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timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A363401 | a(n) = Sum_{k=0..n} 2^(n - k) * Sum_{j=0..k} binomial(k, j) * ((2 - (n mod 2)) * j + 1)^n. Row sums of A363400. | [
"1",
"5",
"68",
"302",
"33104",
"64272",
"43575104",
"30313712",
"111402371328",
"25258008320",
"468857355838464",
"32779942009344",
"2941165554120118272",
"61149815860711424",
"25734702989598729256960",
"155090406558662064128",
"299529317622247725531725824",
"513370937392454603833344"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A363400",
"A363401"
]
| null | Peter Luschny, Jun 02 2023 | 2023-06-02T08:39:37 | oeisdata/seq/A363/A363401.seq | f5d85ca9857c9e9b33213f08517a05d7 |
A363402 | a(n) = n * (4^n - 2^n) / Clausen(n, 0). | [
"0",
"2",
"12",
"56",
"480",
"992",
"4032",
"16256",
"261120",
"784896",
"1047552",
"4192256",
"33546240",
"67100672",
"268419072",
"1073709056",
"34359214080",
"17179738112",
"206157643776",
"274877382656",
"2199021158400",
"4398044413952",
"17592181850112",
"70368735789056",
"1125899839733760",
"5629499366440960"
]
| [
"nonn"
]
| 5 | 0 | 2 | [
"A160014",
"A363395",
"A363402",
"A363403"
]
| null | Peter Luschny, Jun 08 2023 | 2023-06-08T08:50:19 | oeisdata/seq/A363/A363402.seq | 87691ea6460a9b60190da9ddfba8d7f4 |
A363403 | a(n) = (4^n - 2^n) / Clausen(n, 1). | [
"0",
"1",
"2",
"28",
"8",
"496",
"96",
"8128",
"2176",
"130816",
"15872",
"2096128",
"6144",
"33550336",
"44736512",
"536854528",
"8421376",
"8589869056",
"86114304",
"137438691328",
"3331850240",
"2199022206976",
"127479578624",
"35184367894528",
"103104380928",
"562949936644096",
"750599926710272",
"9007199187632128"
]
| [
"nonn"
]
| 5 | 0 | 3 | [
"A160014",
"A363395",
"A363402",
"A363403"
]
| null | Peter Luschny, Jun 08 2023 | 2023-06-08T08:50:13 | oeisdata/seq/A363/A363403.seq | ea60eeabd620173a5da04518057b44a7 |
A363404 | G.f. satisfies A(x) = exp( Sum_{k>=1} (A(x^k) + A(w*x^k) + A(w^2*x^k))/3 * x^k/k ), where w = exp(2*Pi*i/3). | [
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"4",
"5",
"5",
"10",
"12",
"13",
"26",
"34",
"36",
"73",
"96",
"104",
"210",
"288",
"315",
"638",
"881",
"974",
"1975",
"2777",
"3089",
"6276",
"8895",
"9970",
"20272",
"29000",
"32668",
"66508",
"95703",
"108347",
"220771",
"319483",
"363141",
"740615",
"1076331",
"1227826",
"2505979",
"3655912",
"4183309",
"8544123",
"12504292",
"14347462"
]
| [
"nonn"
]
| 17 | 0 | 5 | [
"A195865",
"A363336",
"A363404",
"A363405"
]
| null | Seiichi Manyama, May 31 2023 | 2023-06-01T11:11:46 | oeisdata/seq/A363/A363404.seq | a008c8607e9c98a980085e3a6707dda8 |
A363405 | G.f. satisfies A(x) = exp( Sum_{k>=1} (A(x^k) + A(i*x^k) + A(-x^k) + A(i^3*x^k))/4 * x^k/k ), where i = sqrt(-1). | [
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"4",
"5",
"5",
"5",
"10",
"12",
"13",
"13",
"26",
"34",
"36",
"37",
"74",
"97",
"105",
"107",
"215",
"293",
"320",
"328",
"658",
"905",
"998",
"1025",
"2058",
"2878",
"3194",
"3292",
"6611",
"9316",
"10412",
"10748",
"21594",
"30697",
"34470",
"35663",
"71668",
"102446",
"115575",
"119761",
"240740",
"345940",
"391726",
"406571",
"817453",
"1179322",
"1339851"
]
| [
"nonn"
]
| 20 | 0 | 6 | [
"A195865",
"A363337",
"A363404",
"A363405"
]
| null | Seiichi Manyama, May 31 2023 | 2023-06-01T11:11:42 | oeisdata/seq/A363/A363405.seq | 23fc158a1e0f51f2d252a8700b426cee |
A363406 | Start with list L = 1,2,3,4,.... For n = 1,2,3,..., iterate as follows: let j = L(1) and k = L(j+1), get a(n) = j + k, and remove j and k from L. | [
"3",
"9",
"13",
"17",
"23",
"27",
"33",
"37",
"43",
"47",
"51",
"57",
"61",
"67",
"71",
"75",
"81",
"85",
"91",
"95",
"99",
"105",
"109",
"115",
"119",
"125",
"129",
"133",
"139",
"143",
"149",
"153",
"157",
"163",
"167",
"173",
"177",
"183",
"187",
"191",
"197",
"201",
"207",
"211",
"215",
"221",
"225",
"231",
"235",
"241",
"245",
"249",
"255",
"259",
"265",
"269",
"273",
"279",
"283",
"289",
"293",
"297"
]
| [
"nonn"
]
| 42 | 1 | 1 | [
"A004641",
"A363406"
]
| null | Ali Sada and David James Sycamore, May 31 2023 | 2024-12-20T12:36:19 | oeisdata/seq/A363/A363406.seq | 81d07554130c82dfadb678163dcac38d |
A363407 | Sum of divisors of 4*n-3 of form 4*k+3. | [
"0",
"0",
"3",
"0",
"0",
"10",
"0",
"0",
"14",
"0",
"0",
"18",
"7",
"0",
"22",
"0",
"0",
"26",
"0",
"18",
"30",
"0",
"0",
"34",
"0",
"0",
"60",
"0",
"0",
"42",
"11",
"0",
"46",
"26",
"0",
"50",
"0",
"0",
"54",
"0",
"30",
"84",
"0",
"0",
"62",
"0",
"0",
"100",
"0",
"0",
"70",
"0",
"30",
"74",
"38",
"0",
"93",
"0",
"0",
"82",
"0",
"42",
"86",
"34",
"0",
"90",
"0",
"0",
"140",
"0",
"0",
"132",
"0",
"0",
"140",
"50",
"0",
"106",
"0",
"0",
"110",
"0",
"54",
"114",
"0",
"42",
"156"
]
| [
"nonn"
]
| 17 | 1 | 3 | [
"A050452",
"A359240",
"A363407",
"A364084"
]
| null | Seiichi Manyama, Jul 08 2023 | 2023-07-08T08:04:51 | oeisdata/seq/A363/A363407.seq | 59c833817fe5446a10ce92ab8b569aed |
A363408 | Squares whose base-3 expansion has no 2. | [
"0",
"1",
"4",
"9",
"36",
"81",
"121",
"256",
"324",
"361",
"729",
"841",
"1089",
"2304",
"2916",
"3025",
"3249",
"6561",
"6889",
"7569",
"9801",
"20449",
"20736",
"26244",
"26569",
"27225",
"29241",
"59049",
"60025",
"62001",
"68121",
"68644",
"88209",
"177241",
"184041",
"186624",
"203401",
"236196",
"237169",
"239121",
"245025",
"263169",
"531441",
"534361",
"540225",
"558009"
]
| [
"nonn",
"base"
]
| 15 | 1 | 3 | [
"A000290",
"A005836",
"A176189",
"A363408",
"A363428"
]
| null | Robert Israel, May 31 2023 | 2023-06-11T14:17:14 | oeisdata/seq/A363/A363408.seq | f5ad6a39f01723386d2844156e67eeca |
A363409 | a(n) = the real part of Product_{k = 1..n} (1 + k*sqrt(-2)). | [
"1",
"1",
"-3",
"-21",
"27",
"927",
"387",
"-78111",
"-211167",
"10887129",
"61228629",
"-2278564101",
"-20995423317",
"669639978711",
"9055735268283",
"-263207953694367",
"-4900375484030367",
"133357760824723281",
"3278778524907635277",
"-84617763517115570709",
"-2669012118280627019109"
]
| [
"sign",
"easy"
]
| 19 | 0 | 3 | [
"A105750",
"A363409",
"A363410",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2024-01-29T08:42:52 | oeisdata/seq/A363/A363409.seq | d131196efa73d41c8e144c9f6dc9509e |
A363410 | a(n)= 1/sqrt(2) * the imaginary part of Product_{k = 1..n} (1 + k*sqrt(-2)). | [
"0",
"1",
"3",
"-6",
"-90",
"45",
"5607",
"8316",
"-616572",
"-2517075",
"106354215",
"779869134",
"-26562900078",
"-299503403199",
"9075456298755",
"144911485323000",
"-4066415773786872",
"-87372799002303111",
"2313066895842715947",
"64609858869087786210",
"-1627745411473223627970"
]
| [
"sign",
"easy"
]
| 18 | 0 | 3 | [
"A105750",
"A105751",
"A363409",
"A363410",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2023-06-10T07:33:31 | oeisdata/seq/A363/A363410.seq | 43d3936b7b687bf22b89ce346dfdb140 |
A363411 | a(n) = the real part of Product_{k = 0..n} 1 + k*sqrt(-3). | [
"1",
"1",
"-5",
"-32",
"112",
"2212",
"-5348",
"-292880",
"276976",
"64180144",
"60400144",
"-21123205376",
"-68151050240",
"9766562233792",
"57568265355328",
"-6044149831446272",
"-54001800190537472",
"4827069458763086080",
"59568915131392086784",
"-4835221290238425841664",
"-77896195282519949963264"
]
| [
"sign",
"easy"
]
| 18 | 0 | 3 | [
"A105750",
"A363409",
"A363411",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2025-03-27T04:38:11 | oeisdata/seq/A363/A363411.seq | f385b025e24c7824c257b8edff094eb7 |
A363412 | a(n) = 1/sqrt(3) * the imaginary part of Product_{k = 0..n} 1 + k*sqrt(-3). | [
"0",
"1",
"3",
"-12",
"-140",
"420",
"13692",
"-23744",
"-2366784",
"126000",
"641927440",
"1306329024",
"-252172135488",
"-1138135788608",
"135593735484480",
"999117715814400",
"-95707279587325952",
"-1013737882826462976",
"85873512374909086464",
"1217682899871358735360",
"-95486742904897158097920"
]
| [
"sign",
"easy"
]
| 19 | 0 | 3 | [
"A105750",
"A105751",
"A363409",
"A363412",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2025-03-27T04:42:07 | oeisdata/seq/A363/A363412.seq | 225cf866c232d7c50be9d5602301b339 |
A363413 | a(n) = the real part of Product_{k = 0..n} 1 + k*sqrt(-4). | [
"1",
"1",
"-7",
"-43",
"245",
"4045",
"-20795",
"-729335",
"3118985",
"217496825",
"-667140175",
"-97338843875",
"149451128125",
"61156245509125",
"18055448952125",
"-51399370203595375",
"-123577855227019375",
"55722247285947360625",
"266112415762709595625",
"-75739843360243364046875",
"-560236984557463079546875"
]
| [
"sign",
"easy"
]
| 13 | 0 | 3 | [
"A105750",
"A363409",
"A363413",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2023-06-10T05:27:19 | oeisdata/seq/A363/A363413.seq | ca0879650ae4308da5ebe463bd5631a1 |
A363414 | a(n) = (1/2) * the imaginary part of Product_{k = 0..n} 1 + k*sqrt(-4). | [
"0",
"1",
"3",
"-18",
"-190",
"1035",
"25305",
"-120260",
"-5954940",
"22115925",
"2197084175",
"-5141457750",
"-1173207584250",
"769657081375",
"856957094209125",
"1127788828491000",
"-821262134429035000",
"-2922085673288364375",
"1000078365473764126875",
"6056214264965246443750",
"-1508740652939902034493750"
]
| [
"sign",
"easy"
]
| 16 | 0 | 3 | [
"A105750",
"A105751",
"A363409",
"A363414",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2023-06-10T05:28:11 | oeisdata/seq/A363/A363414.seq | 58180fe7f86fbaf8b0ce8156e3a3a296 |
A363415 | a(n) = the real part of Product_{k = 0..n} 1 + k*sqrt(-5). | [
"1",
"1",
"-9",
"-54",
"426",
"6426",
"-50274",
"-1465884",
"10992996",
"552727476",
"-3792193524",
"-312571718424",
"1853425616616",
"248005863100296",
"-1173524207653224",
"-263102748395914224",
"865735128320476176",
"359884863190774985616",
"-584551982838131141904",
"-616984573598760535235424",
"-155177934223071790979424"
]
| [
"sign",
"easy"
]
| 15 | 0 | 3 | [
"A105750",
"A363409",
"A363415",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2025-03-27T05:43:54 | oeisdata/seq/A363/A363415.seq | dc055cb5dba2ef70ecc926f239d23c9b |
A363416 | a(n) = 1/sqrt(5) * the imaginary part of Product_{k = 0..n} 1 + k*sqrt(-5). | [
"0",
"1",
"3",
"-24",
"-240",
"1890",
"40446",
"-311472",
"-12038544",
"86898420",
"5614173180",
"-36099955584",
"-3786960576672",
"20307572439336",
"3492389655843480",
"-14110473458954880",
"-4223754447793582464",
"10493742733654512528",
"6488421280167604253616",
"-4618066393756887442560",
"-12344309538368967592151040"
]
| [
"sign",
"easy"
]
| 16 | 0 | 3 | [
"A105750",
"A105751",
"A363409",
"A363415",
"A363416"
]
| null | Peter Bala, Jun 01 2023 | 2023-06-10T05:17:30 | oeisdata/seq/A363/A363416.seq | 31d67a25d002734309d14a8e59c3a1e9 |
A363417 | a(n) = Sum_{j=0..2^n - 1} b(j) for n >= 0 where b(n) = (A023416(n) + 1)*b(A053645(n)) + [A036987(n) = 0]*b(A266341(n)) for n > 0 with b(0) = 1. | [
"1",
"2",
"6",
"23",
"106",
"566",
"3415",
"22872",
"167796",
"1334596",
"11414192",
"104270906",
"1011793389",
"10379989930",
"112134625986",
"1271209859403",
"15077083642150",
"186588381229340",
"2403775013224000",
"32168379148440968",
"446341838086450308",
"6410107231501731012",
"95136428354649665256"
]
| [
"nonn"
]
| 43 | 0 | 2 | [
"A000523",
"A023416",
"A036987",
"A053645",
"A266341",
"A284005",
"A329369",
"A341392",
"A347205",
"A363417"
]
| null | Mikhail Kurkov, Jun 11 2023 [verification needed] | 2024-04-21T22:11:00 | oeisdata/seq/A363/A363417.seq | 14120e071dba4a57cd136e483c62fd3b |
A363418 | Square array read by ascending antidiagonals: T(n,k) = [x^(n*k)] ((1 + x)/(1 - x))^k for n, k >= 1. | [
"2",
"2",
"8",
"2",
"16",
"38",
"2",
"24",
"146",
"192",
"2",
"32",
"326",
"1408",
"1002",
"2",
"40",
"578",
"4672",
"14002",
"5336",
"2",
"48",
"902",
"11008",
"69002",
"142000",
"28814",
"2",
"56",
"1298",
"21440",
"216002",
"1038984",
"1459810",
"157184",
"2",
"64",
"1766",
"36992",
"525002",
"4320608",
"15856206",
"15158272",
"864146"
]
| [
"nonn",
"tabl",
"easy"
]
| 25 | 1 | 1 | [
"A002003",
"A035607",
"A103885",
"A333715",
"A362724",
"A362733",
"A363418",
"A363419"
]
| null | Peter Bala, Jun 12 2023 | 2024-01-05T14:28:00 | oeisdata/seq/A363/A363418.seq | 90dd44ecb0bf8a2f7a5eaed22a3045a3 |
A363419 | Square array read by ascending antidiagonals: T(n,k) = 1/n * [x^k] 1/((1 - x)*(1 - x^2))^(n*k) for n, k >= 1. | [
"1",
"1",
"5",
"1",
"7",
"19",
"1",
"9",
"46",
"85",
"1",
"11",
"82",
"327",
"376",
"1",
"13",
"127",
"793",
"2376",
"1715",
"1",
"15",
"181",
"1547",
"7876",
"17602",
"7890",
"1",
"17",
"244",
"2653",
"19376",
"79686",
"132056",
"36693",
"1",
"19",
"316",
"4175",
"40001",
"247205",
"816684",
"1000263",
"171820",
"1",
"21",
"397",
"6177",
"73501",
"614389",
"3195046",
"8450585",
"7632433",
"809380"
]
| [
"nonn",
"tabl",
"easy"
]
| 11 | 0 | 3 | [
"A348410",
"A362724",
"A362733",
"A363418",
"A363419"
]
| null | Peter Bala, Jun 13 2023 | 2023-06-23T15:55:47 | oeisdata/seq/A363/A363419.seq | 4f66db5d557523ca825d58190fb0ca03 |
A363420 | Let D be the largest digit of a(n) + a(n+1). The successive Ds reproduce the successive digits of the sequence. By construction, we do not accept any zero in the sequence. This is the lexicographically earliest sequence of distinct terms > 0 with this property. | [
"1",
"9",
"81",
"2",
"8",
"4",
"14",
"26",
"74",
"66",
"36",
"24",
"3",
"11",
"5",
"21",
"12",
"34",
"68",
"46",
"57",
"43",
"58",
"47",
"55",
"45",
"56",
"64",
"39",
"65",
"41",
"7",
"17",
"19",
"6",
"31",
"13",
"18",
"27",
"51",
"53",
"22",
"23",
"28",
"15",
"35",
"16",
"44",
"62",
"42",
"61",
"29",
"32",
"73",
"67",
"33",
"37",
"63",
"54",
"946",
"25",
"38",
"75",
"925",
"76",
"127",
"873"
]
| [
"base",
"nonn"
]
| 13 | 1 | 2 | [
"A332803",
"A363420"
]
| null | Eric Angelini, Jul 03 2023 | 2023-08-02T11:52:28 | oeisdata/seq/A363/A363420.seq | 7372dd672d9367c22a4ad7abeed41e57 |
A363421 | a(n) = Sum_{k=0..n}(n^[not(k | n)] - n^[k | n]), where '[ ]' denotes the Iverson bracket. | [
"1",
"0",
"-1",
"0",
"-3",
"8",
"-5",
"24",
"7",
"32",
"27",
"80",
"11",
"120",
"91",
"112",
"105",
"224",
"119",
"288",
"171",
"280",
"315",
"440",
"207",
"480",
"475",
"520",
"459",
"728",
"435",
"840",
"651",
"832",
"891",
"952",
"665",
"1224",
"1147",
"1216",
"975",
"1520",
"1107",
"1680",
"1419",
"1496",
"1755",
"2024",
"1363",
"2112",
"1911",
"2200",
"2091"
]
| [
"sign"
]
| 40 | 0 | 5 | [
"A000005",
"A113704",
"A363421",
"A363734",
"A363735"
]
| null | Peter Luschny, Jun 27 2023 | 2023-08-06T08:15:56 | oeisdata/seq/A363/A363421.seq | b7ee2e75bf2ac774f12af30667a416e9 |
A363422 | Numbers k which satisfy k = concat(a,b,...) and a*b*... = reverse(k), for some two or more a,b,... | [
"351",
"621",
"886",
"5931",
"86673",
"97533",
"425322",
"430762",
"920781",
"3524751",
"4495491",
"4834872",
"5594151",
"5941971",
"6218001",
"6801381",
"6916671",
"8630841",
"32331001",
"44235301",
"57982563",
"67968432",
"68577483",
"69617484",
"71673981",
"88873491",
"89943354",
"119910901",
"338752611"
]
| [
"nonn",
"base"
]
| 23 | 1 | 1 | [
"A265737",
"A267939",
"A281555",
"A363422"
]
| null | David L. Reens, Jun 01 2023 | 2023-07-27T12:16:40 | oeisdata/seq/A363/A363422.seq | 5417aa4677a954f572314ee70e60baf3 |
A363423 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(3*x^k) * x^k/k ). | [
"1",
"1",
"4",
"40",
"1126",
"92440",
"22559276",
"16468584194",
"36033333480881",
"236450784546518006",
"4654297351684653345788",
"274836259327539399144691019",
"48686693681325683653963188907344",
"25874153864215746591981599665978198380"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A000081",
"A179470",
"A359018",
"A363423",
"A363424"
]
| null | Seiichi Manyama, Jun 01 2023 | 2023-06-02T10:19:17 | oeisdata/seq/A363/A363423.seq | 7bbd1d91bc3e9ca678f7053efb741078 |
A363424 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(4*x^k) * x^k/k ). | [
"1",
"1",
"5",
"85",
"5535",
"1422815",
"1458410395",
"5975113492155",
"97902240525033630",
"6416219161308006188750",
"1681979772433159156954845846",
"1763685303864317080584539713676102",
"7397434088431352859937186709876628421294"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A000081",
"A179470",
"A359186",
"A363423",
"A363424"
]
| null | Seiichi Manyama, Jun 01 2023 | 2023-06-02T10:19:14 | oeisdata/seq/A363/A363424.seq | ba98dc19c92db9fd70ce4baf8399e568 |
A363425 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(2*x^k) * x^k/k ). | [
"1",
"1",
"2",
"10",
"89",
"1521",
"50300",
"3271556",
"422093896",
"108481853032",
"55651639993132",
"57043042723263188",
"116881250986006852062",
"478862542730584327952230",
"3923320929876295358082556380",
"64283613915707884845087288240332"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A004111",
"A179470",
"A318368",
"A363425",
"A363426",
"A363427"
]
| null | Seiichi Manyama, Jun 01 2023 | 2023-06-02T10:19:10 | oeisdata/seq/A363/A363425.seq | af4c15f3f783679be354b0b279521d7f |
A363426 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(3*x^k) * x^k/k ). | [
"1",
"1",
"3",
"30",
"840",
"68934",
"16821865",
"12280119400",
"26868936914550",
"176313989066991255",
"3470564614854890465955",
"204936840860491674903711726",
"36304151491699938200267389259775",
"19293550877461959142221066537253871070"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A004111",
"A363338",
"A363423",
"A363425",
"A363426",
"A363427"
]
| null | Seiichi Manyama, Jun 01 2023 | 2023-06-02T10:19:07 | oeisdata/seq/A363/A363426.seq | aeba86ed383b8e02f3317cd07a90ce7a |
A363427 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(4*x^k) * x^k/k ). | [
"1",
"1",
"4",
"68",
"4422",
"1136646",
"1165077220",
"4773325045092",
"78210934437541505",
"5125710024629047469249",
"1343679254641311248179226112",
"1408951161809404147369817577873792",
"5909570902737024213107077083032728540592"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A004111",
"A363339",
"A363424",
"A363425",
"A363426",
"A363427"
]
| null | Seiichi Manyama, Jun 01 2023 | 2023-06-02T10:19:03 | oeisdata/seq/A363/A363427.seq | 1a9370c01984554ab8368915b2406efb |
A363428 | Squares whose base-3 expansion has no 0. | [
"1",
"4",
"16",
"25",
"49",
"121",
"400",
"484",
"1444",
"1849",
"3364",
"5476",
"10201",
"10609",
"10816",
"12769",
"17161",
"19321",
"19600",
"155236",
"169744",
"274576",
"286225",
"344569",
"346921",
"450241",
"502681",
"863041",
"885481",
"984064",
"1042441",
"4008004",
"4190209",
"4596736",
"7203856",
"7263025",
"7706176",
"12752041",
"14326225",
"14341369",
"23833924"
]
| [
"nonn",
"base"
]
| 17 | 1 | 2 | [
"A000290",
"A032924",
"A363408",
"A363428"
]
| null | Robert Israel, Jun 01 2023 | 2023-06-19T10:43:13 | oeisdata/seq/A363/A363428.seq | 9aa31c492a078ffe50026e868bdc288a |
A363429 | Number of set partitions of [n] such that each block has at most one even element. | [
"1",
"1",
"2",
"5",
"10",
"37",
"77",
"372",
"799",
"4736",
"10427",
"73013",
"163967",
"1322035",
"3017562",
"27499083",
"63625324",
"646147067",
"1512354975",
"16926317722",
"40012800675",
"489109544320",
"1166271373797",
"15455199988077",
"37134022033885",
"530149003318273",
"1282405154139046",
"19619325078384593"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A000110",
"A110132",
"A124421",
"A134980",
"A363429",
"A363430"
]
| null | Alois P. Heinz, Jun 01 2023 | 2023-06-01T16:48:18 | oeisdata/seq/A363/A363429.seq | c593285efd12ba1580c523efccaf5931 |
A363430 | Number of set partitions of [n] such that each block has at most one odd element. | [
"1",
"1",
"2",
"3",
"10",
"17",
"77",
"141",
"799",
"1540",
"10427",
"20878",
"163967",
"338233",
"3017562",
"6376149",
"63625324",
"137144475",
"1512354975",
"3315122947",
"40012800675",
"88981537570",
"1166271373797",
"2626214876310",
"37134022033885",
"84540738911653",
"1282405154139046",
"2948058074576995"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A000110",
"A110138",
"A124423",
"A134980",
"A363429",
"A363430"
]
| null | Alois P. Heinz, Jun 01 2023 | 2023-06-01T16:59:53 | oeisdata/seq/A363/A363430.seq | bc2932dd365eb5e0385e5887d646f3da |
A363431 | Number of 123-avoiding stabilized-interval-free permutations of size n. | [
"1",
"1",
"1",
"2",
"5",
"14",
"44",
"150",
"496",
"1758",
"6018",
"21782",
"76414",
"280448",
"1001752",
"3714032",
"13450270",
"50259604",
"183995056",
"691863078",
"2555043320",
"9657267848",
"35921300392",
"136360740016",
"510267869416",
"1944193285228",
"7312488701868",
"27950641500876",
"105590010259396",
"404724123141348",
"1534775681029994"
]
| [
"nonn"
]
| 14 | 0 | 4 | [
"A075834",
"A363431"
]
| null | Juan B. Gil, Jun 22 2023 | 2023-09-01T04:46:04 | oeisdata/seq/A363/A363431.seq | a802a13f8ab8bde1b4dee2bdc142338e |
A363432 | Number of 231-avoiding stabilized-interval-free permutations of size n. | [
"1",
"1",
"1",
"1",
"2",
"6",
"18",
"54",
"170",
"551",
"1817",
"6092",
"20722",
"71325",
"248055",
"870402",
"3077861",
"10959008",
"39261382",
"141430953",
"512002865",
"1861872379",
"6798330676",
"24915934639",
"91630864177",
"338048560865",
"1250793108398",
"4640542045919",
"17260221009367",
"64349394615738",
"240434325753052"
]
| [
"nonn"
]
| 10 | 0 | 5 | [
"A000108",
"A075834",
"A363432"
]
| null | Juan B. Gil, Jun 22 2023 | 2023-07-29T03:18:37 | oeisdata/seq/A363/A363432.seq | f1ef791a22f931cd192f18b81d62c0f2 |
A363433 | Number of (123,231)-avoiding stabilized-interval-free permutations of size n. | [
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"3",
"5",
"5",
"7",
"7",
"10",
"9",
"13",
"12",
"16",
"15",
"20",
"18",
"24",
"22",
"28",
"26",
"33",
"30",
"38",
"35",
"43",
"40",
"49",
"45",
"55",
"51",
"61",
"57",
"68",
"63",
"75",
"70",
"82",
"77",
"90",
"84",
"98",
"92",
"106",
"100",
"115",
"108",
"124",
"117",
"133",
"126",
"143",
"135",
"153",
"145",
"163",
"155",
"174",
"165",
"185",
"176",
"196"
]
| [
"nonn",
"easy"
]
| 19 | 0 | 6 | [
"A075834",
"A363431",
"A363432",
"A363433"
]
| null | Juan B. Gil, Jun 30 2023 | 2023-11-18T18:08:54 | oeisdata/seq/A363/A363433.seq | 5c663f4db7ae2d9da1242194a75675a0 |
A363434 | Total number of blocks containing only elements of the same parity in all partitions of [n]. | [
"0",
"1",
"2",
"7",
"24",
"97",
"412",
"1969",
"9898",
"54461",
"313944",
"1947613",
"12603100",
"86760255",
"620559230",
"4682462777",
"36586620348",
"299664171115",
"2534306825064",
"22355119509231",
"203115201624030",
"1917124624702475",
"18598998656476220",
"186822424157036439",
"1925326063016510832"
]
| [
"nonn"
]
| 23 | 0 | 3 | [
"A000035",
"A124424",
"A363434",
"A363435",
"A363451",
"A363452",
"A363453"
]
| null | Alois P. Heinz, Jun 01 2023 | 2023-09-10T09:47:38 | oeisdata/seq/A363/A363434.seq | d64ffb97a754b9050b17c428e58fff7d |
A363435 | Number of partitions of [2n] having exactly n blocks with all elements of the same parity. | [
"1",
"0",
"5",
"42",
"569",
"9470",
"191804",
"4534502",
"122544881",
"3721101192",
"125331498349",
"4634063018948",
"186515332107196",
"8114659545679752",
"379362605925991692",
"18961051425453713478",
"1008752282616284996865",
"56905048753221935350268",
"3392250956149146382053539"
]
| [
"nonn"
]
| 21 | 0 | 3 | [
"A124424",
"A363434",
"A363435",
"A363451"
]
| null | Alois P. Heinz, Jun 01 2023 | 2023-10-21T03:26:58 | oeisdata/seq/A363/A363435.seq | 21477be4fd818145b5c50d0384138a65 |
A363436 | Array read by ascending antidiagonals: A(n, k) = k*n^2, with k >= 0. | [
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"4",
"2",
"0",
"0",
"9",
"8",
"3",
"0",
"0",
"16",
"18",
"12",
"4",
"0",
"0",
"25",
"32",
"27",
"16",
"5",
"0",
"0",
"36",
"50",
"48",
"36",
"20",
"6",
"0",
"0",
"49",
"72",
"75",
"64",
"45",
"24",
"7",
"0",
"0",
"64",
"98",
"108",
"100",
"80",
"54",
"28",
"8",
"0",
"0",
"81",
"128",
"147",
"144",
"125",
"96",
"63",
"32",
"9",
"0",
"0",
"100",
"162",
"192",
"196",
"180",
"150",
"112",
"72",
"36",
"10",
"0"
]
| [
"nonn",
"easy",
"tabl"
]
| 28 | 0 | 8 | [
"A000007",
"A000290",
"A000578",
"A001105",
"A001477",
"A002415",
"A004247",
"A008586",
"A008591",
"A008598",
"A008607",
"A016742",
"A016766",
"A016802",
"A016850",
"A033428",
"A033429",
"A033581",
"A033582",
"A033583",
"A033584",
"A044102",
"A064761",
"A064762",
"A064763",
"A135453",
"A139098",
"A144555",
"A152691",
"A152742",
"A195321",
"A195322",
"A195323",
"A195824",
"A244630",
"A244631",
"A244632",
"A244633",
"A244634",
"A244635",
"A244636",
"A363436"
]
| null | Stefano Spezia, Jul 08 2023 | 2023-08-02T14:40:59 | oeisdata/seq/A363/A363436.seq | 38dee17a71a2d8e65b8dad926c5975c3 |
A363437 | Decimal expansion of the volume of the regular tetrahedron inscribed in the unit-radius sphere. | [
"5",
"1",
"3",
"2",
"0",
"0",
"2",
"3",
"9",
"2",
"7",
"9",
"6",
"6",
"7",
"3",
"4",
"6",
"2",
"3",
"0",
"3",
"5",
"4",
"4",
"7",
"1",
"5",
"5",
"7",
"2",
"9",
"5",
"5",
"1",
"6",
"1",
"3",
"1",
"2",
"0",
"1",
"5",
"5",
"6",
"6",
"8",
"4",
"5",
"5",
"7",
"2",
"2",
"3",
"1",
"2",
"7",
"6",
"4",
"6",
"5",
"1",
"2",
"4",
"3",
"0",
"2",
"0",
"2",
"3",
"7",
"5",
"3",
"8",
"0",
"3",
"8",
"5",
"1",
"9",
"6",
"1",
"7",
"2",
"1",
"9",
"1",
"4",
"6",
"2",
"7",
"4",
"2",
"8",
"8",
"8",
"4",
"6",
"6",
"8",
"6",
"6",
"8",
"5",
"2"
]
| [
"nonn",
"cons"
]
| 8 | 0 | 1 | [
"A020781",
"A020829",
"A118273",
"A122553",
"A137914",
"A156546",
"A187110",
"A210974",
"A232812",
"A236555",
"A339259",
"A363437",
"A363438"
]
| null | Amiram Eldar, Jun 02 2023 | 2025-02-07T13:43:24 | oeisdata/seq/A363/A363437.seq | e13da09d82d5a11b48a3c0629ad194ca |
A363438 | Decimal expansion of the volume of the regular dodecahedron inscribed in the unit-radius sphere. | [
"2",
"7",
"8",
"5",
"1",
"6",
"3",
"8",
"6",
"3",
"1",
"2",
"2",
"6",
"2",
"2",
"9",
"6",
"7",
"2",
"9",
"2",
"5",
"5",
"4",
"9",
"1",
"2",
"7",
"3",
"5",
"9",
"4",
"6",
"9",
"8",
"7",
"8",
"9",
"9",
"3",
"2",
"1",
"7",
"7",
"2",
"0",
"7",
"6",
"3",
"3",
"1",
"9",
"9",
"2",
"6",
"3",
"7",
"0",
"2",
"4",
"1",
"4",
"7",
"4",
"1",
"6",
"2",
"5",
"5",
"1",
"5",
"0",
"3",
"2",
"9",
"1",
"0",
"6",
"4",
"9",
"3",
"0",
"9",
"4",
"4",
"4",
"8",
"5",
"1",
"3",
"4",
"7",
"6",
"6",
"4",
"8",
"0",
"8",
"8",
"0",
"6",
"5",
"4",
"2"
]
| [
"nonn",
"cons"
]
| 7 | 1 | 1 | [
"A001622",
"A102769",
"A118273",
"A122553",
"A131595",
"A179296",
"A232810",
"A237603",
"A239798",
"A339259",
"A341906",
"A363437",
"A363438"
]
| null | Amiram Eldar, Jun 02 2023 | 2025-02-07T13:44:09 | oeisdata/seq/A363/A363438.seq | e78e1868783c6253c2be3f05e6fe29b4 |
A363439 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ). | [
"1",
"3",
"18",
"108",
"702",
"4698",
"32913",
"236844",
"1747170",
"13131639",
"100239444",
"774932832",
"6055105590",
"47742847875",
"379381851684",
"3035174325246",
"24426965179593",
"197622494260479",
"1606332527049645",
"13111628672610153",
"107428845309125157"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A000081",
"A179469",
"A363423",
"A363439",
"A363440"
]
| null | Seiichi Manyama, Jun 02 2023 | 2023-06-03T09:01:51 | oeisdata/seq/A363/A363439.seq | 49b26ff7c3b326789fd88e73c2c881b0 |
A363440 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (4*x)^k/k ). | [
"1",
"4",
"32",
"256",
"2208",
"19712",
"183808",
"1763328",
"17332992",
"173621248",
"1766188288",
"18196260864",
"189474570240",
"1990887063552",
"21082432966656",
"224766598100992",
"2410570956881920",
"25988893875994624",
"281505478557407232",
"3062014088362049536"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A000081",
"A179469",
"A363424",
"A363439",
"A363440"
]
| null | Seiichi Manyama, Jun 02 2023 | 2023-06-03T09:01:48 | oeisdata/seq/A363/A363440.seq | 01b7ded2ecab60cf39fb033e086f8974 |
A363441 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ). | [
"1",
"2",
"4",
"16",
"52",
"208",
"840",
"3520",
"15008",
"65344",
"288408",
"1288416",
"5813744",
"26460800",
"121333200",
"559991712",
"2599385536",
"12127405952",
"56837861376",
"267473333120",
"1263354463056",
"5987210061184",
"28461008374480",
"135672151034304",
"648406644570048"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A004111",
"A179469",
"A363425",
"A363441",
"A363442",
"A363443"
]
| null | Seiichi Manyama, Jun 02 2023 | 2023-06-03T09:01:40 | oeisdata/seq/A363/A363441.seq | 2c6edfe9352f0905f835411e5adc2171 |
A363442 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (3*x)^k/k ). | [
"1",
"3",
"9",
"54",
"270",
"1620",
"9828",
"61884",
"397062",
"2597508",
"17232831",
"115722918",
"784996434",
"5371325217",
"37029240315",
"256948639344",
"1793271890988",
"12579466538187",
"88645665923244",
"627235978623318",
"4454619888380355",
"31743030458459169",
"226890102674671245"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A004111",
"A363426",
"A363439",
"A363441",
"A363442",
"A363443"
]
| null | Seiichi Manyama, Jun 02 2023 | 2023-06-03T09:01:57 | oeisdata/seq/A363/A363442.seq | a533f2e1a3467a6bcff808ead33fe5a7 |
A363443 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (4*x)^k/k ). | [
"1",
"4",
"16",
"128",
"864",
"6912",
"55936",
"470016",
"4025600",
"35144704",
"311190784",
"2789206016",
"25254028288",
"230652174336",
"2122466561024",
"19659305379840",
"183146187440128",
"1714933158969344",
"16131631511164928",
"152366562180972544"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A004111",
"A363427",
"A363440",
"A363441",
"A363442",
"A363443"
]
| null | Seiichi Manyama, Jun 02 2023 | 2023-06-03T09:01:54 | oeisdata/seq/A363/A363443.seq | 3f63e626e367a81f7e16de73097d44e2 |
A363444 | a(n) = n for n <= 3; for n > 3, a(n) is the smallest positive number that has not yet appeared that includes as factors the distinct prime factors of a(n-2) and a(n-1) that are not shared between a(n-2) and a(n-1). | [
"1",
"2",
"3",
"6",
"4",
"9",
"12",
"8",
"15",
"30",
"10",
"18",
"45",
"20",
"24",
"60",
"5",
"36",
"90",
"25",
"42",
"210",
"35",
"48",
"420",
"70",
"21",
"120",
"140",
"63",
"150",
"280",
"84",
"75",
"350",
"126",
"105",
"40",
"168",
"315",
"50",
"252",
"525",
"80",
"294",
"630",
"55",
"462",
"840",
"110",
"231",
"1050",
"220",
"693",
"1260",
"330",
"77",
"1470",
"660",
"154",
"735",
"990",
"308",
"945",
"1320",
"616",
"1155"
]
| [
"nonn"
]
| 16 | 1 | 2 | [
"A098550",
"A336957",
"A351495",
"A359804",
"A362600",
"A362754",
"A363444"
]
| null | Scott R. Shannon, Jun 02 2023 | 2023-06-07T00:08:36 | oeisdata/seq/A363/A363444.seq | 00e7b7b822d16493f5c3524112bba59b |
A363445 | Turn sequence of a fractal-like curve which is also the perimeter around an aperiodic tiling based on the "hat" monotile. See the comments section for details. | [
"3",
"-2",
"3",
"-2",
"3",
"2",
"0",
"2",
"-3",
"2",
"3",
"2",
"-3",
"2",
"3",
"-2",
"3",
"-2",
"3",
"-2",
"0",
"2",
"-3",
"2",
"3",
"-2",
"0",
"2",
"-3",
"2",
"3",
"-2",
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"2",
"-3",
"2",
"3",
"2",
"-3",
"-2",
"3",
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"-2",
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"2",
"-3",
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"3",
"2",
"-3",
"-2",
"3",
"-2",
"3",
"-2",
"3",
"-2",
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"2",
"-3",
"-2",
"3",
"-2",
"0",
"2",
"-3",
"2",
"3",
"-2",
"0",
"2",
"-3",
"2",
"3",
"2",
"-3",
"-2",
"3",
"-2",
"0",
"2",
"-3",
"-2"
]
| [
"sign"
]
| 73 | 1 | 1 | [
"A003500",
"A003699",
"A033890",
"A052530",
"A061278",
"A108946",
"A363348",
"A363445"
]
| null | Thomas Scheuerle, Jul 09 2023 | 2025-01-06T22:05:10 | oeisdata/seq/A363/A363445.seq | 7e3565c374765a7ea469bd05bc12c174 |
A363446 | Increasing sequence such that a(1) = 1 and a(n) is the least integer such that every segment of the sequence a(1),a(2),...,a(n) has a unique sum of elements. | [
"1",
"2",
"4",
"5",
"8",
"10",
"14",
"21",
"25",
"26",
"28",
"31",
"36",
"38",
"55",
"56",
"66",
"68",
"88",
"91",
"92",
"94",
"102",
"125",
"127",
"136",
"140",
"158",
"162",
"164",
"180",
"182",
"201",
"217",
"220",
"226",
"228",
"240",
"241",
"259",
"261",
"275",
"314",
"331",
"337",
"342",
"356",
"366",
"380",
"391",
"408",
"432",
"441",
"444",
"456",
"469",
"478",
"548",
"560",
"565",
"574",
"577",
"580",
"586",
"628",
"639",
"696",
"701",
"707",
"730",
"731",
"732",
"733",
"752",
"759",
"773",
"849",
"877",
"890",
"922"
]
| [
"nonn"
]
| 44 | 1 | 2 | [
"A101274",
"A276661",
"A363446"
]
| null | Bartlomiej Pawlik, Jul 09 2023 | 2023-08-05T21:56:14 | oeisdata/seq/A363/A363446.seq | 965dfe31e9756440cbfcc4daf49cd6b2 |
A363447 | a(0) = 0; a(n) = a(a(n-1))-1 mod (n+1) for all n >= 1. | [
"0",
"1",
"0",
"3",
"2",
"5",
"4",
"1",
"0",
"9",
"8",
"11",
"10",
"7",
"0",
"15",
"14",
"17",
"16",
"13",
"6",
"3",
"2",
"23",
"22",
"1",
"0",
"27",
"26",
"29",
"28",
"25",
"0",
"33",
"32",
"35",
"34",
"31",
"24",
"21",
"2",
"41",
"40",
"1",
"0",
"45",
"44",
"47",
"46",
"43",
"0",
"51",
"50",
"53",
"52",
"49",
"42",
"39",
"20",
"5",
"4",
"1",
"0",
"63",
"62",
"65",
"64",
"61",
"0",
"69",
"68",
"71"
]
| [
"nonn",
"easy",
"look"
]
| 18 | 0 | 4 | [
"A145465",
"A268176",
"A363447"
]
| null | Curtis Bechtel, Jun 02 2023 | 2024-07-17T20:28:36 | oeisdata/seq/A363/A363447.seq | 9e8b5c885c89b658b66c0c336fa29d41 |
A363448 | Number of noncrossing partitions of the n-set with no pair of singletons {i} and {j} that can be merged into {i,j} and leave the partition a noncrossing partition. | [
"1",
"1",
"1",
"4",
"9",
"26",
"77",
"232",
"725",
"2299",
"7415",
"24223",
"79983",
"266553",
"895333",
"3028093",
"10303085",
"35243330",
"121128329",
"418080561",
"1448564695",
"5036434577",
"17566314287",
"61445833012",
"215503978367",
"757666696926",
"2669811026147",
"9427368738487",
"33353695100085",
"118217920021287"
]
| [
"nonn",
"hard"
]
| 83 | 0 | 4 | [
"A000108",
"A363448",
"A363449"
]
| null | Julien Rouyer, Jun 02 2023 | 2025-01-27T11:35:05 | oeisdata/seq/A363/A363448.seq | e52eb6945f6722643d1e1a0530fbb78f |
A363449 | Number of noncrossing partitions of the n-set with some pair of singletons {i} and {j} that can be merged into {i,j} and leave the partition a noncrossing-partition. | [
"0",
"0",
"1",
"1",
"5",
"16",
"55",
"197",
"705",
"2563",
"9381",
"34563",
"128029",
"476347",
"1779107",
"6666752",
"25054585",
"94401460",
"356510371",
"1349182629",
"5115555725",
"19429832443",
"73916249353",
"281613780638",
"1074400168957",
"4104279704526",
"15697542046005",
"60106182177517",
"230394256650275",
"884024296630081",
"3395269379129779"
]
| [
"nonn",
"hard"
]
| 61 | 0 | 5 | [
"A000108",
"A363448",
"A363449"
]
| null | Julien Rouyer, Jun 02 2023 | 2024-07-21T19:58:14 | oeisdata/seq/A363/A363449.seq | 5755a87731fe4cbd46ba040e67df590c |
A363450 | Partial sums of A180405. | [
"2",
"3",
"7",
"13",
"16",
"23",
"31",
"41",
"52",
"67",
"79",
"97",
"111",
"127",
"149",
"173",
"192",
"223",
"251",
"271",
"294",
"331",
"367",
"397",
"423",
"457",
"486",
"521",
"563",
"601",
"641",
"673",
"712",
"757",
"809",
"853",
"907",
"953",
"1009",
"1069",
"1112",
"1163",
"1213",
"1277",
"1361",
"1409",
"1458",
"1511",
"1579",
"1637",
"1699",
"1777",
"1847",
"1913",
"1970"
]
| [
"nonn",
"easy"
]
| 23 | 1 | 1 | [
"A180405",
"A363379",
"A363450"
]
| null | Neal Gersh Tolunsky, Jun 02 2023 | 2023-06-06T08:17:47 | oeisdata/seq/A363/A363450.seq | 1ea127aac862b202d79b5f1d5eaad543 |
A363451 | Number of partitions of [n] such that the number of blocks containing only odd elements equals the number of blocks containing only even elements. | [
"1",
"0",
"2",
"2",
"9",
"23",
"99",
"353",
"1778",
"7927",
"45273",
"238797",
"1526331",
"9215950",
"65020448",
"439742641",
"3388075807",
"25270974635",
"210763775071",
"1713657668021",
"15359474721088",
"134902169999841",
"1291589459223627",
"12165062702520422",
"123780591852786693",
"1242763745129587332"
]
| [
"nonn"
]
| 18 | 0 | 3 | [
"A000110",
"A363434",
"A363435",
"A363451",
"A363454"
]
| null | Alois P. Heinz, Jun 02 2023 | 2023-10-20T08:52:02 | oeisdata/seq/A363/A363451.seq | 3cb40748fcf91faa796b593a37b17bd3 |
A363452 | Total number of blocks containing only odd elements in all partitions of [n]. | [
"0",
"1",
"1",
"5",
"12",
"62",
"206",
"1189",
"4949",
"31775",
"156972",
"1110280",
"6301550",
"48637701",
"310279615",
"2591820857",
"18293310174",
"164218811718",
"1267153412532",
"12152174863961",
"101557600812015",
"1035203191874931",
"9299499328238110",
"100314319611860936",
"962663031508255416"
]
| [
"nonn"
]
| 19 | 0 | 4 | [
"A000110",
"A094577",
"A124420",
"A363434",
"A363452",
"A363453"
]
| null | Alois P. Heinz, Jun 02 2023 | 2023-12-08T07:12:15 | oeisdata/seq/A363/A363452.seq | 9e29b64cbf26b4d624968a5c66d1af03 |
A363453 | Total number of blocks containing only even elements in all partitions of [n]. | [
"0",
"0",
"1",
"2",
"12",
"35",
"206",
"780",
"4949",
"22686",
"156972",
"837333",
"6301550",
"38122554",
"310279615",
"2090641920",
"18293310174",
"135445359397",
"1267153412532",
"10202944645270",
"101557600812015",
"881921432827544",
"9299499328238110",
"86508104545175503",
"962663031508255416"
]
| [
"nonn"
]
| 21 | 0 | 4 | [
"A000110",
"A094577",
"A124422",
"A363434",
"A363452",
"A363453"
]
| null | Alois P. Heinz, Jun 02 2023 | 2023-12-08T07:11:44 | oeisdata/seq/A363/A363453.seq | b0cbf4386cad47aab8a0342305ee7243 |
A363454 | Number of partitions of [n] such that the number of blocks containing only odd elements equals the number of blocks containing only even elements and no block contains both odd and even elements. | [
"1",
"0",
"1",
"1",
"2",
"4",
"11",
"28",
"87",
"266",
"952",
"3381",
"13513",
"53915",
"237113",
"1046732",
"5016728",
"24186664",
"125121009",
"652084528",
"3615047527",
"20211789423",
"119384499720",
"711572380960",
"4455637803543",
"28162688795697",
"186152008588691",
"1242276416218540",
"8636436319397292"
]
| [
"nonn"
]
| 17 | 0 | 5 | [
"A000110",
"A047797",
"A124419",
"A124425",
"A363451",
"A363454"
]
| null | Alois P. Heinz, Jun 02 2023 | 2023-06-02T21:57:23 | oeisdata/seq/A363/A363454.seq | 6da3acd4e7c5225004f8f0d7363bddcd |
A363455 | The number of distinct primorial numbers (A002110) larger than 1 in the representation of A025487(n) as a product of primorial numbers. | [
"0",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"2",
"2",
"2",
"1",
"2",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"3",
"2",
"2",
"2",
"2",
"1",
"2",
"3",
"2",
"2",
"2",
"1",
"2",
"1",
"2",
"2",
"2",
"1",
"3",
"2",
"2",
"2",
"2",
"2",
"1",
"3",
"2",
"1",
"3",
"2",
"3",
"2",
"2",
"2",
"2",
"2",
"1",
"3",
"2",
"2",
"3",
"2",
"2",
"3",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"1",
"1",
"3",
"2",
"2",
"3",
"2",
"3",
"3"
]
| [
"nonn"
]
| 8 | 1 | 6 | [
"A002110",
"A006939",
"A025487",
"A051282",
"A071625",
"A100778",
"A304886",
"A363455",
"A363456"
]
| null | Amiram Eldar, Jun 03 2023 | 2023-06-03T07:26:45 | oeisdata/seq/A363/A363455.seq | b5132b922d91a4fdb6d83954d51c328e |
A363456 | Positions of the terms of the Chernoff sequence (A006939) in A025487. | [
"1",
"2",
"6",
"27",
"150",
"900",
"5697",
"37226",
"246280",
"1648592",
"11204274"
]
| [
"nonn",
"more"
]
| 8 | 0 | 2 | [
"A006939",
"A025487",
"A098718",
"A098719",
"A293635",
"A306802",
"A346043",
"A346407",
"A363455",
"A363456"
]
| null | Amiram Eldar, Jun 03 2023 | 2025-04-22T21:55:07 | oeisdata/seq/A363/A363456.seq | 84fd491b43333d6e919483967e982ae4 |
A363457 | Positions of products of distinct primorial numbers (A129912) in the sequence of products of primorial numbers (A025487). | [
"1",
"2",
"4",
"6",
"9",
"13",
"20",
"22",
"27",
"29",
"43",
"54",
"55",
"66",
"72",
"89",
"93",
"112",
"114",
"123",
"140",
"147",
"150",
"175",
"186",
"223",
"232",
"242",
"246",
"274",
"279",
"285",
"290",
"332",
"371",
"376",
"425",
"433",
"439",
"442",
"488",
"500",
"518",
"535",
"539",
"570",
"619",
"624",
"656",
"718",
"747",
"761",
"783",
"789",
"816",
"831",
"860"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A002110",
"A025487",
"A051282",
"A129912",
"A363455",
"A363457"
]
| null | Amiram Eldar, Jun 03 2023 | 2025-04-27T03:22:50 | oeisdata/seq/A363/A363457.seq | 2af87ea5f3e5eedeb35fa85d0b49b510 |
A363458 | Numbers k such that k and k+1 are both in A363457. | [
"1",
"54",
"242883",
"246962",
"261643",
"266001",
"353893",
"380287",
"425818",
"457055",
"542950",
"581942",
"595440",
"831264",
"917311",
"980235",
"1256341",
"1719654",
"6239931",
"8237549",
"8378312",
"10995744",
"11650985",
"15123420",
"15194370",
"15442721",
"19628056",
"20034738",
"20308106",
"26218271",
"36099782"
]
| [
"nonn"
]
| 5 | 1 | 2 | [
"A002110",
"A025487",
"A129912",
"A363457",
"A363458"
]
| null | Amiram Eldar, Jun 03 2023 | 2023-06-03T07:27:58 | oeisdata/seq/A363/A363458.seq | c8b719bcdab3cbc3208f118b7dc01a7c |
A363459 | Sum of the first n prime powers A246655. | [
"2",
"5",
"9",
"14",
"21",
"29",
"38",
"49",
"62",
"78",
"95",
"114",
"137",
"162",
"189",
"218",
"249",
"281",
"318",
"359",
"402",
"449",
"498",
"551",
"610",
"671",
"735",
"802",
"873",
"946",
"1025",
"1106",
"1189",
"1278",
"1375",
"1476",
"1579",
"1686",
"1795",
"1908",
"2029",
"2154",
"2281",
"2409",
"2540",
"2677",
"2816",
"2965",
"3116",
"3273",
"3436"
]
| [
"nonn"
]
| 22 | 1 | 1 | [
"A000961",
"A007504",
"A024918",
"A057820",
"A246655",
"A363459"
]
| null | Bartlomiej Pawlik, Jun 03 2023 | 2025-06-22T06:31:14 | oeisdata/seq/A363/A363459.seq | 55f0ec203b12e1d2d8b30145fdbd7204 |
A363460 | a(n) is the permanent of the n X n matrix formed by placing 1..n^2 in L-shaped gnomons in alternating directions. | [
"1",
"1",
"11",
"556",
"74964",
"21700112",
"11500685084",
"10057140949968",
"13496937368200000",
"26331147893897760544",
"71606290155732170272320",
"262516365211410942628577408",
"1262517559940020030446967822592",
"7786463232979127181938238723356160",
"60414239829783205320232261233394491136"
]
| [
"nonn"
]
| 19 | 0 | 3 | [
"A006527",
"A037270",
"A060736",
"A061349",
"A081344",
"A220603",
"A220604",
"A363376",
"A363460"
]
| null | Stefano Spezia, Jun 03 2023 | 2023-06-08T08:52:20 | oeisdata/seq/A363/A363460.seq | 36dc0ad805eb2e14322da04ac2694014 |
A363461 | Least n-untouchable number. | [
"2",
"208",
"388",
"298",
"838"
]
| [
"nonn",
"more"
]
| 7 | 1 | 1 | [
"A005114",
"A152454",
"A283152",
"A284147",
"A284156",
"A284187",
"A363461"
]
| null | Jinyuan Wang, Jun 03 2023 | 2023-06-22T05:59:29 | oeisdata/seq/A363/A363461.seq | 8b5bb55decb588bada16bd997b827957 |
A363462 | Numbers k for which the arithmetic derivative k' (A003415) is a Fibonacci number (A000045). | [
"1",
"2",
"3",
"5",
"6",
"7",
"11",
"13",
"15",
"17",
"18",
"19",
"22",
"23",
"29",
"31",
"37",
"38",
"41",
"43",
"47",
"53",
"59",
"61",
"67",
"71",
"73",
"75",
"79",
"83",
"89",
"93",
"97",
"101",
"103",
"106",
"107",
"109",
"113",
"127",
"131",
"137",
"139",
"145",
"149",
"151",
"157",
"163",
"167",
"173",
"179",
"181",
"191",
"193",
"197",
"199",
"211",
"223",
"227",
"229"
]
| [
"nonn"
]
| 16 | 1 | 2 | [
"A000040",
"A000045",
"A003415",
"A362141",
"A363462"
]
| null | Marius A. Burtea, Jul 05 2023 | 2023-08-05T22:02:29 | oeisdata/seq/A363/A363462.seq | 7120258ae2cf1d35c55d37f6934ad8d7 |
A363463 | a(n) is the smallest number k with exactly n of its divisors in A052294. | [
"1",
"3",
"6",
"12",
"18",
"48",
"36",
"192",
"72",
"84",
"144",
"3072",
"168",
"5985",
"576",
"336",
"504",
"26505",
"672",
"45045",
"840",
"1344",
"6510",
"129675",
"2016",
"1680",
"11970",
"4620",
"4032",
"389025",
"3360",
"888615",
"6552",
"13020",
"53010",
"6720",
"8736",
"855855",
"90090",
"23940",
"13104",
"2411955",
"17472",
"2417415",
"26040"
]
| [
"nonn",
"base"
]
| 9 | 0 | 2 | [
"A052294",
"A363463"
]
| null | Marius A. Burtea, Jul 08 2023 | 2023-08-05T22:02:48 | oeisdata/seq/A363/A363463.seq | 9449bb65ef6f87009b00b854553cc884 |
A363464 | Numbers k in A052294 with arithmetic derivative k' (A003415) in A052294. | [
"6",
"9",
"10",
"14",
"18",
"20",
"21",
"22",
"24",
"25",
"33",
"34",
"35",
"38",
"40",
"42",
"44",
"48",
"49",
"52",
"62",
"65",
"66",
"68",
"69",
"70",
"76",
"80",
"84",
"88",
"91",
"93",
"94",
"96",
"100",
"104",
"110",
"115",
"117",
"118",
"121",
"132",
"133",
"134",
"138",
"140",
"143",
"144",
"145",
"148",
"152",
"155",
"158",
"164",
"174",
"182",
"185",
"186",
"188",
"192"
]
| [
"nonn",
"base"
]
| 21 | 1 | 1 | [
"A000120",
"A003415",
"A052294",
"A057733",
"A081092",
"A092506",
"A104070",
"A123250",
"A363464"
]
| null | Marius A. Burtea, Jul 08 2023 | 2023-08-05T22:04:21 | oeisdata/seq/A363/A363464.seq | 40720ce9c3a0a566047101fcbae11337 |
A363465 | G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^3 / (k*x^(2*k)) ). | [
"1",
"1",
"1",
"4",
"10",
"35",
"113",
"405",
"1447",
"5369",
"20143",
"76908",
"296800",
"1157784",
"4554142",
"18050308",
"72003513",
"288880549",
"1164867528",
"4718481975",
"19190711729",
"78338352168",
"320851617424",
"1318115448886",
"5430133003281",
"22427330328214",
"92847100210382",
"385217596191075",
"1601483701650310"
]
| [
"nonn"
]
| 6 | 1 | 4 | [
"A007562",
"A052751",
"A363387",
"A363465",
"A363466",
"A363467"
]
| null | Ilya Gutkovskiy, Jun 03 2023 | 2023-06-03T14:22:13 | oeisdata/seq/A363/A363465.seq | b6da575543f79dbf9122f52bd528d8a1 |
A363466 | G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^4 / (k*x^(3*k)) ). | [
"1",
"1",
"1",
"5",
"15",
"61",
"240",
"1019",
"4387",
"19462",
"87649",
"401077",
"1856698",
"8685295",
"40978465",
"194806667",
"932141498",
"4486014160",
"21699575863",
"105443142514",
"514469464550",
"2519437043753",
"12379461876092",
"61013509071216",
"301553269618318",
"1494229881209940",
"7421627743464582",
"36942997716584746"
]
| [
"nonn"
]
| 6 | 1 | 4 | [
"A007562",
"A052773",
"A363387",
"A363465",
"A363466",
"A363468"
]
| null | Ilya Gutkovskiy, Jun 03 2023 | 2023-06-03T14:22:16 | oeisdata/seq/A363/A363466.seq | 73e85ae395bb280a57daaefb5c8417c5 |
A363467 | G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^3 / (k*x^(2*k)) ). | [
"1",
"1",
"1",
"3",
"9",
"25",
"88",
"292",
"1031",
"3685",
"13433",
"49608",
"185465",
"699963",
"2664650",
"10217130",
"39428179",
"153009240",
"596761737",
"2337875430",
"9195732624",
"36301739221",
"143780858517",
"571191310205",
"2275409450019",
"9087376470138",
"36377539265376",
"145937953205705",
"586645566919856"
]
| [
"nonn"
]
| 6 | 1 | 4 | [
"A007560",
"A052755",
"A363388",
"A363465",
"A363467",
"A363468"
]
| null | Ilya Gutkovskiy, Jun 03 2023 | 2023-06-03T14:22:30 | oeisdata/seq/A363/A363467.seq | 08c812890d872ce965a8d244960357e1 |
A363468 | G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^4 / (k*x^(3*k)) ). | [
"1",
"1",
"1",
"4",
"14",
"48",
"201",
"812",
"3455",
"14961",
"65954",
"294884",
"1334526",
"6098879",
"28114885",
"130561444",
"610244889",
"2868547475",
"13552299256",
"64316483918",
"306473091394",
"1465727378317",
"7033293786125",
"33851816310445",
"163384902125185",
"790589562321385",
"3834540111072545",
"18638976010097900"
]
| [
"nonn"
]
| 6 | 1 | 4 | [
"A007560",
"A052775",
"A363388",
"A363466",
"A363467",
"A363468"
]
| null | Ilya Gutkovskiy, Jun 03 2023 | 2023-06-03T14:22:34 | oeisdata/seq/A363/A363468.seq | 6d03c8f51eef8ab664f3812517529c79 |
A363469 | Multiplicative order of 2 modulo 2*prime(n)+1. | [
"4",
"3",
"10",
"4",
"11",
"18",
"12",
"12",
"23",
"58",
"6",
"20",
"82",
"28",
"36",
"106",
"24",
"20",
"36",
"60",
"42",
"52",
"83",
"178",
"12",
"84",
"66",
"28",
"18",
"226",
"8",
"131",
"20",
"30",
"132",
"100",
"12",
"36",
"132",
"346",
"179",
"110",
"191",
"42",
"156",
"18",
"138",
"148",
"12",
"72",
"466",
"239",
"66",
"251",
"204",
"40",
"210",
"180",
"36",
"562",
"54",
"586"
]
| [
"nonn"
]
| 20 | 1 | 1 | [
"A002326",
"A363469"
]
| null | Alain Rocchelli, Jun 03 2023 | 2023-06-10T08:09:48 | oeisdata/seq/A363/A363469.seq | 5fcd5a4849c08177cac473d5130b1a56 |
A363470 | G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ). | [
"1",
"2",
"-1",
"-6",
"7",
"42",
"-58",
"-366",
"513",
"3406",
"-4846",
"-33310",
"48304",
"339446",
"-499133",
"-3565468",
"5294439",
"38312242",
"-57332347",
"-419177900",
"631252549",
"4654229300",
"-7045498256",
"-52310262192",
"79531957334",
"593986308994",
"-906439292326",
"-6803984285256"
]
| [
"sign"
]
| 17 | 0 | 2 | [
"A000151",
"A200438",
"A363470",
"A363471"
]
| null | Seiichi Manyama, Jun 03 2023 | 2023-06-04T11:47:23 | oeisdata/seq/A363/A363470.seq | 1549af6c993e05da8900e85f10a7b857 |
A363471 | G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} A(-x^k) * x^k/k ). | [
"1",
"3",
"-3",
"-26",
"48",
"444",
"-920",
"-9126",
"19587",
"204214",
"-449496",
"-4841001",
"10856283",
"119585034",
"-271813440",
"-3044796399",
"6991433415",
"79341313335",
"-183641493481",
"-2105713558467",
"4905239040894",
"56722082044512",
"-132833292089826",
"-1546827734185557"
]
| [
"sign"
]
| 16 | 0 | 2 | [
"A006964",
"A200402",
"A363470",
"A363471"
]
| null | Seiichi Manyama, Jun 03 2023 | 2023-06-04T11:47:29 | oeisdata/seq/A363/A363471.seq | e2b85158f342e2497c9fb94c9d264498 |
A363472 | Total number of blocks in all partitions of [n] where each block has at least one odd element and at least one even element. | [
"0",
"0",
"1",
"1",
"5",
"13",
"55",
"193",
"941",
"4081",
"22351",
"113761",
"694565",
"4030153",
"27107095",
"175738753",
"1289775821",
"9209233921",
"73147903471",
"568928274961",
"4857161139365",
"40796613003433",
"372190216061335",
"3352314486348433",
"32518958606637101",
"312271731474218881"
]
| [
"nonn"
]
| 29 | 0 | 5 | [
"A124425",
"A362495",
"A363454",
"A363472"
]
| null | Alois P. Heinz, Jun 05 2023 | 2023-06-05T14:53:07 | oeisdata/seq/A363/A363472.seq | f061e9853a1ed79e8a78e403664ed60b |
A363473 | Triangle read by rows: T(n, k) = k * prime(n - k + A061395(k)) for 1 < k <= n, and T(n, 1) = A008578(n). | [
"1",
"2",
"4",
"3",
"6",
"9",
"5",
"10",
"15",
"8",
"7",
"14",
"21",
"12",
"25",
"11",
"22",
"33",
"20",
"35",
"18",
"13",
"26",
"39",
"28",
"55",
"30",
"49",
"17",
"34",
"51",
"44",
"65",
"42",
"77",
"16",
"19",
"38",
"57",
"52",
"85",
"66",
"91",
"24",
"27",
"23",
"46",
"69",
"68",
"95",
"78",
"119",
"40",
"45",
"50",
"29",
"58",
"87",
"76",
"115",
"102",
"133",
"56",
"63",
"70",
"121",
"31",
"62",
"93",
"92",
"145",
"114",
"161",
"88",
"99",
"110",
"143",
"36"
]
| [
"nonn",
"easy",
"tabl"
]
| 39 | 1 | 2 | [
"A000040",
"A001747",
"A001749",
"A001750",
"A008578",
"A061395",
"A112773",
"A138636",
"A253560",
"A272470",
"A363473"
]
| null | Werner Schulte, Jan 05 2024 | 2024-01-07T14:03:47 | oeisdata/seq/A363/A363473.seq | d3542cbedfd5ef67d9a9e4e383b5be9c |
A363474 | G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ). | [
"1",
"2",
"-3",
"-14",
"22",
"138",
"-213",
"-1536",
"2474",
"18928",
"-31451",
"-248992",
"420804",
"3416514",
"-5844716",
"-48349920",
"83503128",
"700674606",
"-1219159874",
"-10345673158",
"18109290380",
"155082913608",
"-272798814028",
"-2353889042848",
"4157686512816",
"36104006239798"
]
| [
"sign"
]
| 15 | 0 | 2 | [
"A005753",
"A306768",
"A363470",
"A363474",
"A363475"
]
| null | Seiichi Manyama, Jun 03 2023 | 2023-06-05T08:54:55 | oeisdata/seq/A363/A363474.seq | 865d70b1ade2732cee0b93a74fbb20b3 |
A363475 | G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ). | [
"1",
"3",
"-6",
"-44",
"96",
"918",
"-2073",
"-22278",
"52629",
"597627",
"-1451736",
"-17065641",
"42205373",
"508415817",
"-1273766637",
"-15623442097",
"39528583206",
"491601500847",
"-1253383246330",
"-15759867676416",
"40430096479776",
"512914242127868",
"-1322511998532891"
]
| [
"sign"
]
| 14 | 0 | 2 | [
"A052757",
"A306768",
"A363471",
"A363474",
"A363475"
]
| null | Seiichi Manyama, Jun 03 2023 | 2023-06-05T08:47:17 | oeisdata/seq/A363/A363475.seq | 198b9bab7a3bf1f5938931e25778af27 |
A363476 | a(n) = Fibonacci(n)^2 * Fibonacci(n+1)^3. | [
"0",
"1",
"8",
"108",
"1125",
"12800",
"140608",
"1565109",
"17333064",
"192329500",
"2132531225",
"23651979264",
"262296652032",
"2908947562937",
"32260582549000",
"357775937196300",
"3967793428038237",
"44003514081895936",
"488006404120114496",
"5412074146674562125",
"60020821224245910600"
]
| [
"nonn",
"easy"
]
| 18 | 0 | 3 | [
"A000045",
"A066258",
"A197424",
"A363476"
]
| null | Feryal Alayont, Jun 03 2023 | 2023-06-20T22:29:03 | oeisdata/seq/A363/A363476.seq | 76eecaaa50f77ed6d2a5ccb9103436fa |
A363477 | Numbers that are integer averages of first k odd primes for some k. | [
"3",
"4",
"5",
"133",
"169",
"1117",
"2406",
"3564",
"6141",
"7429",
"8220",
"8475",
"14193",
"33543",
"121049",
"211785",
"877650",
"5948070",
"8494543",
"27820975",
"41428418",
"130490020",
"139053727",
"200325407",
"291720414",
"893706168",
"977748014",
"2103851425",
"2173904606",
"5996888467",
"15790305181"
]
| [
"nonn"
]
| 15 | 1 | 1 | [
"A050248",
"A071148",
"A097961",
"A363477"
]
| null | Ya-Ping Lu, Jun 07 2023 | 2023-06-16T13:46:02 | oeisdata/seq/A363/A363477.seq | abd1fc2e84861e2d59cbb2db5501d444 |
A363478 | E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x)^3). | [
"1",
"1",
"9",
"142",
"3481",
"115476",
"4849639",
"246746662",
"14756605329",
"1014635520424",
"78869009859751",
"6839463570354306",
"654661145565724345",
"68559809182824171148",
"7797979656027302949159",
"957275139494698134599806",
"126152927575064012671549729"
]
| [
"nonn"
]
| 18 | 0 | 3 | [
"A362771",
"A362773",
"A363478"
]
| null | Seiichi Manyama, Aug 17 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A363/A363478.seq | 493b5cc94ec7bcd43df52913c89b0f5d |
A363479 | E.g.f. satisfies A(x) = exp(x * A(x)^3 * (1 + x * A(x)^3)). | [
"1",
"1",
"9",
"160",
"4381",
"162816",
"7663669",
"437164288",
"29317265625",
"2260685099008",
"197088986941921",
"19170218777296896",
"2058199476739788661",
"241779221463040000000",
"30847476924400409437389",
"4247859315849037948911616",
"627960846411135123552180529"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A088695",
"A361094",
"A363358",
"A363479"
]
| null | Seiichi Manyama, Aug 17 2023 | 2023-08-17T08:16:16 | oeisdata/seq/A363/A363479.seq | aafbe2aeac946437bb31f5926ce5caa1 |
A363480 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(2*x^k)^2 * x^k/k ). | [
"1",
"1",
"5",
"49",
"923",
"32603",
"2198413",
"288677317",
"74816592016",
"38536646525164",
"39578607089767640",
"81176446754286348780",
"332742981886258629407221",
"2726830211640382050679262877",
"44684572695377447660556579448947"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A005750",
"A179470",
"A363480",
"A363481"
]
| null | Seiichi Manyama, Jun 04 2023 | 2023-06-04T12:07:10 | oeisdata/seq/A363/A363480.seq | 4829dd1141b7c7d57b8adbf3fdba0bb5 |
A363481 | G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(2*x^k) * x^k/k ). | [
"1",
"2",
"11",
"108",
"1969",
"67542",
"4473663",
"582167944",
"150236569819",
"77226088637142",
"79235069050108841",
"162432444097491547308",
"665648716390456030366881",
"5454326724964994060395500598",
"89374602386639273949112262243227"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A000151",
"A179469",
"A179470",
"A363480",
"A363481"
]
| null | Seiichi Manyama, Jun 04 2023 | 2023-06-05T08:53:44 | oeisdata/seq/A363/A363481.seq | 9ec4d842b3091d6b8d3dc45386d9295b |
A363482 | Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(...(n-1)-n/(-5))))). | [
"13",
"23",
"7",
"49",
"13",
"83",
"103",
"5",
"149",
"1",
"29",
"233",
"53",
"23",
"67",
"373",
"59",
"1",
"499",
"109",
"593",
"643",
"139",
"107",
"1",
"863",
"71",
"197",
"1049",
"223",
"1",
"179",
"53",
"1399",
"59",
"1553",
"71",
"1",
"257",
"1",
"1973",
"2063",
"431",
"173",
"67",
"349",
"2543",
"1",
"2749",
"571",
"2963",
"439",
"1",
"3299",
"683",
"3533",
"281",
"151",
"557",
"1",
"4153"
]
| [
"nonn",
"changed"
]
| 29 | 3 | 1 | [
"A006530",
"A038901",
"A051403",
"A362086",
"A363102",
"A363482"
]
| null | Mohammed Bouras, Jun 04 2023 | 2025-07-13T19:53:25 | oeisdata/seq/A363/A363482.seq | a765067202be92a1b37c45e7007170f8 |
A363483 | a(n) is the least k that has exactly n divisors whose arithmetic derivative is odd. | [
"1",
"2",
"15",
"6",
"18",
"405",
"30",
"162",
"945",
"90",
"1458",
"295245",
"210",
"450",
"25515",
"810",
"10395",
"455625",
"630",
"1062882",
"31185",
"7290",
"4050",
"156905298045",
"1890",
"354375",
"18600435",
"3150",
"280665",
"114383962274805",
"5670",
"36450",
"135135",
"590490",
"1506635235",
"3189375",
"6930",
"101250",
"922640625",
"5314410",
"22050"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A353235",
"A363483"
]
| null | Robert Israel, Jun 05 2023 | 2023-06-11T14:17:44 | oeisdata/seq/A363/A363483.seq | 5cff8f162c00e96d5354ff2ccbb73439 |
A363484 | Number of integer partitions of n covering an initial interval of positive integers with a unique mode. | [
"0",
"1",
"1",
"1",
"2",
"3",
"2",
"5",
"6",
"6",
"8",
"11",
"12",
"17",
"20",
"21",
"27",
"35",
"38",
"50",
"56",
"65",
"76",
"95",
"105",
"125",
"146",
"167",
"198",
"233",
"252",
"305",
"351",
"394",
"457",
"522",
"585",
"681",
"778",
"878",
"994",
"1135",
"1269",
"1446",
"1638",
"1828",
"2067",
"2339",
"2613",
"2940",
"3301",
"3684",
"4143",
"4634",
"5156",
"5771"
]
| [
"nonn"
]
| 8 | 0 | 5 | [
"A000009",
"A000041",
"A002865",
"A008284",
"A025147",
"A096765",
"A097979",
"A105039",
"A117989",
"A243737",
"A362607",
"A362608",
"A362609",
"A362610",
"A362612",
"A362614",
"A362615",
"A363262",
"A363263",
"A363264",
"A363484",
"A363485"
]
| null | Gus Wiseman, Jun 05 2023 | 2023-06-07T08:31:52 | oeisdata/seq/A363/A363484.seq | c96ce05340d397d35ddaa1f8a6f77e93 |
A363485 | Number of integer partitions of n covering an initial interval of positive integers with more than one mode. | [
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"0",
"0",
"2",
"2",
"1",
"3",
"1",
"2",
"6",
"5",
"3",
"8",
"4",
"8",
"11",
"13",
"9",
"17",
"17",
"19",
"25",
"24",
"23",
"44",
"35",
"39",
"54",
"55",
"63",
"83",
"79",
"86",
"104",
"119",
"125",
"157",
"164",
"178",
"220",
"237",
"251",
"297",
"324",
"357",
"413",
"439",
"486",
"562",
"607",
"673",
"765",
"828",
"901",
"1040",
"1117",
"1220"
]
| [
"nonn"
]
| 6 | 0 | 7 | [
"A000009",
"A000041",
"A002865",
"A008284",
"A025147",
"A071178",
"A096765",
"A105039",
"A117989",
"A243737",
"A362607",
"A362608",
"A362609",
"A362610",
"A362611",
"A362612",
"A362614",
"A362615",
"A363263",
"A363264",
"A363484",
"A363485"
]
| null | Gus Wiseman, Jun 06 2023 | 2023-06-07T08:31:48 | oeisdata/seq/A363/A363485.seq | 2c3971f2c24c80b04ae9307fe04a1451 |
A363486 | Low mode in the multiset of prime indices of n. | [
"0",
"1",
"2",
"1",
"3",
"1",
"4",
"1",
"2",
"1",
"5",
"1",
"6",
"1",
"2",
"1",
"7",
"2",
"8",
"1",
"2",
"1",
"9",
"1",
"3",
"1",
"2",
"1",
"10",
"1",
"11",
"1",
"2",
"1",
"3",
"1",
"12",
"1",
"2",
"1",
"13",
"1",
"14",
"1",
"2",
"1",
"15",
"1",
"4",
"3",
"2",
"1",
"16",
"2",
"3",
"1",
"2",
"1",
"17",
"1",
"18",
"1",
"2",
"1",
"3",
"1",
"19",
"1",
"2",
"1",
"20",
"1",
"21",
"1",
"3",
"1",
"4",
"1",
"22",
"1",
"2",
"1"
]
| [
"nonn"
]
| 16 | 1 | 3 | [
"A000040",
"A000961",
"A001222",
"A056239",
"A112798",
"A124943",
"A124944",
"A215366",
"A241131",
"A326567",
"A326568",
"A327473",
"A327476",
"A356862",
"A359178",
"A360013",
"A360015",
"A362605",
"A362606",
"A362607",
"A362608",
"A362609",
"A362610",
"A362611",
"A362612",
"A362613",
"A362614",
"A362615",
"A362616",
"A363486",
"A363487",
"A363723",
"A363941",
"A363942",
"A363943",
"A363944"
]
| null | Gus Wiseman, Jun 23 2023 | 2023-07-05T21:37:45 | oeisdata/seq/A363/A363486.seq | 4fbca8ed7157eec249a4b71fb275fef7 |
A363487 | High mode in the multiset of prime indices of n. | [
"0",
"1",
"2",
"1",
"3",
"2",
"4",
"1",
"2",
"3",
"5",
"1",
"6",
"4",
"3",
"1",
"7",
"2",
"8",
"1",
"4",
"5",
"9",
"1",
"3",
"6",
"2",
"1",
"10",
"3",
"11",
"1",
"5",
"7",
"4",
"2",
"12",
"8",
"6",
"1",
"13",
"4",
"14",
"1",
"2",
"9",
"15",
"1",
"4",
"3",
"7",
"1",
"16",
"2",
"5",
"1",
"8",
"10",
"17",
"1",
"18",
"11",
"2",
"1",
"6",
"5",
"19",
"1",
"9",
"4",
"20",
"1",
"21",
"12",
"3",
"1",
"5",
"6",
"22",
"1",
"2"
]
| [
"nonn"
]
| 9 | 1 | 3 | [
"A000040",
"A000961",
"A001222",
"A056239",
"A112798",
"A124943",
"A124944",
"A215366",
"A241131",
"A326567",
"A326568",
"A327473",
"A327476",
"A356862",
"A359178",
"A359908",
"A360013",
"A360015",
"A362605",
"A362606",
"A362607",
"A362608",
"A362609",
"A362610",
"A362611",
"A362612",
"A362613",
"A362614",
"A362615",
"A362616",
"A363486",
"A363487",
"A363723",
"A363729",
"A363941",
"A363942",
"A363943",
"A363944"
]
| null | Gus Wiseman, Jul 04 2023 | 2023-07-05T21:37:39 | oeisdata/seq/A363/A363487.seq | 63825edc228eae8f838f64f0ef9bc9b4 |
A363488 | Even numbers whose prime factorization has at least as many 2's as non-2's. | [
"2",
"4",
"6",
"8",
"10",
"12",
"14",
"16",
"20",
"22",
"24",
"26",
"28",
"32",
"34",
"36",
"38",
"40",
"44",
"46",
"48",
"52",
"56",
"58",
"60",
"62",
"64",
"68",
"72",
"74",
"76",
"80",
"82",
"84",
"86",
"88",
"92",
"94",
"96",
"100",
"104",
"106",
"112",
"116",
"118",
"120",
"122",
"124",
"128",
"132",
"134",
"136",
"140",
"142",
"144",
"146",
"148",
"152",
"156",
"158",
"160"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A000079",
"A001222",
"A025065",
"A027336",
"A056239",
"A067538",
"A072978",
"A112798",
"A124943",
"A124944",
"A215366",
"A238495",
"A316413",
"A326567",
"A326568",
"A344296",
"A359889",
"A359908",
"A360005",
"A360013",
"A360015",
"A363486",
"A363487",
"A363488",
"A363941",
"A363942",
"A363943",
"A363944",
"A363945",
"A363949",
"A364056"
]
| null | Gus Wiseman, Jul 06 2023 | 2023-07-08T23:06:34 | oeisdata/seq/A363/A363488.seq | 24cd55eb40579c6dc1028b42a5730912 |
A363489 | Rounded mean of the multiset of prime indices of n. | [
"0",
"1",
"2",
"1",
"3",
"2",
"4",
"1",
"2",
"2",
"5",
"1",
"6",
"2",
"2",
"1",
"7",
"2",
"8",
"2",
"3",
"3",
"9",
"1",
"3",
"4",
"2",
"2",
"10",
"2",
"11",
"1",
"4",
"4",
"4",
"2",
"12",
"4",
"4",
"2",
"13",
"2",
"14",
"2",
"2",
"5",
"15",
"1",
"4",
"2",
"4",
"3",
"16",
"2",
"4",
"2",
"5",
"6",
"17",
"2",
"18",
"6",
"3",
"1",
"4",
"3",
"19",
"3",
"6",
"3",
"20",
"1",
"21",
"6",
"3",
"3",
"4",
"3",
"22",
"1",
"2",
"7"
]
| [
"nonn"
]
| 10 | 1 | 3 | [
"A000040",
"A001222",
"A056239",
"A067538",
"A088529",
"A088530",
"A112798",
"A124010",
"A316413",
"A326567",
"A326568",
"A327473",
"A327476",
"A327482",
"A359889",
"A360005",
"A363489",
"A363943",
"A363944",
"A363945",
"A363946",
"A363947",
"A363948",
"A363949",
"A363951",
"A364059",
"A364060",
"A364061"
]
| null | Gus Wiseman, Jul 07 2023 | 2023-07-08T23:06:29 | oeisdata/seq/A363/A363489.seq | f07f73ca49f2127be74c6274f7dbcd47 |
A363490 | Lexicographically earliest infinite sequence of distinct terms > 0 such that one digit of a(n) is strictly smaller than one digit of a(n+1). | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"19",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"20",
"10",
"11",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"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"
]
| [
"base",
"nonn"
]
| 19 | 1 | 2 | [
"A294069",
"A363490"
]
| null | Eric Angelini, Jun 05 2023 | 2023-06-24T13:28:08 | oeisdata/seq/A363/A363490.seq | 06eb15916b7b45a8b738e280573c4718 |
A363491 | Numbers k such that 2^k - 5 is a semiprime. | [
"7",
"13",
"14",
"16",
"19",
"28",
"30",
"31",
"40",
"42",
"51",
"54",
"55",
"58",
"62",
"68",
"85",
"88",
"96",
"111",
"112",
"116",
"128",
"148",
"160",
"162",
"188",
"192",
"198",
"220",
"222",
"236",
"242",
"276",
"300",
"318",
"319",
"320",
"332",
"372",
"373",
"398",
"420",
"428",
"432",
"458",
"460",
"482",
"505",
"520",
"532",
"542",
"546",
"556",
"650",
"692",
"714"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A001358",
"A085724",
"A363374",
"A363491"
]
| null | Kevin P. Thompson, Jun 05 2023 | 2025-04-22T16:05:19 | oeisdata/seq/A363/A363491.seq | 3b2e584b114bd6738768d4ea73102613 |
A363492 | Numbers k such that the partition number p(k) = A000041(k) can be written as a product of smaller partition numbers. | [
"0",
"1",
"7",
"8",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"17",
"18",
"19",
"21",
"24",
"39"
]
| [
"nonn",
"more"
]
| 10 | 1 | 3 | [
"A000041",
"A034878",
"A194345",
"A363492",
"A363636"
]
| null | Pontus von Brömssen, Jun 05 2023 | 2023-07-15T06:35:42 | oeisdata/seq/A363/A363492.seq | 404de9ec84009121380984a7104feceb |
A363493 | Number T(n,k) of partitions of [n] having exactly k parity changes within their blocks, n>=0, 0<=k<=max(0,n-1), read by rows. | [
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"4",
"6",
"4",
"1",
"10",
"18",
"17",
"6",
"1",
"25",
"61",
"68",
"38",
"10",
"1",
"75",
"210",
"292",
"202",
"83",
"14",
"1",
"225",
"778",
"1252",
"1116",
"576",
"170",
"22",
"1",
"780",
"3008",
"5670",
"5928",
"3899",
"1490",
"341",
"30",
"1",
"2704",
"12219",
"26114",
"32382",
"25320",
"12655",
"3856",
"678",
"46",
"1",
"10556",
"52268",
"126073",
"177666",
"163695",
"98282",
"39230",
"9418",
"1319",
"62",
"1"
]
| [
"nonn",
"tabf"
]
| 31 | 0 | 5 | [
"A000012",
"A000110",
"A027383",
"A124419",
"A152874",
"A363493",
"A363495",
"A363496",
"A363511",
"A363519",
"A363588"
]
| null | Alois P. Heinz, Jun 05 2023 | 2023-09-05T09:38:00 | oeisdata/seq/A363/A363493.seq | ff55467a9ff5eff0794ba471c6f4a665 |
A363494 | Expansion of Lenstra's profinite constant l ("el"). | [
"0",
"0",
"1",
"0",
"2",
"1",
"0",
"0",
"0",
"9",
"4",
"10",
"10",
"8",
"6",
"7",
"4",
"10",
"18",
"13",
"16",
"4",
"0",
"16",
"1",
"7",
"4",
"23",
"11",
"17",
"13",
"1",
"5",
"33",
"26"
]
| [
"nonn",
"more"
]
| 7 | 1 | 5 | null | null | Jeffrey Shallit, Jun 05 2023 | 2023-06-18T02:52:26 | oeisdata/seq/A363/A363494.seq | d6691421a367c8010bf26e79d37670a0 |
A363495 | Number of partitions of [2n+1] having exactly n parity changes within their blocks. | [
"1",
"2",
"17",
"202",
"3899",
"98282",
"3270604",
"134513166",
"6744026175",
"400657370384",
"27819913699591",
"2222485356153758",
"202085549223540498",
"20700107045049813072",
"2369116259054858660518",
"300712325745715659503258",
"42064844140178917094949029",
"6448050588990736076081469470"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A363493",
"A363495"
]
| null | Alois P. Heinz, Jun 05 2023 | 2023-06-06T17:05:33 | oeisdata/seq/A363/A363495.seq | 7a27989c1a8d6cbe619a319615365606 |
A363496 | Total number of parity changes within the blocks of all partitions of [n]. | [
"0",
"0",
"1",
"4",
"17",
"74",
"356",
"1808",
"9923",
"57442",
"354407",
"2296028",
"15704028",
"112266048",
"841442105",
"6564854864",
"53413489773",
"450789496454",
"3950844987040",
"35809477617544",
"335901221506491",
"3250110998386534",
"32453151223493139",
"333520967584364248",
"3528754456836294712"
]
| [
"nonn"
]
| 15 | 0 | 4 | [
"A000110",
"A077613",
"A363493",
"A363496",
"A363549"
]
| null | Alois P. Heinz, Jun 05 2023 | 2023-06-12T17:25:36 | oeisdata/seq/A363/A363496.seq | 4c7d1a5c3fcdade426b0828ee34a1f37 |
A363497 | a(n) = Sum_{k=0..n} floor(sqrt(k))^3. | [
"0",
"1",
"2",
"3",
"11",
"19",
"27",
"35",
"43",
"70",
"97",
"124",
"151",
"178",
"205",
"232",
"296",
"360",
"424",
"488",
"552",
"616",
"680",
"744",
"808",
"933",
"1058",
"1183",
"1308",
"1433",
"1558",
"1683",
"1808",
"1933",
"2058",
"2183",
"2399",
"2615",
"2831",
"3047",
"3263",
"3479",
"3695",
"3911",
"4127",
"4343",
"4559",
"4775",
"4991",
"5334"
]
| [
"nonn",
"easy"
]
| 45 | 0 | 3 | [
"A000196",
"A022554",
"A174060",
"A363497",
"A363498",
"A363499"
]
| null | Hans J. H. Tuenter, Jun 05 2023 | 2023-06-15T07:44:10 | oeisdata/seq/A363/A363497.seq | 0775772cf9766ddb68ed80d8de86b52b |
A363498 | a(n) = Sum_{k=0..n} floor(sqrt(k))^4. | [
"0",
"1",
"2",
"3",
"19",
"35",
"51",
"67",
"83",
"164",
"245",
"326",
"407",
"488",
"569",
"650",
"906",
"1162",
"1418",
"1674",
"1930",
"2186",
"2442",
"2698",
"2954",
"3579",
"4204",
"4829",
"5454",
"6079",
"6704",
"7329",
"7954",
"8579",
"9204",
"9829",
"11125",
"12421",
"13717",
"15013",
"16309",
"17605",
"18901",
"20197",
"21493",
"22789"
]
| [
"nonn",
"easy"
]
| 31 | 0 | 3 | [
"A000196",
"A022554",
"A174060",
"A363497",
"A363498",
"A363499"
]
| null | Hans J. H. Tuenter, Jun 05 2023 | 2023-07-20T20:17:09 | oeisdata/seq/A363/A363498.seq | 38178768414a5034e95ecc8ff977051f |
A363499 | a(n) = Sum_{k=0..n} floor(sqrt(k))^5. | [
"0",
"1",
"2",
"3",
"35",
"67",
"99",
"131",
"163",
"406",
"649",
"892",
"1135",
"1378",
"1621",
"1864",
"2888",
"3912",
"4936",
"5960",
"6984",
"8008",
"9032",
"10056",
"11080",
"14205",
"17330",
"20455",
"23580",
"26705",
"29830",
"32955",
"36080",
"39205",
"42330",
"45455",
"53231",
"61007",
"68783",
"76559",
"84335",
"92111",
"99887"
]
| [
"nonn",
"easy"
]
| 35 | 0 | 3 | [
"A000196",
"A022554",
"A174060",
"A363497",
"A363498",
"A363499"
]
| null | Hans J. H. Tuenter, Jun 05 2023 | 2023-07-20T07:22:48 | oeisdata/seq/A363/A363499.seq | 757542cf2430cd277664126da47291bb |
A363500 | Numbers k between twin primes p, q where k+p and k+q are also twin primes, and k*p and k*q are between twin primes. | [
"6",
"109505970",
"1519435260",
"22606027290",
"25980888360",
"33995114580",
"42029719620",
"45284475810",
"56527358160",
"63402770550",
"73924546080",
"82625597670",
"121883654550",
"150444654360",
"192416460810",
"210205659510",
"258719413680",
"270709718160",
"284455564050",
"309050171430"
]
| [
"nonn"
]
| 54 | 1 | 1 | [
"A066388",
"A363500",
"A364263"
]
| null | Bryce Case, Jr. and Antonio Gimenez, Jun 05 2023 | 2024-06-28T22:24:20 | oeisdata/seq/A363/A363500.seq | a56173be70aba9a2db44a93674b7ef06 |
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