"A380015",
"A380017",
"A380019"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-23T04:47:54 |
oeisdata/seq/A380/A380017.seq
|
49ba98b23bb7e93051ed9c06683064a3
|
A380018
|
Expansion of e.g.f. 1/(exp(-4*x) - 4*x)^(1/4).
|
[
"1",
"2",
"16",
"256",
"5856",
"175296",
"6486016",
"285756416",
"14606007296",
"849615763456",
"55415153442816",
"4005309938466816",
"317750919017168896",
"27449350209163821056",
"2564871898004949303296",
"257753802183061443444736",
"27720748513211258671988736",
"3176821722223524679312736256"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A072597",
"A380014",
"A380016",
"A380018"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-09T08:00:30 |
oeisdata/seq/A380/A380018.seq
|
cf7c334b4d844350f6301bde5e0b7be4
|
A380019
|
Expansion of e.g.f. 1/(1 - 4*x*exp(x))^(1/4).
|
[
"1",
"1",
"7",
"78",
"1249",
"26100",
"673101",
"20655082",
"735030913",
"29759100264",
"1350726180085",
"67929497104326",
"3749296817347137",
"225321905599163308",
"14646040616615433949",
"1023818460912628352490",
"76589660469522857865601",
"6105092923000191785913552",
"516586509938516858800548453"
] |
[
"nonn"
] | 7 | 0 | 3 |
[
"A006153",
"A380015",
"A380017",
"A380019"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-09T07:59:55 |
oeisdata/seq/A380/A380019.seq
|
0104f1142bd49a00af0d554fd91ccebf
|
A380020
|
Expansion of e.g.f. 1/sqrt(exp(-2*x) - 2*x*exp(-x)).
|
[
"1",
"2",
"8",
"55",
"540",
"6861",
"106828",
"1968443",
"41884496",
"1010558161",
"27259824996",
"812935829355",
"26556802948624",
"943118750625377",
"36176486632451012",
"1490585029223430691",
"65656827447552549504",
"3078782615385684631809",
"153127047650469476373316"
] |
[
"nonn"
] | 6 | 0 | 2 |
[
"A380014",
"A380015",
"A380020"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-09T08:00:20 |
oeisdata/seq/A380/A380020.seq
|
6ce44f2401aa6d8e70a91fe0d68bb192
|
A380021
|
Expansion of e.g.f. 1/(exp(-3*x) - 3*x*exp(-2*x))^(1/3).
|
[
"1",
"2",
"9",
"77",
"977",
"16281",
"335173",
"8208901",
"233037185",
"7522621505",
"272096862821",
"10899761462085",
"478990330829233",
"22910468287983121",
"1184832950732237381",
"65877062190857942981",
"3918656527419803705729",
"248317978064709144523521",
"16699787528059828201246021"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A380016",
"A380017",
"A380021"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-09T08:00:16 |
oeisdata/seq/A380/A380021.seq
|
9ef0f4d8542549df4bdda824f409bccb
|
A380022
|
Expansion of e.g.f. 1/(exp(-4*x) - 4*x*exp(-3*x))^(1/4).
|
[
"1",
"2",
"10",
"103",
"1608",
"33201",
"850108",
"25961489",
"920672000",
"37177954705",
"1684020384036",
"84552655333785",
"4660526554922032",
"279769833061460249",
"18167873577214204964",
"1268970734106516345721",
"94861592588266224161664",
"7556876103775629510620193",
"639078655735155260051464132"
] |
[
"nonn"
] | 5 | 0 | 2 |
[
"A380018",
"A380019",
"A380022"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-09T08:00:10 |
oeisdata/seq/A380/A380022.seq
|
851ddfa74a95de02c0293a46a7b653ac
|
A380023
|
a(n) = a(n-1) * a(n-2) * (1 - 2 / (n * (n-1))), with a(1) = 2, a(2) = 3.
|
[
"2",
"3",
"4",
"10",
"36",
"336",
"11520",
"3732480",
"41803776000",
"152564385447936000",
"6261807987664209366220800000",
"940854207318376503485146088437972992000000000",
"5815917000990435607656487842294594291938222391518950745702400000000000000"
] |
[
"nonn"
] | 36 | 1 | 1 |
[
"A000045",
"A230053",
"A380023"
] | null |
Hamza K. Özer, Jan 09 2025
| 2025-03-16T22:56:15 |
oeisdata/seq/A380/A380023.seq
|
d4121b7e9e2e6135b357e17fddb99b3c
|
A380024
|
a(n) = 4^n - 3^n - binomial(n,2)*3^(n-2).
|
[
"0",
"1",
"6",
"28",
"121",
"511",
"2152",
"9094",
"38563",
"163729",
"694282",
"2934592",
"12348541",
"51697075",
"215291356",
"891989002",
"3677964295",
"15099277669",
"61745907934",
"251632677604",
"1022414950465",
"4143511249831",
"16755357788176",
"67628131638478",
"272531374722091"
] |
[
"nonn",
"easy"
] | 28 | 0 | 3 |
[
"A005061",
"A086443",
"A380024",
"A380651"
] | null |
Enrique Navarrete, Feb 05 2025
| 2025-03-03T16:28:48 |
oeisdata/seq/A380/A380024.seq
|
b5e092b87516b7421da56eab3a969d6f
|
A380025
|
Area of smallest rectangle of grid cells such that it is possible to mark a connected subset of the cells so that the lengths of runs of marked cells have lengths from 2 to n, each length appearing exactly once.
|
[
"2",
"6",
"12",
"15",
"24",
"35",
"40",
"54",
"65",
"77",
"96",
"112",
"126",
"150",
"160"
] |
[
"nonn",
"more"
] | 34 | 2 | 1 |
[
"A351516",
"A380025"
] | null |
Rodolfo Kurchan, Jan 09 2025
| 2025-02-01T23:12:57 |
oeisdata/seq/A380/A380025.seq
|
954562c93b088ecdd68114e8875c40a2
|
A380026
|
a(n) is the smallest prime p such that p - a(n-1) is a primorial, starting with a(1)=2.
|
[
"2",
"3",
"5",
"7",
"13",
"19",
"229",
"439",
"2749",
"5059",
"7369",
"9679",
"39709",
"42019",
"6469735249",
"5766152219975951659023630035336134306565384015606066326325804059",
"5766152219975951659023630035336134306565384015606073747063938869",
"5766152219975951659023630035336134306565384015606073747287031739"
] |
[
"nonn"
] | 26 | 1 | 1 |
[
"A000720",
"A002110",
"A100380",
"A380026",
"A380027"
] | null |
Hayden Chesnut, Jan 09 2025
| 2025-01-21T15:10:24 |
oeisdata/seq/A380/A380026.seq
|
f06e8619ce3e4550eb955906545b5e02
|
A380027
|
a(n) is the largest prime p such that p - a(n-1) is a primorial, starting with a(1) = 2.
|
[
"2",
"3",
"5",
"11",
"41",
"9699731"
] |
[
"nonn"
] | 40 | 1 | 1 |
[
"A002110",
"A265109",
"A380026",
"A380027"
] | null |
Hayden Chesnut, Jan 09 2025
| 2025-02-08T14:09:38 |
oeisdata/seq/A380/A380027.seq
|
e8eb9af877e8adcf05f473e350e8666f
|
A380028
|
Expansion of e.g.f. sqrt(1 - 2*x*exp(x)).
|
[
"1",
"-1",
"-3",
"-12",
"-79",
"-760",
"-9561",
"-147994",
"-2716239",
"-57632040",
"-1387518625",
"-37365406606",
"-1112793904311",
"-36312032900884",
"-1288357188957489",
"-49380149141206290",
"-2033232328710195871",
"-89506187915127440560",
"-4194948681994077973377",
"-208545134727411799745878"
] |
[
"sign",
"easy"
] | 9 | 0 | 3 |
[
"A002420",
"A380015",
"A380028"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-04-22T13:00:59 |
oeisdata/seq/A380/A380028.seq
|
bbf30d885caf4f0795ed3f291897d7ea
|
A380029
|
Expansion of e.g.f. (1 - 3*x*exp(x))^(1/3).
|
[
"1",
"-1",
"-4",
"-25",
"-252",
"-3545",
"-63806",
"-1397781",
"-36069272",
"-1071165745",
"-35977484250",
"-1348257912221",
"-55766033179220",
"-2523251585908521",
"-123972318738063446",
"-6572554273909419685",
"-373979858167243433136",
"-22731929051273411113313",
"-1470009560015441800798514"
] |
[
"sign",
"easy"
] | 9 | 0 | 3 |
[
"A004990",
"A380017",
"A380029",
"A380030"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-10T10:09:59 |
oeisdata/seq/A380/A380029.seq
|
cafc477ab003cd49ec646cfec20b6c69
|
A380030
|
Expansion of e.g.f. (1 - 3*x*exp(x))^(2/3).
|
[
"1",
"-2",
"-6",
"-26",
"-208",
"-2570",
"-42332",
"-865718",
"-21110224",
"-597416786",
"-19239912340",
"-694646155742",
"-27785653906232",
"-1219574936748506",
"-58274685177526300",
"-3011159013528002150",
"-167299112903683007392",
"-9945379044947061586850",
"-629870278061691615041828"
] |
[
"sign",
"easy"
] | 9 | 0 | 2 |
[
"A004989",
"A380029",
"A380030"
] | null |
Seiichi Manyama, Jan 09 2025
| 2025-01-10T10:09:55 |
oeisdata/seq/A380/A380030.seq
|
1cec698f65e3fc5b2ffa8a4a831ad112
|
A380031
|
Smallest integer of d digits, greater than 1 and not ending in 0, whose constant congruence speed is not yet constant at height d + 2.
|
[
"5",
"807",
"81666295807",
"81907922943",
"161423787862411847003581666295807",
"115161423787862411847003581666295807",
"45115161423787862411847003581666295807",
"44317662666830362972182803640476581907922943",
"776138023544317662666830362972182803640476581907922943"
] |
[
"nonn",
"base",
"hard"
] | 8 | 1 | 1 |
[
"A068407",
"A290372",
"A290373",
"A290374",
"A290375",
"A317905",
"A370211",
"A370775",
"A371129",
"A371671",
"A372490",
"A373387",
"A379906",
"A380031"
] | null |
Marco Ripà, Jan 10 2025
| 2025-01-18T09:27:03 |
oeisdata/seq/A380/A380031.seq
|
418b0e3f05a00e84e1eda1802d346d1a
|
A380032
|
Number of pairs (d, k/d), d | k, d < k/d, such that gcd(d, k/d) > 1 and d | k/d but rad(k/d) does not divide d, where k is in A126706.
|
[
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"3",
"2",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1"
] |
[
"nonn"
] | 6 | 1 | 6 |
[
"A001221",
"A025487",
"A126706",
"A380032"
] | null |
Michael De Vlieger, Jan 11 2025
| 2025-01-15T08:43:12 |
oeisdata/seq/A380/A380032.seq
|
2f517adca4b27f7516a6f5b935e93074
|
A380033
|
Numbers that set records in A380032.
|
[
"12",
"36",
"144",
"576",
"720",
"900",
"2880",
"3600",
"14400",
"32400",
"44100",
"57600",
"129600",
"176400",
"705600",
"1587600",
"2822400",
"6350400",
"11289600",
"21344400",
"25401600",
"57153600",
"85377600",
"101606400",
"192099600",
"341510400",
"768398400",
"1366041600",
"3073593600",
"6915585600",
"12294374400"
] |
[
"nonn"
] | 6 | 1 | 1 |
[
"A025487",
"A061742",
"A126706",
"A364710",
"A380032",
"A380033",
"A380034"
] | null |
Michael De Vlieger, Jan 11 2025
| 2025-01-15T08:43:21 |
oeisdata/seq/A380/A380033.seq
|
3a63f1df3b5333059cb49c0f49c5bebd
|
A380034
|
Records in A380032.
|
[
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"12",
"13",
"14",
"15",
"17",
"21",
"28",
"31",
"35",
"41",
"42",
"45",
"51",
"54",
"60",
"61",
"67",
"75",
"89",
"90",
"111",
"118",
"133",
"147",
"155",
"163",
"176",
"185",
"186",
"195",
"205",
"231",
"246",
"277",
"307",
"323",
"343",
"368",
"369",
"377",
"383",
"411",
"429",
"455",
"471",
"479",
"490",
"502",
"545",
"565",
"567",
"627"
] |
[
"nonn"
] | 5 | 1 | 2 |
[
"A380032",
"A380033",
"A380034"
] | null |
Michael De Vlieger, Jan 11 2025
| 2025-01-15T08:43:31 |
oeisdata/seq/A380/A380034.seq
|
9b059504f786b8b84a08d8aef4e9bf44
|
A380035
|
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)) ).
|
[
"1",
"1",
"5",
"42",
"517",
"8420",
"171201",
"4181128",
"119339081",
"3900501648",
"143703797725",
"5893732487456",
"266358266633229",
"13153210420876864",
"704697559381904921",
"40714369264722337920",
"2523456287242464370321",
"167019778198736205721856",
"11757749450929277192860725"
] |
[
"nonn"
] | 23 | 0 | 3 |
[
"A380015",
"A380035",
"A380042"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:53 |
oeisdata/seq/A380/A380035.seq
|
08659662642e01a6cd49ad9269298b65
|
A380036
|
Smallest number which is not a triangular number mod n.
|
[
"1",
"2",
"2",
"4",
"2",
"2",
"2",
"8",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"16",
"5",
"2",
"4",
"2",
"2",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"2",
"32",
"2",
"5",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"4",
"4",
"2",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"64",
"2",
"2",
"5",
"5",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"2",
"2",
"7",
"2",
"2",
"4",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"4"
] |
[
"nonn"
] | 32 | 1 | 2 |
[
"A000079",
"A000217",
"A117484",
"A343713",
"A380036"
] | null |
Ethan E. Wood, Jan 10 2025
| 2025-01-30T13:53:24 |
oeisdata/seq/A380/A380036.seq
|
f192d5ad6212e70f51dabc4e8b1bde93
|
A380037
|
For n >= 1, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) as 1 more than the number of positive terms between a(m+1) and a(n-1). Otherwise, a(n+1) = -1. Start with a(1) = 0.
|
[
"0",
"-1",
"-1",
"1",
"-1",
"2",
"-1",
"2",
"1",
"3",
"-1",
"4",
"-1",
"2",
"4",
"2",
"2",
"1",
"7",
"-1",
"7",
"1",
"3",
"10",
"-1",
"5",
"-1",
"2",
"8",
"-1",
"3",
"5",
"4",
"14",
"-1",
"5",
"3",
"5",
"2",
"9",
"-1",
"6",
"-1",
"2",
"3",
"6",
"3",
"2",
"4",
"13",
"-1",
"8",
"18",
"-1",
"3",
"6",
"8",
"4",
"7",
"30",
"-1",
"7",
"2",
"12",
"-1",
"4",
"6",
"9",
"22",
"-1",
"5",
"26"
] |
[
"sign"
] | 33 | 1 | 6 |
[
"A181391",
"A380037"
] | null |
Connor Criss, Jan 10 2025
| 2025-01-23T12:51:36 |
oeisdata/seq/A380/A380037.seq
|
1eaf5206cd3c3f379f4b8add7a8c9d6d
|
A380038
|
Triangle read by rows: T(n, k) = T(n-k, k) - T(n-k+1, k-1), T(n, 0) = A010815(n-1), and T(0, 0) = 1.
|
[
"1",
"1",
"-1",
"-1",
"0",
"1",
"-1",
"1",
"0",
"0",
"0",
"1",
"0",
"-1",
"0",
"0",
"1",
"-1",
"0",
"0",
"0",
"1",
"0",
"-1",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"0",
"1",
"0",
"0",
"0",
"1",
"-1",
"-1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"1",
"1",
"0",
"-1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"1",
"1"
] |
[
"sign",
"tabl"
] | 20 | 0 | null |
[
"A000041",
"A000217",
"A008284",
"A010815",
"A072233",
"A078616",
"A380038"
] | null |
Friedjof Tellkamp, Jan 12 2025
| 2025-02-12T12:46:28 |
oeisdata/seq/A380/A380038.seq
|
794cdeb2fc98667f82b386d08df4deeb
|
A380039
|
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(1/3).
|
[
"1",
"1",
"6",
"61",
"908",
"17865",
"438286",
"12901735",
"443475432",
"17443879057",
"773018191610",
"38117147134671",
"2070381313048588",
"122841147634754185",
"7905667340470592070",
"548555101319868261655",
"40825552788531622527056",
"3244188226183716688784289",
"274164589130871765969460594"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A380017",
"A380039",
"A380040",
"A380041"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:57 |
oeisdata/seq/A380/A380039.seq
|
e8888d46d54e8e4de4889beea0ab6f15
|
A380040
|
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(2/3).
|
[
"1",
"2",
"14",
"170",
"3000",
"69930",
"2033212",
"70972734",
"2894590064",
"135164076722",
"7113787010100",
"416759006663142",
"26903080612468744",
"1897553477118350922",
"145204649027247413996",
"11982094054396851014030",
"1060673494236770414806752",
"100265097180082772515691874",
"10080871201186661027182272868"
] |
[
"nonn"
] | 9 | 0 | 2 |
[
"A380039",
"A380040",
"A380041"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:46 |
oeisdata/seq/A380/A380040.seq
|
854aeb09c5d645ee3c70d8cfea6a7ab6
|
A380041
|
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^2) )^(1/3).
|
[
"1",
"1",
"6",
"67",
"1124",
"25325",
"718606",
"24629395",
"990296504",
"45718478137",
"2383877762810",
"138578689119431",
"8887132981365508",
"623319005140469989",
"47465740413056117894",
"3900149351529967753435",
"343951717449176947732976",
"32405206661688405897284849",
"3248370338004030319683766642"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A380017",
"A380039",
"A380041"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:49 |
oeisdata/seq/A380/A380041.seq
|
b0183af7ec3b5db820a28a7ebe0363bf
|
A380042
|
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)^2) ).
|
[
"1",
"1",
"5",
"48",
"697",
"13640",
"336771",
"10053778",
"352334753",
"14183529480",
"645073504435",
"32715111226886",
"1830671281889649",
"112049330303532388",
"7446824171300128811",
"534068807341887943770",
"41111698162393482004801",
"3381089519620006418116976",
"295869084136630532211207843"
] |
[
"nonn"
] | 11 | 0 | 3 |
[
"A161633",
"A201470",
"A380015",
"A380035",
"A380042",
"A380043"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:39 |
oeisdata/seq/A380/A380042.seq
|
5a5f3b05f74af38e2787833c1fbc3819
|
A380043
|
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^3) )^(1/3).
|
[
"1",
"1",
"6",
"73",
"1364",
"34585",
"1110406",
"43200535",
"1975744856",
"103892750209",
"6176282882570",
"409635957376591",
"29988473838531748",
"2402004132488328433",
"208956515057627326094",
"19619264794744128427495",
"1977503574407863125008816",
"212975277029523353673126529",
"24408338689788753822318157330"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A161633",
"A380039",
"A380041",
"A380042",
"A380043"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:43 |
oeisdata/seq/A380/A380043.seq
|
1ecaacae4c8254dca0d32360024e66b7
|
A380044
|
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x)*A(x) ).
|
[
"1",
"1",
"7",
"81",
"1393",
"32025",
"924831",
"32208337",
"1314511297",
"61553580849",
"3253663709335",
"191661481308561",
"12451241630689137",
"884434637282286025",
"68195094329460133231",
"5672843158404577658385",
"506413381554227338302721",
"48290505275596520116029537",
"4899034372132659112326787239"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A295238",
"A380044",
"A380045"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:27:04 |
oeisdata/seq/A380/A380044.seq
|
e89ed538b5f16583ebb5bd915cba0f60
|
A380045
|
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x)*A(x) )^(1/3).
|
[
"1",
"1",
"8",
"109",
"2220",
"60585",
"2079166",
"86098929",
"4179685560",
"232849349425",
"14645304783450",
"1026614846280441",
"79371261554884036",
"6709919722961129337",
"615776691767279304822",
"60968162469515187248545",
"6478143744223567852425456",
"735290556968263062361451745",
"88790542940636437330983140146"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A295238",
"A380044",
"A380045"
] | null |
Seiichi Manyama, Jan 10 2025
| 2025-01-11T10:26:55 |
oeisdata/seq/A380/A380045.seq
|
8431d11817e987754579fabd9ce53a62
|
A380046
|
E.g.f. A(x) satisfies A(x) = 1 + 2*x*exp(x)*A(x)^(1/2).
|
[
"1",
"2",
"8",
"36",
"176",
"840",
"3312",
"4592",
"-85888",
"-893664",
"1375040",
"165097152",
"2297399040",
"-437916544",
"-676590342400",
"-13778476089600",
"-35262701498368",
"5528190100333056",
"159800245551129600",
"1036568296401259520",
"-77532370748157030400",
"-3135837171024874272768"
] |
[
"sign"
] | 10 | 0 | 2 |
[
"A006153",
"A380046",
"A380047",
"A380050"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-11T10:26:40 |
oeisdata/seq/A380/A380046.seq
|
2b3b091954a47226dacc4d49de7bb430
|
A380047
|
E.g.f. A(x) satisfies A(x) = 1 + 3*x*exp(x)*A(x)^(1/3).
|
[
"1",
"3",
"12",
"45",
"132",
"135",
"-702",
"6573",
"111576",
"-634581",
"-19482690",
"104641713",
"5438689380",
"-21226768017",
"-2173847986086",
"3249084663765",
"1168505502268848",
"2167390942251219",
"-807540016560944778",
"-5035872168333504807",
"693302551375611396540",
"8209523136574257223383"
] |
[
"sign"
] | 8 | 0 | 2 |
[
"A006153",
"A380046",
"A380047",
"A380051"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-11T10:26:35 |
oeisdata/seq/A380/A380047.seq
|
a3d132fcf83063b2ccd49415c88184a7
|
A380048
|
a(n) = A000045(n) * A001003(n).
|
[
"0",
"1",
"3",
"22",
"135",
"985",
"7224",
"55627",
"436653",
"3503666",
"28537245",
"235558347",
"1965437136",
"16552173909",
"140505456663",
"1200968926590",
"10327551834411",
"89286693775373",
"775611959272392",
"6766372185052247",
"59256729852910425",
"520754062920338026",
"4590973472772299193",
"40591542233796808247"
] |
[
"nonn",
"easy"
] | 10 | 0 | 3 |
[
"A000045",
"A001003",
"A380048"
] | null |
Vladimir Kruchinin, Jan 11 2025
| 2025-01-11T18:49:38 |
oeisdata/seq/A380/A380048.seq
|
ae717345b609433fee63f8989da76ca6
|
A380049
|
Partial sums of A072203.
|
[
"0",
"1",
"3",
"4",
"6",
"7",
"9",
"12",
"14",
"15",
"17",
"20",
"24",
"27",
"29",
"30",
"32",
"35",
"39",
"44",
"48",
"51",
"55",
"58",
"60",
"61",
"63",
"66",
"70",
"75",
"81",
"88",
"94",
"99",
"103",
"106",
"110",
"113",
"115",
"116",
"118",
"121",
"125",
"130",
"136",
"141",
"147",
"154",
"160",
"167",
"173",
"180",
"188",
"195",
"201",
"206",
"210",
"213",
"217",
"220",
"224",
"227",
"231",
"234",
"236"
] |
[
"nonn"
] | 38 | 1 | 3 |
[
"A058933",
"A072203",
"A380049"
] | null |
Tsuyoshi Hanatate, Jan 10 2025
| 2025-06-27T17:20:39 |
oeisdata/seq/A380/A380049.seq
|
8642b795fc4fdbb495665c1a02c9f649
|
A380050
|
E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*exp(x)*A(x) ).
|
[
"1",
"1",
"3",
"9",
"25",
"25",
"-429",
"-4151",
"-8175",
"320625",
"5241475",
"23329801",
"-705579159",
"-18521117303",
"-150119840493",
"3366485315145",
"138253031778721",
"1780881865542625",
"-28047359274759549",
"-1854674541474191351",
"-34985197604145203655",
"332608115115937927161"
] |
[
"sign"
] | 11 | 0 | 3 |
[
"A006153",
"A297010",
"A380044",
"A380050",
"A380051"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-11T10:26:32 |
oeisdata/seq/A380/A380050.seq
|
97542c8834ce3af3f1835af15cdad5ba
|
A380051
|
E.g.f. A(x) satisfies A(x) = ( 1 + 3*x*exp(x)*A(x) )^(1/3).
|
[
"1",
"1",
"2",
"1",
"-12",
"-15",
"526",
"1617",
"-49608",
"-302111",
"8126010",
"85724001",
"-2020009628",
"-34232466255",
"696686324166",
"18267485751985",
"-310973114236944",
"-12533263924965183",
"168118610439268594",
"10727427541319225793",
"-100693940482485604260",
"-11178369799980253348079"
] |
[
"sign"
] | 7 | 0 | 3 |
[
"A006153",
"A380047",
"A380050",
"A380051"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-11T10:26:28 |
oeisdata/seq/A380/A380051.seq
|
3c0a4729c2871a3fa5e7f757c37070ea
|
A380052
|
a(n) is the largest number whose cube is an n-digit cube which has the maximum sum of digits (A373727(n)).
|
[
"2",
"4",
"9",
"19",
"46",
"92",
"208",
"453",
"942",
"1966",
"4289",
"9949",
"12599",
"43795",
"99829",
"215083",
"446423",
"989353",
"2131842",
"4081435",
"9850783",
"20714797",
"43967926",
"92827483",
"190349299",
"464110759",
"989554129",
"2132590453",
"4559677342",
"9654499999",
"21253161559",
"31037622999",
"99594689449",
"181610950229"
] |
[
"nonn",
"base"
] | 23 | 1 | 1 |
[
"A373727",
"A379298",
"A379869",
"A380052",
"A380193",
"A380566",
"A380797"
] | null |
Zhining Yang, Jan 11 2025
| 2025-04-03T14:59:21 |
oeisdata/seq/A380/A380052.seq
|
fc46c3c24fb0cfa96a3863f10bdbb9f1
|
A380053
|
E.g.f. (exp(x) - 1)/cos(x).
|
[
"1",
"1",
"4",
"7",
"36",
"91",
"624",
"2087",
"18256",
"76231",
"814144",
"4078867",
"51475776",
"300870571",
"4381112064",
"29265244847",
"482962852096",
"3629392540111",
"66942218896384",
"558956224522027",
"11394877025289216",
"104659828714136851",
"2336793875186479104",
"23414201065072302407",
"568240131312188379136"
] |
[
"nonn"
] | 14 | 1 | 3 |
[
"A000364",
"A002084",
"A380053",
"A380054",
"A380055",
"A380057"
] | null |
Paul D. Hanna, Jan 24 2025
| 2025-01-25T04:38:16 |
oeisdata/seq/A380/A380053.seq
|
4e8ab5df9fcebc8fa220d24231e115eb
|
A380054
|
G.f. A(x) satisfies: A( A(x)^3 - A(x)^4 ) = x*A(x)^2.
|
[
"1",
"1",
"2",
"4",
"10",
"27",
"78",
"234",
"722",
"2275",
"7288",
"23662",
"77676",
"257372",
"859592",
"2890838",
"9781066",
"33271759",
"113720380",
"390354292",
"1345099574",
"4651222825",
"16134691254",
"56132722306",
"195807489940",
"684712787166",
"2399784312560",
"8428460653683",
"29660054158020",
"104564729164209",
"369263035193928"
] |
[
"nonn"
] | 12 | 1 | 3 |
[
"A268655",
"A380054"
] | null |
Paul D. Hanna, Jan 27 2025
| 2025-01-28T08:40:03 |
oeisdata/seq/A380/A380054.seq
|
3942bfd38ce657f75f1a2c01fe687bf1
|
A380055
|
E.g.f. satisfies A(x) = log( 1 + x*cos(A(x)) ).
|
[
"1",
"-1",
"-1",
"18",
"-86",
"-210",
"8840",
"-80080",
"-266220",
"19991520",
"-274725100",
"-1006434000",
"123657316600",
"-2328145274000",
"-8148732243600",
"1621702497792000",
"-39454300872662000",
"-113331522571488000",
"38748502249144766000",
"-1172806114215446464000",
"-2126467491228525900000",
"1525200888587905488960000"
] |
[
"sign"
] | 11 | 1 | 4 |
[
"A380053",
"A380055",
"A380057"
] | null |
Paul D. Hanna, Jan 24 2025
| 2025-01-25T04:36:42 |
oeisdata/seq/A380/A380055.seq
|
88cf46399b226c78ec50e66da9b84921
|
A380056
|
E.g.f. (exp(x) - 1)/cos(2*x).
|
[
"1",
"1",
"13",
"25",
"441",
"1261",
"30213",
"115025",
"3529201",
"16792021",
"629401213",
"3593565625",
"159175688361",
"1060279600381",
"54189700721013",
"412526870321825",
"23894940183997921",
"204641610743378341",
"13248060325188261613",
"126065945039257743625",
"9020317522757414377881",
"94419130586604915837901"
] |
[
"nonn"
] | 10 | 1 | 3 |
[
"A000364",
"A380053",
"A380056",
"A380555"
] | null |
Paul D. Hanna, Jan 28 2025
| 2025-02-18T07:36:40 |
oeisdata/seq/A380/A380056.seq
|
58407c3541a0f4f5e1bfbaf23dfbdbd4
|
A380057
|
E.g.f. satisfies A(x) = real( 1 + x*A(x)^i ), where i^2 = -1.
|
[
"1",
"1",
"0",
"-3",
"12",
"10",
"-660",
"5600",
"8400",
"-951660",
"12715200",
"21635900",
"-4308744000",
"80314007800",
"115204471200",
"-44501789202000",
"1083368456352000",
"782537744170000",
"-876176569052928000",
"26724653123017850000",
"-10930955906482560000",
"-29304692085200613900000",
"1088420125090964265600000"
] |
[
"sign"
] | 20 | 0 | 4 |
[
"A380053",
"A380055",
"A380057",
"A380058"
] | null |
Paul D. Hanna, Jan 24 2025
| 2025-01-25T09:52:23 |
oeisdata/seq/A380/A380057.seq
|
392b7d1d7b209f5a112355d48b8f9507
|
A380058
|
G.f. A(x) satisfies: A( A(x)^4 - A(x)^5 ) = x*A(x)^3.
|
[
"1",
"1",
"2",
"5",
"13",
"37",
"111",
"345",
"1103",
"3603",
"11971",
"40328",
"137423",
"472829",
"1640328",
"5731315",
"20150376",
"71235454",
"253061855",
"902922756",
"3234281950",
"11626416055",
"41928973015",
"151656509670",
"550021604731",
"1999753822557",
"7287331086431",
"26612272636168",
"97375824946785",
"356957982413881"
] |
[
"nonn"
] | 7 | 1 | 3 |
[
"A268655",
"A380054",
"A380058"
] | null |
Paul D. Hanna, Jan 28 2025
| 2025-01-29T12:45:48 |
oeisdata/seq/A380/A380058.seq
|
447ca767d87f4ad27c1090aeb89cb124
|
A380059
|
G.f. A(x) satisfies: A(x)^4 = x * A( A(x)^3 + A(x)^4 ).
|
[
"1",
"1",
"1",
"2",
"7",
"22",
"61",
"172",
"528",
"1696",
"5461",
"17591",
"57356",
"189786",
"634137",
"2131628",
"7205426",
"24500143",
"83760349",
"287672215",
"991932713",
"3432816902",
"11920342010",
"41521046864",
"145032773711",
"507902711094",
"1782900884412",
"6272354908197",
"22111650029873",
"78097290365451",
"276324399241123",
"979311618314876"
] |
[
"nonn"
] | 6 | 1 | 4 |
[
"A272485",
"A380059"
] | null |
Paul D. Hanna, Jan 28 2025
| 2025-01-29T12:45:55 |
oeisdata/seq/A380/A380059.seq
|
522efa9e55bf0d877a96741b5f2815b8
|
A380060
|
G.f. A(x) satisfies A(x) = Sum_{n=-oo..+oo} x^(n^2) * (A(x) - x^n)^n/(1 - x^n*A(x))^n.
|
[
"1",
"2",
"4",
"16",
"66",
"284",
"1256",
"5752",
"26944",
"128538",
"622560",
"3053224",
"15132720",
"75679956",
"381430176",
"1935464936",
"9879523418",
"50695803612",
"261364074484",
"1353156913528",
"7032341655200",
"36673080496896",
"191847911851336",
"1006497470833352",
"5294344082015344",
"27916789231188726",
"147534225848777456"
] |
[
"nonn"
] | 15 | 0 | 2 |
[
"A380060",
"A380680"
] | null |
Paul D. Hanna, Feb 06 2025
| 2025-07-03T13:14:04 |
oeisdata/seq/A380/A380060.seq
|
618c371fbb9cfda4a6110ae6900ef0d6
|
A380061
|
G.f. A(x) satisfies 1 + 2*A(x) = Sum_{n>=0} (x + A(x)^n)^n.
|
[
"1",
"1",
"3",
"6",
"22",
"64",
"238",
"813",
"3064",
"11276",
"43290",
"165781",
"647916",
"2541826",
"10085272",
"40216458",
"161537304",
"651906163",
"2644581776",
"10771863433",
"44052178217",
"180771472434",
"744215912074",
"3072704927332",
"12720703058636",
"52791694969046",
"219588568135410",
"915306832688642",
"3822734157002821",
"15994557980983589"
] |
[
"nonn"
] | 10 | 1 | 3 |
[
"A380061",
"A380062",
"A380063",
"A380064"
] | null |
Paul D. Hanna, Jan 11 2025
| 2025-01-22T03:56:23 |
oeisdata/seq/A380/A380061.seq
|
8e735f0b39a9ff9e1e06ddad99341a30
|
A380062
|
G.f. A(x) satisfies 1 + 3*A(x) = Sum_{n>=0} (x + 2*A(x)^n)^n.
|
[
"1",
"1",
"5",
"13",
"67",
"267",
"1333",
"6257",
"31649",
"159205",
"824227",
"4295599",
"22706441",
"120952097",
"649957785",
"3515569465",
"19134939879",
"104700236227",
"575656327477",
"3178537378181",
"17618587510649",
"98000687531045",
"546850545803695",
"3060334365371927",
"17172225926646469",
"96593865520419529",
"544573760947543421"
] |
[
"nonn"
] | 11 | 1 | 3 |
[
"A380061",
"A380062",
"A380063",
"A380064"
] | null |
Paul D. Hanna, Jan 11 2025
| 2025-01-22T03:59:04 |
oeisdata/seq/A380/A380062.seq
|
c1164720c858c51b94556a35fa8d4062
|
A380063
|
G.f. A(x) satisfies 1 + 4*A(x) = Sum_{n>=0} (x + 3*A(x)^n)^n.
|
[
"1",
"1",
"7",
"22",
"136",
"682",
"4030",
"23539",
"143026",
"883696",
"5546230",
"35293039",
"226922620",
"1473059344",
"9637454320",
"63493041340",
"420841313770",
"2804372957419",
"18777007427668",
"126261555174991",
"852293214690055",
"5773260342048436",
"39231225884581288",
"267363603092143528",
"1826957733209857000",
"12514655218275667486"
] |
[
"nonn"
] | 10 | 1 | 3 |
[
"A380061",
"A380062",
"A380063",
"A380064"
] | null |
Paul D. Hanna, Jan 11 2025
| 2025-01-22T04:03:18 |
oeisdata/seq/A380/A380063.seq
|
45af729c9568ac5abfb087489d3d9341
|
A380064
|
G.f. A(x) satisfies 1 + 5*A(x) = Sum_{n>=0} (x + 4*A(x)^n)^n.
|
[
"1",
"1",
"9",
"33",
"229",
"1381",
"9169",
"63225",
"440257",
"3164657",
"22959933",
"169226413",
"1259998401",
"9468455953",
"71735232745",
"547149712977",
"4199096527653",
"32397250554709",
"251152306142033",
"1955325586152313",
"15281679449617745",
"119849879841490737",
"942933049414865245",
"7440178358444340061",
"58862772743085470513"
] |
[
"nonn"
] | 10 | 1 | 3 |
[
"A380061",
"A380062",
"A380063",
"A380064"
] | null |
Paul D. Hanna, Jan 11 2025
| 2025-01-22T04:06:02 |
oeisdata/seq/A380/A380064.seq
|
0e828b8dc915724d280f385d9e25469c
|
A380065
|
G.f. A(x) satisfies 2 = Sum_{n=-oo..+oo} x^(2*n) * (A(x) - x^(2*n+1))^(n-1).
|
[
"1",
"3",
"14",
"98",
"785",
"6702",
"59968",
"554872",
"5266164",
"50982561",
"501511295",
"4998413255",
"50366515829",
"512257729704",
"5251739403578",
"54216242355803",
"563112825354739",
"5880229017352112",
"61697782946493598",
"650137346153943901",
"6877281106762452016",
"73003969200802059386",
"777423197278368997747"
] |
[
"nonn"
] | 12 | 0 | 2 |
[
"A379765",
"A380065"
] | null |
Paul D. Hanna, Jan 24 2025
| 2025-01-25T05:39:13 |
oeisdata/seq/A380/A380065.seq
|
b68597559fe74b03380d496bebca76f1
|
A380066
|
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n*A(x)^n * (A(x)^n + x)^(n-1) * (A(x) + x^n)^(n-1).
|
[
"1",
"6",
"62",
"826",
"13562",
"254846",
"5214422",
"113062754",
"2559413794",
"59941050914",
"1443598614402",
"35601934520718",
"896388775541106",
"22991857186720770",
"599842769589183382",
"15901090578161918966",
"428007773140084378006",
"11693991740550538593478",
"324291504285820478308174",
"9129716934077168140311170"
] |
[
"nonn"
] | 10 | 0 | 2 |
[
"A380066",
"A381362",
"A381363",
"A381364",
"A381365"
] | null |
Paul D. Hanna, Feb 01 2025
| 2025-02-21T14:36:17 |
oeisdata/seq/A380/A380066.seq
|
cc344b521b34dfb4597faa9564e4139b
|
A380067
|
G.f. A(x) satisfies 0 = Sum_{n=-oo..+oo} (-x)^n * (A(x) - (-x)^n)^(3*n+1).
|
[
"1",
"2",
"9",
"76",
"605",
"5351",
"49789",
"480401",
"4766086",
"48292018",
"497690157",
"5200558352",
"54971657745",
"586748531155",
"6315126497084",
"68461134239364",
"746869322310992",
"8193320926852194",
"90327637946283912",
"1000230167386765676",
"11120012336000921992",
"124071390413266176706",
"1388854343860145268801"
] |
[
"nonn"
] | 6 | 0 | 2 |
[
"A380067",
"A380068"
] | null |
Paul D. Hanna, Jan 23 2025
| 2025-01-23T12:29:22 |
oeisdata/seq/A380/A380067.seq
|
b406df2b923c4f3a2e919fc47ace933a
|
A380068
|
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n * (A(x) + x^n)^(2*n-1).
|
[
"1",
"4",
"36",
"312",
"3440",
"40956",
"518160",
"6806320",
"92021528",
"1271748364",
"17886165344",
"255159368504",
"3683262020928",
"53700117957756",
"789606760314200",
"11696040806690484",
"174362944317804916",
"2614112736300210308",
"39388817610142696848",
"596167096482669128248",
"9059675614901834999980",
"138177866602598729509112"
] |
[
"nonn"
] | 8 | 0 | 2 |
[
"A379763",
"A379765",
"A380068"
] | null |
Paul D. Hanna, Jan 23 2025
| 2025-01-23T11:52:52 |
oeisdata/seq/A380/A380068.seq
|
3f13f08d38b46c6fce7791fb72c9823b
|
A380069
|
Semiprime 12-gonal numbers.
|
[
"33",
"217",
"793",
"4681",
"6697",
"9073",
"22177",
"58969",
"80137",
"96049",
"113401",
"132193",
"197209",
"221761",
"289441",
"382537",
"470017",
"607609",
"671977",
"694153",
"935713",
"1042417",
"1069993",
"1493857",
"1627921",
"1803601",
"1876393",
"2181961",
"2261953",
"2510569",
"2639737",
"2727649",
"3093697",
"3285361",
"3383353"
] |
[
"nonn"
] | 17 | 1 | 1 |
[
"A000384",
"A001358",
"A051624",
"A380069"
] | null |
Massimo Kofler, Jan 11 2025
| 2025-02-04T19:29:48 |
oeisdata/seq/A380/A380069.seq
|
a17fd630aa2d8d5fd170e1d38cad22a1
|
A380070
|
Square pyramidal numbers sp(n) with a zeroless decimal representation such that (product of decimal digits of sp(n)) / n is an integer.
|
[
"1",
"55",
"385",
"5525",
"7714",
"9455",
"31395",
"116795",
"3382596",
"6597495",
"14352975",
"38381931",
"63866976",
"67938794",
"151289984",
"726434136",
"2733212496",
"2769972525",
"6477521344",
"13765386816",
"16149163995",
"17585156875",
"19598599944",
"78466472175",
"129166736265",
"371557934784",
"597944938275",
"982218617856"
] |
[
"nonn",
"base"
] | 17 | 1 | 2 |
[
"A000330",
"A007954",
"A052382",
"A380070"
] | null |
Ctibor O. Zizka, Jan 11 2025
| 2025-01-12T09:13:16 |
oeisdata/seq/A380/A380070.seq
|
047b5f1f494a88a73590bbae0381a77a
|
A380071
|
Integers with at least 1 instance of 2 or more Pythagorean proper factorizations that yield the same diagonal length.
|
[
"880",
"1344",
"3120",
"3240",
"3840",
"4032",
"4400",
"5184",
"5280",
"6144",
"6300",
"6480",
"6720",
"7680",
"8448",
"8640",
"10752",
"11520",
"11880",
"12096",
"14080",
"14592",
"14784",
"14960",
"15120",
"15360",
"16128",
"16200",
"16560",
"17820",
"18240",
"18432",
"19200",
"19440",
"20700",
"21120",
"21504",
"21840",
"22000"
] |
[
"nonn"
] | 10 | 1 | 1 |
[
"A380071",
"A380436"
] | null |
Charles L. Hohn, Jan 11 2025
| 2025-03-11T16:21:15 |
oeisdata/seq/A380/A380071.seq
|
2d3643bcbb26e1c98e7613163fd43753
|
A380072
|
Ordered hypotenuses of Pythagorean triangles having legs that add up to a square.
|
[
"35",
"41",
"140",
"164",
"205",
"221",
"315",
"369",
"389",
"391",
"560",
"656",
"689",
"775",
"820",
"875",
"884",
"1025",
"1189",
"1260",
"1476",
"1556",
"1564",
"1565",
"1625",
"1715",
"1739",
"1781",
"1845",
"1855",
"1989",
"2009",
"2240",
"2624",
"2756",
"2835",
"3100",
"3280",
"3321",
"3500",
"3501",
"3519",
"3536",
"3865",
"3869",
"4100",
"4105"
] |
[
"nonn"
] | 10 | 1 | 1 |
[
"A000290",
"A007913",
"A009000",
"A088319",
"A379830",
"A380072",
"A380073",
"A380074"
] | null |
Felix Huber, Jan 18 2025
| 2025-01-25T23:01:34 |
oeisdata/seq/A380/A380072.seq
|
0dc5b6f0bd584d0c867c8f7c9594d73f
|
A380073
|
Long legs of Pythagorean triangles having legs that add up to a square ordered by increasing hypotenuse.
|
[
"28",
"40",
"112",
"160",
"156",
"204",
"252",
"360",
"340",
"345",
"448",
"640",
"561",
"744",
"624",
"700",
"816",
"1000",
"861",
"1008",
"1440",
"1360",
"1380",
"1173",
"1624",
"1372",
"1645",
"1581",
"1404",
"1729",
"1836",
"1960",
"1792",
"2560",
"2244",
"2268",
"2976",
"2496",
"3240",
"2800",
"3060",
"3105",
"3264",
"3577",
"3285",
"4000",
"3816"
] |
[
"nonn"
] | 9 | 1 | 1 |
[
"A000290",
"A007913",
"A046084",
"A089548",
"A379830",
"A380072",
"A380073",
"A380074"
] | null |
Felix Huber, Jan 18 2025
| 2025-01-25T19:04:32 |
oeisdata/seq/A380/A380073.seq
|
242816293c59b9c41fb2edd6cb208f01
|
A380074
|
Short legs of Pythagorean triangles having legs that add up to a square ordered by increasing hypotenuse.
|
[
"21",
"9",
"84",
"36",
"133",
"85",
"189",
"81",
"189",
"184",
"336",
"144",
"400",
"217",
"532",
"525",
"340",
"225",
"820",
"756",
"324",
"756",
"736",
"1036",
"57",
"1029",
"564",
"820",
"1197",
"672",
"765",
"441",
"1344",
"576",
"1600",
"1701",
"868",
"2128",
"729",
"2100",
"1701",
"1656",
"1360",
"1464",
"2044",
"900",
"1513",
"2541",
"781",
"2340",
"3280"
] |
[
"nonn"
] | 9 | 1 | 1 |
[
"A000290",
"A007913",
"A046083",
"A089547",
"A379830",
"A380072",
"A380073",
"A380074"
] | null |
Felix Huber, Jan 18 2025
| 2025-01-25T23:01:39 |
oeisdata/seq/A380/A380074.seq
|
f36cb1a5f0940f3e1d173fa14d388242
|
A380075
|
Records in A379899.
|
[
"2",
"3",
"7",
"11",
"13",
"17",
"29",
"37",
"41",
"53",
"59",
"67",
"71",
"79",
"83",
"103",
"107",
"127",
"131",
"139",
"151",
"163",
"167",
"179",
"181",
"193",
"197",
"229",
"233",
"241",
"257",
"269",
"277",
"281",
"293",
"313",
"317",
"337",
"349",
"353",
"373",
"389",
"397",
"401",
"409",
"421",
"433",
"449",
"457",
"461",
"509",
"521",
"541",
"557",
"569",
"571"
] |
[
"nonn"
] | 10 | 1 | 1 |
[
"A379899",
"A380075",
"A380076"
] | null |
Paolo Xausa, Jan 11 2025
| 2025-01-11T18:47:24 |
oeisdata/seq/A380/A380075.seq
|
525e53ef9164b4766a0084af9c1cffc7
|
A380076
|
Indices of records in A379899.
|
[
"1",
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"10",
"11",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"42",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"105",
"106",
"107",
"108",
"109",
"110",
"111",
"112",
"113",
"114"
] |
[
"nonn"
] | 6 | 1 | 2 |
[
"A379899",
"A380075",
"A380076"
] | null |
Paolo Xausa, Jan 11 2025
| 2025-01-11T18:47:31 |
oeisdata/seq/A380/A380076.seq
|
1912ed6574f868d4851be087bf54c577
|
A380077
|
Expansion of e.g.f. (1/x) * Series_Reversion( x * sqrt(1 - 2*x*exp(x)) ).
|
[
"1",
"1",
"7",
"87",
"1621",
"40485",
"1271841",
"48220207",
"2143450009",
"109350344745",
"6298638659245",
"404371344546411",
"28633701543626037",
"2217105596852342989",
"186362307297569836993",
"16901012222196104542695",
"1644911203243501609414321",
"171017059743998995011125457",
"18916512667390427993433246357"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A213644",
"A380035",
"A380077",
"A380078"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-12T07:56:04 |
oeisdata/seq/A380/A380077.seq
|
919c378b973c63084bc9d7ab82f97685
|
A380078
|
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - 3*x*exp(x))^(1/3) ).
|
[
"1",
"1",
"8",
"115",
"2484",
"72005",
"2626846",
"115688349",
"5974568552",
"354154378249",
"23704428986010",
"1768459611322481",
"145525743200753356",
"13095070459815108141",
"1279226572751177845718",
"134827003107939467441845",
"15250595677663579282034256",
"1842758049329907303778372625"
] |
[
"nonn"
] | 12 | 0 | 3 |
[
"A213644",
"A380039",
"A380077",
"A380078"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-12T07:56:32 |
oeisdata/seq/A380/A380078.seq
|
5d55171e9ff8422b256d78436ad6ac94
|
A380079
|
Start with a list of the positive integers L in increasing order. Then, at turn n>=1, element n jumps from its current position, m, to position m+n. Then a(n) = L(m+1).
|
[
"2",
"1",
"2",
"5",
"3",
"7",
"4",
"5",
"10",
"6",
"7",
"13",
"8",
"15",
"9",
"10",
"18",
"11",
"20",
"12",
"13",
"23",
"14",
"15",
"26",
"16",
"28",
"17",
"18",
"31",
"19",
"20",
"34",
"21",
"36",
"22",
"23",
"39",
"24",
"41",
"25",
"26",
"44",
"27",
"28",
"47",
"29",
"49",
"30",
"31",
"52",
"32",
"54",
"33",
"34",
"57",
"35",
"36",
"60",
"37",
"62",
"38",
"39",
"65",
"40",
"41",
"68",
"42",
"70",
"43",
"44",
"73",
"45",
"75"
] |
[
"nonn"
] | 57 | 1 | 1 |
[
"A003622",
"A368050",
"A380079"
] | null |
Ali Sada and David Nacin, Jan 11 2025
| 2025-05-09T07:19:25 |
oeisdata/seq/A380/A380079.seq
|
3faded0931a5c90ce47f4e7bfa1d19c7
|
A380080
|
Expansion of e.g.f. (1/x) * Series_Reversion( x / sqrt(1 + 2*x*exp(x)) ).
|
[
"1",
"1",
"3",
"15",
"109",
"1045",
"12501",
"179599",
"3015657",
"57988809",
"1257058585",
"30337358491",
"806837271021",
"23448335293981",
"739379851041573",
"25143044445680295",
"917252832237053521",
"35735484803144976145",
"1480838869407287923569",
"65038486139094829172275",
"3017945328547452509505045"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A161633",
"A380050",
"A380080",
"A380081"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-12T07:56:27 |
oeisdata/seq/A380/A380080.seq
|
cc3c57b24f4a0ed255a7693cf0d94f4c
|
A380081
|
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + 3*x*exp(x))^(1/3) ).
|
[
"1",
"1",
"2",
"7",
"36",
"245",
"2086",
"21357",
"255704",
"3507625",
"54258570",
"934600601",
"17743468612",
"368146983789",
"8288468950958",
"201258635444245",
"5243025162331056",
"145871455305823697",
"4316920830720239122",
"135408946029576741297",
"4487574630295937337500",
"156686063319198543135061"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A161633",
"A380051",
"A380080",
"A380081"
] | null |
Seiichi Manyama, Jan 11 2025
| 2025-01-12T07:54:39 |
oeisdata/seq/A380/A380081.seq
|
64a22dd5ebb711d0a311a5149eb49c51
|
A380082
|
Number of Boolean intervals of rank 2 in the weak order of the Coxeter group of type C_n, for n >= 2.
|
[
"0",
"12",
"288",
"5760",
"115200",
"2419200",
"54190080",
"1300561920",
"33443020800",
"919683072000",
"26977370112000",
"841693947494400",
"27852417898905600",
"974834626461696000",
"35993893900124160000",
"1398619877261967360000",
"57063690992288268288000",
"2439472789920323469312000",
"109058783549379166863360000"
] |
[
"nonn"
] | 36 | 2 | 2 | null | null |
J. Carlos Martínez Mori, Feb 18 2025
| 2025-06-02T15:29:01 |
oeisdata/seq/A380/A380082.seq
|
4554e7842dea773efccf5d8b9fbf3d72
|
A380083
|
a(n) = Pell(n^2)/Pell(n).
|
[
"1",
"6",
"197",
"39236",
"45232349",
"304285766994",
"11928254138546089",
"2725453049877127789064",
"3629520789795568149638626009",
"28171611459441395148628640333550174",
"1274457582507820938168220698796661580252461",
"336039604487720392926819615640785342048933644491212"
] |
[
"nonn",
"easy"
] | 27 | 1 | 2 |
[
"A000129",
"A002203",
"A051294",
"A204327",
"A380083",
"A383742"
] | null |
Seiichi Manyama, May 08 2025
| 2025-05-08T07:12:03 |
oeisdata/seq/A380/A380083.seq
|
0cdd86ba8602c79d048faff679b83013
|
A380084
|
a(n) is the smallest k such that tau(k*2^n + 1) is equal to 2^n where tau = A000005.
|
[
"0",
"1",
"5",
"13",
"59",
"502",
"3086",
"32728",
"421769",
"8386552",
"65004026",
"2038040548",
"35000607914",
"1421414035177",
"16443388379486",
"254428547171833",
"8299070462599934",
"414388820258496592",
"12913991195998809671",
"269894765095528969273",
"9577265986738655465699",
"486911530180828201016287"
] |
[
"nonn"
] | 25 | 0 | 3 |
[
"A000005",
"A377634",
"A380084"
] | null |
Juri-Stepan Gerasimov, Jan 11 2025
| 2025-02-03T23:05:05 |
oeisdata/seq/A380/A380084.seq
|
7d93e11afa82503d84bc62be28ef06df
|
A380085
|
The largest unitary divisor of n that is a term in A276078.
|
[
"1",
"2",
"3",
"1",
"5",
"6",
"7",
"1",
"9",
"10",
"11",
"3",
"13",
"14",
"15",
"1",
"17",
"18",
"19",
"5",
"21",
"22",
"23",
"3",
"25",
"26",
"1",
"7",
"29",
"30",
"31",
"1",
"33",
"34",
"35",
"9",
"37",
"38",
"39",
"5",
"41",
"42",
"43",
"11",
"45",
"46",
"47",
"3",
"49",
"50",
"51",
"13",
"53",
"2",
"55",
"7",
"57",
"58",
"59",
"15",
"61",
"62",
"63",
"1",
"65",
"66",
"67",
"17",
"69",
"70",
"71"
] |
[
"nonn",
"easy",
"mult"
] | 10 | 1 | 2 |
[
"A000720",
"A077610",
"A276078",
"A325127",
"A377515",
"A380085",
"A380086",
"A380087",
"A380088"
] | null |
Amiram Eldar, Jan 11 2025
| 2025-01-12T03:52:10 |
oeisdata/seq/A380/A380085.seq
|
188228b3ecf60f2edc5fe3775be27f96
|
A380086
|
The number of unitary divisors of n that are terms in A276078.
|
[
"1",
"2",
"2",
"1",
"2",
"4",
"2",
"1",
"2",
"4",
"2",
"2",
"2",
"4",
"4",
"1",
"2",
"4",
"2",
"2",
"4",
"4",
"2",
"2",
"2",
"4",
"1",
"2",
"2",
"8",
"2",
"1",
"4",
"4",
"4",
"2",
"2",
"4",
"4",
"2",
"2",
"8",
"2",
"2",
"4",
"4",
"2",
"2",
"2",
"4",
"4",
"2",
"2",
"2",
"4",
"2",
"4",
"4",
"2",
"4",
"2",
"4",
"4",
"1",
"4",
"8",
"2",
"2",
"4",
"8",
"2",
"2",
"2",
"4",
"4",
"2",
"4",
"8",
"2",
"2",
"1",
"4",
"2",
"4",
"4",
"4",
"4"
] |
[
"nonn",
"easy",
"mult"
] | 11 | 1 | 2 |
[
"A000720",
"A005117",
"A034444",
"A077610",
"A276078",
"A325127",
"A377516",
"A380085",
"A380086",
"A380087",
"A380089"
] | null |
Amiram Eldar, Jan 11 2025
| 2025-01-12T03:55:01 |
oeisdata/seq/A380/A380086.seq
|
f26308c352c5cb944d4a0053d7ce2c25
|
A380087
|
The sum of the unitary divisors of n that are terms in A276078.
|
[
"1",
"3",
"4",
"1",
"6",
"12",
"8",
"1",
"10",
"18",
"12",
"4",
"14",
"24",
"24",
"1",
"18",
"30",
"20",
"6",
"32",
"36",
"24",
"4",
"26",
"42",
"1",
"8",
"30",
"72",
"32",
"1",
"48",
"54",
"48",
"10",
"38",
"60",
"56",
"6",
"42",
"96",
"44",
"12",
"60",
"72",
"48",
"4",
"50",
"78",
"72",
"14",
"54",
"3",
"72",
"8",
"80",
"90",
"60",
"24",
"62",
"96",
"80",
"1",
"84",
"144",
"68",
"18",
"96",
"144"
] |
[
"nonn",
"easy",
"mult"
] | 10 | 1 | 2 |
[
"A000720",
"A005117",
"A034448",
"A077610",
"A276078",
"A377517",
"A380085",
"A380086",
"A380087",
"A380090"
] | null |
Amiram Eldar, Jan 11 2025
| 2025-01-12T03:54:33 |
oeisdata/seq/A380/A380087.seq
|
07414c325eff02dfe77944369c13f417
|
A380088
|
The largest unitary divisor of n that is a term in A207481.
|
[
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"1",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"1",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"3",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"1",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"5",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"3",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"7",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"1",
"65",
"66",
"67",
"68",
"69",
"70"
] |
[
"nonn",
"easy",
"mult"
] | 8 | 1 | 2 |
[
"A005117",
"A054743",
"A077610",
"A185359",
"A207481",
"A377518",
"A380085",
"A380088",
"A380089",
"A380090"
] | null |
Amiram Eldar, Jan 12 2025
| 2025-01-12T03:53:28 |
oeisdata/seq/A380/A380088.seq
|
b460cd3ecebde70a2217c2062ca07080
|
A380089
|
The number of unitary divisors of n that are terms in A207481.
|
[
"1",
"2",
"2",
"2",
"2",
"4",
"2",
"1",
"2",
"4",
"2",
"4",
"2",
"4",
"4",
"1",
"2",
"4",
"2",
"4",
"4",
"4",
"2",
"2",
"2",
"4",
"2",
"4",
"2",
"8",
"2",
"1",
"4",
"4",
"4",
"4",
"2",
"4",
"4",
"2",
"2",
"8",
"2",
"4",
"4",
"4",
"2",
"2",
"2",
"4",
"4",
"4",
"2",
"4",
"4",
"2",
"4",
"4",
"2",
"8",
"2",
"4",
"4",
"1",
"4",
"8",
"2",
"4",
"4",
"8",
"2",
"2",
"2",
"4",
"4",
"4",
"4",
"8",
"2",
"2",
"1",
"4",
"2",
"8",
"4",
"4",
"4"
] |
[
"nonn",
"easy",
"mult"
] | 10 | 1 | 2 |
[
"A005117",
"A054743",
"A077610",
"A185359",
"A207481",
"A377519",
"A380086",
"A380088",
"A380089",
"A380090"
] | null |
Amiram Eldar, Jan 12 2025
| 2025-01-12T03:52:58 |
oeisdata/seq/A380/A380089.seq
|
6f1752d3cf46b341f605de7ddea825a3
|
A380090
|
The sum of the unitary divisors of n that are terms in A207481.
|
[
"1",
"3",
"4",
"5",
"6",
"12",
"8",
"1",
"10",
"18",
"12",
"20",
"14",
"24",
"24",
"1",
"18",
"30",
"20",
"30",
"32",
"36",
"24",
"4",
"26",
"42",
"28",
"40",
"30",
"72",
"32",
"1",
"48",
"54",
"48",
"50",
"38",
"60",
"56",
"6",
"42",
"96",
"44",
"60",
"60",
"72",
"48",
"4",
"50",
"78",
"72",
"70",
"54",
"84",
"72",
"8",
"80",
"90",
"60",
"120",
"62",
"96",
"80",
"1",
"84",
"144",
"68",
"90",
"96"
] |
[
"nonn",
"easy",
"mult"
] | 8 | 1 | 2 |
[
"A005117",
"A054743",
"A077610",
"A185359",
"A207481",
"A371242",
"A377520",
"A380087",
"A380088",
"A380089",
"A380090"
] | null |
Amiram Eldar, Jan 12 2025
| 2025-01-12T03:52:30 |
oeisdata/seq/A380/A380090.seq
|
c6fceb0fe76bca90fe5e6510f86a636c
|
A380091
|
Primes p such that phi(p+1) = 2*phi(p-1) where phi = A000010.
|
[
"2",
"3",
"7",
"31",
"991",
"1951",
"2521",
"7411",
"23431",
"26731",
"37441",
"92431",
"131071",
"396631",
"489061",
"532141",
"830551",
"2811691",
"3319171",
"3698941",
"4247167",
"5239411",
"6829681",
"8326711",
"8997871",
"12625831",
"12889231",
"14756743",
"15891121",
"16125721",
"16446301",
"21203071"
] |
[
"nonn"
] | 16 | 1 | 1 |
[
"A000010",
"A066812",
"A067890",
"A258454",
"A380091"
] | null |
Juri-Stepan Gerasimov, Jan 11 2025
| 2025-02-03T23:05:18 |
oeisdata/seq/A380/A380091.seq
|
00b32a42832f595959e34452e6c11576
|
A380092
|
Number of consecutive primes after prime(n) before their concatenation fails to produce a prime.
|
[
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"2",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0"
] |
[
"easy",
"nonn",
"base"
] | 10 | 1 | 11 |
[
"A000040",
"A030459",
"A219271",
"A309191",
"A380092"
] | null |
Robert G. Wilson v, Jan 12 2025
| 2025-01-23T12:37:21 |
oeisdata/seq/A380/A380092.seq
|
0644dba5b9147e6f4ef6e6223ce8231b
|
A380093
|
E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*exp(x*A(x)) ).
|
[
"1",
"1",
"1",
"6",
"13",
"180",
"501",
"13720",
"34777",
"2014992",
"2512585",
"491642976",
"-564313947",
"181714012480",
"-836832558275",
"95473740036480",
"-856984734161999",
"68029327826567424",
"-954950936641491951",
"63368301861354866176",
"-1238053892876418633155",
"74904417332353810338816"
] |
[
"sign"
] | 9 | 0 | 4 |
[
"A161631",
"A380035",
"A380050",
"A380093",
"A380094"
] | null |
Seiichi Manyama, Jan 12 2025
| 2025-01-12T07:54:36 |
oeisdata/seq/A380/A380093.seq
|
68fb39ecaebf827e92542f142b7c66e5
|
A380094
|
E.g.f. A(x) satisfies A(x) = ( 1 + 3*x*exp(x*A(x)) )^(1/3).
|
[
"1",
"1",
"0",
"7",
"-28",
"405",
"-4514",
"75313",
"-1336824",
"28494793",
"-672782950",
"17874984501",
"-521966931716",
"16702822898749",
"-579928752836874",
"21736834275178345",
"-874384126286848624",
"37581186999500130321",
"-1718628399364227445070",
"83327485224351815544925"
] |
[
"sign"
] | 8 | 0 | 4 |
[
"A161631",
"A380051",
"A380093",
"A380094"
] | null |
Seiichi Manyama, Jan 12 2025
| 2025-01-12T07:54:33 |
oeisdata/seq/A380/A380094.seq
|
818ec175258c923d7d33886bff28198c
|
A380095
|
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*A(x)^2*exp(x*A(x)^2) ).
|
[
"1",
"1",
"9",
"156",
"4129",
"147880",
"6696591",
"367141306",
"23648581713",
"1750754472840",
"146492770433095",
"13672570280741086",
"1408330043282040825",
"158697952371711709060",
"19420527592823261136519",
"2564857285665551372127570",
"363619232307437704055993761",
"55079007956127598819416831088"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A213644",
"A379688",
"A380042",
"A380095",
"A380096"
] | null |
Seiichi Manyama, Jan 12 2025
| 2025-01-12T07:56:23 |
oeisdata/seq/A380/A380095.seq
|
f31345672a16c1038f910e5d06350ec6
|
A380096
|
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*A(x)^3*exp(x*A(x)^3) )^(1/3).
|
[
"1",
"1",
"12",
"289",
"10724",
"540745",
"34551886",
"2676439507",
"243782162408",
"25535467766593",
"3024360522754010",
"399665508962874451",
"58301379215119084012",
"9305724270031402836337",
"1613262216112899513140630",
"301870732625016111841693795",
"60639884085040694650040518736"
] |
[
"nonn"
] | 12 | 0 | 3 |
[
"A213644",
"A380043",
"A380095",
"A380096",
"A380097"
] | null |
Seiichi Manyama, Jan 12 2025
| 2025-01-12T07:56:19 |
oeisdata/seq/A380/A380096.seq
|
dd23b6819bfe76c8fbae4327ff13fe66
|
A380097
|
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - 3*x*exp(x)) ).
|
[
"1",
"3",
"42",
"1089",
"42132",
"2182335",
"142084818",
"11159447943",
"1027313395944",
"108517938075387",
"12940759400071710",
"1719811206219287643",
"252076045285741340700",
"40398758175398949144039",
"7028240082095865121961514",
"1319141702032289451776382975",
"265703833060229155917857703888"
] |
[
"nonn"
] | 12 | 0 | 2 |
[
"A213644",
"A379688",
"A380096",
"A380097"
] | null |
Seiichi Manyama, Jan 12 2025
| 2025-01-12T07:56:13 |
oeisdata/seq/A380/A380097.seq
|
1ec7fd0f35c9add4b5cd7ed8f73d09e5
|
A380098
|
Numbers whose sum of cubes of distinct prime factors is prime.
|
[
"165",
"210",
"390",
"399",
"420",
"462",
"495",
"561",
"570",
"595",
"615",
"630",
"651",
"780",
"798",
"825",
"840",
"924",
"957",
"1050",
"1085",
"1140",
"1170",
"1173",
"1197",
"1218",
"1235",
"1245",
"1260",
"1302",
"1386",
"1435",
"1470",
"1482",
"1485",
"1495",
"1554",
"1560",
"1596",
"1615",
"1680",
"1683",
"1705",
"1710",
"1767",
"1771",
"1815",
"1845",
"1848",
"1885",
"1890",
"1938",
"1950",
"1953"
] |
[
"nonn"
] | 10 | 1 | 1 |
[
"A005064",
"A114522",
"A114989",
"A380098"
] | null |
Rafik Khalfi, Jan 12 2025
| 2025-01-14T10:26:32 |
oeisdata/seq/A380/A380098.seq
|
2ac5c02fbfc92d94644b14f50ed97d1e
|
A380099
|
a(n) is the n-digit numerator of the fraction h/k with h and k coprime positive integers at which abs((h/k)^4-Pi) is minimal.
|
[
"4",
"97",
"888",
"9551",
"13549",
"505311",
"4601995",
"87956765",
"298132602"
] |
[
"nonn",
"base",
"frac",
"more"
] | 33 | 1 | 1 |
[
"A000796",
"A092040",
"A130773",
"A210621",
"A355622",
"A364844",
"A380099",
"A380100"
] | null |
Stefano Spezia, Jan 12 2025
| 2025-04-21T10:44:40 |
oeisdata/seq/A380/A380099.seq
|
f97ebbe4e442015da1367323d98d6cbc
|
A380100
|
a(n) is the denominator of the fraction h/k with h and k coprime positive integers at which abs((h/k)^4-Pi) is minimal, with the numerator h of n digits.
|
[
"3",
"73",
"667",
"7174",
"10177",
"379552",
"3456676",
"66066573",
"223935013"
] |
[
"nonn",
"base",
"frac",
"more"
] | 29 | 1 | 1 |
[
"A000583",
"A000796",
"A130773",
"A210621",
"A355623",
"A364845",
"A380099",
"A380100"
] | null |
Stefano Spezia, Jan 12 2025
| 2025-04-21T10:44:49 |
oeisdata/seq/A380/A380100.seq
|
40fecff4777131ead3572e503f5902fe
|
A380101
|
Numbers k such that omega(k-th triangular number) = 2, where omega = A001221.
|
[
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"13",
"16",
"17",
"18",
"22",
"25",
"26",
"31",
"37",
"46",
"49",
"53",
"58",
"61",
"73",
"81",
"82",
"97",
"106",
"121",
"127",
"157",
"162",
"166",
"178",
"193",
"226",
"241",
"242",
"250",
"256",
"262",
"277",
"313",
"337",
"346",
"358",
"361",
"382",
"397",
"421",
"457",
"466",
"478",
"486",
"502",
"541",
"562",
"577",
"586",
"613"
] |
[
"nonn"
] | 22 | 1 | 1 |
[
"A000217",
"A001221",
"A077065",
"A119663",
"A178490",
"A380101"
] | null |
Juri-Stepan Gerasimov, Jan 12 2025
| 2025-03-13T02:54:42 |
oeisdata/seq/A380/A380101.seq
|
28255c16b9c704d6652806ce3bd67e5d
|
A380102
|
Minimal absolute discriminants |d| of imaginary quadratic number fields K = Q(sqrt(d)), d < 0, with elementary bicyclic 3-class group Cl_3(K)=(3,3) and second 3-class group M=Gal(F_3^2(K)/K) of assigned even coclass cc(M)=2,4,6,8,...
|
[
"3896",
"27156",
"423640",
"99888340"
] |
[
"nonn",
"hard",
"more"
] | 9 | 1 | 1 |
[
"A242862",
"A242863",
"A379524",
"A380102"
] | null |
Daniel Constantin Mayer, Jan 12 2025
| 2025-01-25T23:01:11 |
oeisdata/seq/A380/A380102.seq
|
be129c8f04485a78ccd09322c62df41e
|
A380103
|
Minimal conductors c of cyclic cubic number fields K with elementary bicyclic 3-class group Cl_3(K)=(3,3) and second 3-class group M=Gal(F_3^2(K)/K) of assigned coclass cc(M)=0,1,2,3,...
|
[
"657",
"2439",
"7657",
"41839",
"231469"
] |
[
"nonn",
"hard",
"more"
] | 8 | 1 | 1 |
[
"A379524",
"A380103"
] | null |
Daniel Constantin Mayer, Jan 15 2025
| 2025-01-25T23:02:05 |
oeisdata/seq/A380/A380103.seq
|
8618ebfa55ba140de2debe67d21fb02b
|
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