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
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A355101
|
E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(exp(x) - 1).
|
[
"1",
"3",
"18",
"189",
"2952",
"63225",
"1759374",
"61261200",
"2595618720",
"130963993263",
"7734817065600",
"527276606418837",
"41005535326851456",
"3602215645092352314",
"354438336568129922052",
"38776184401330464272910",
"4686507224871009709115232",
"622194587177907979874119473"
] |
[
"nonn"
] | 10 | 0 | 2 |
[
"A048801",
"A355092",
"A355100",
"A355101"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:40:41 |
oeisdata/seq/A355/A355101.seq
|
77744e6a71c524e1de657d5684c93e57
|
A355102
|
E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(1 - exp(-x)).
|
[
"1",
"2",
"8",
"36",
"112",
"-500",
"-10056",
"24220",
"2184480",
"-8762868",
"-1076904200",
"13388615108",
"954279034416",
"-32517111227484",
"-1095519424670888",
"104108720480963940",
"63376017498217152",
"-394143964914859213828",
"17135457626785509446184",
"1359360091138085321022956"
] |
[
"sign"
] | 9 | 0 | 2 |
[
"A354574",
"A355093",
"A355102",
"A355103"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:40:46 |
oeisdata/seq/A355/A355102.seq
|
a5e123c9ec9152b1b52c4f8133a349aa
|
A355103
|
E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(1 - exp(-x)).
|
[
"1",
"3",
"18",
"135",
"1008",
"4815",
"-38826",
"-1199646",
"-563904",
"519188373",
"3420802620",
"-474196640841",
"-4490175699792",
"845516022777504",
"3767994187790868",
"-2565470448416339190",
"31376572722070203168",
"11396618210613478642335",
"-523335368250939507824250"
] |
[
"sign"
] | 9 | 0 | 2 |
[
"A354574",
"A355094",
"A355102",
"A355103"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:40:50 |
oeisdata/seq/A355/A355103.seq
|
80b08dad699acedbedd205a5bd0e921d
|
A355104
|
E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(log(1+x)).
|
[
"1",
"2",
"8",
"36",
"128",
"-120",
"-5904",
"8792",
"1015808",
"-7346016",
"-403678560",
"9772765552",
"226781102016",
"-17673167204576",
"72041280334240",
"38308664521315920",
"-1705420687695700992",
"-64315848872486436736",
"11313330167773175073408",
"-326450445457848188386944"
] |
[
"sign"
] | 9 | 0 | 2 |
[
"A354729",
"A355096",
"A355104",
"A355105"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:40:54 |
oeisdata/seq/A355/A355104.seq
|
068e59665cfbbb362c479e9ec3c80bd0
|
A355105
|
E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(log(1+x)).
|
[
"1",
"3",
"18",
"135",
"1044",
"6210",
"-5994",
"-760347",
"-3009960",
"261689616",
"1960394400",
"-220644396522",
"-1043258760828",
"366570209524896",
"-3109452797977470",
"-972076070389224105",
"36160406771040130320",
"3274635904971823559880",
"-331428842765036684941320"
] |
[
"sign"
] | 8 | 0 | 2 |
[
"A354729",
"A355097",
"A355104",
"A355105"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:40:58 |
oeisdata/seq/A355/A355105.seq
|
19417c784140f9b0e88dbb70e7b20acb
|
A355106
|
E.g.f. A(x) satisfies: A(x) = 1 + 2 * x * A(-log(1-x)).
|
[
"1",
"2",
"8",
"60",
"704",
"11640",
"254736",
"7071512",
"241414400",
"9898632864",
"478455967200",
"26853032524912",
"1728192188667072",
"126200480666269984",
"10363161616018802080",
"949530356895864383280",
"96418968027002031636480",
"10785892383962319840160640"
] |
[
"nonn"
] | 10 | 0 | 2 |
[
"A354730",
"A355098",
"A355106",
"A355107"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:41:02 |
oeisdata/seq/A355/A355106.seq
|
da96bbc7dc9a1826eb53bff541e52f06
|
A355107
|
E.g.f. A(x) satisfies: A(x) = 1 + 3 * x * A(-log(1-x)).
|
[
"1",
"3",
"18",
"189",
"2988",
"65070",
"1845666",
"65593773",
"2838648888",
"146342004696",
"8832171768840",
"615243982098438",
"48886929048261636",
"4387169287407671856",
"440884788552635315490",
"49250783623005351369405",
"6076420246639538049330288",
"823299493223605468234344696"
] |
[
"nonn"
] | 8 | 0 | 2 |
[
"A354730",
"A355099",
"A355106",
"A355107"
] | null |
Seiichi Manyama, Jun 19 2022
| 2022-06-19T08:41:06 |
oeisdata/seq/A355/A355107.seq
|
84b5cdca60b27513cdec0f972b3fad08
|
A355108
|
Maximal number of root ancestral configurations among matching gene trees and species trees with n leaves.
|
[
"0",
"1",
"2",
"4",
"6",
"10",
"15",
"25",
"35",
"55",
"80",
"130",
"182",
"286",
"416",
"676",
"936",
"1456",
"2106",
"3406",
"4758",
"7462",
"10842",
"17602",
"24372",
"37912",
"54837",
"88687",
"123891",
"194299",
"282309",
"458329",
"634349",
"986389",
"1426439",
"2306539",
"3221843",
"5052451",
"7340711",
"11917231",
"16500521"
] |
[
"nonn"
] | 25 | 1 | 3 |
[
"A003095",
"A004019",
"A091980",
"A306390",
"A355108"
] | null |
Noah A Rosenberg, Jun 19 2022
| 2022-06-25T12:54:35 |
oeisdata/seq/A355/A355108.seq
|
0a5cd2f9fe8fc0528bd5b20b6f5819f6
|
A355109
|
a(n) = 1 + Sum_{k=1..n-1} binomial(n-1,k) * 2^(k-1) * a(k).
|
[
"1",
"1",
"2",
"7",
"44",
"493",
"9974",
"372403",
"26247008",
"3559692121",
"942403603562",
"491777568765151",
"508938530329020692",
"1048381120745440503877",
"4307758467916752367544414",
"35349370769806113877653011083",
"579693879415731511179957972407624"
] |
[
"nonn"
] | 6 | 0 | 3 |
[
"A000110",
"A126443",
"A352859",
"A352860",
"A355109"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-19T12:30:35 |
oeisdata/seq/A355/A355109.seq
|
6b7e242d405408f8da77e92193591156
|
A355110
|
Expansion of e.g.f. 2 / (3 - 2*x - exp(2*x)).
|
[
"1",
"2",
"10",
"76",
"768",
"9696",
"146896",
"2596448",
"52449536",
"1191944704",
"30097334784",
"835973778432",
"25330620762112",
"831497823494144",
"29394162040580096",
"1113330929935101952",
"44979662118902366208",
"1930798895281527717888",
"87756941394038739828736",
"4210241529540625311727616"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A004123",
"A006155",
"A007405",
"A122704",
"A343672",
"A355110",
"A355111",
"A355112",
"A355113",
"A355114"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-21T12:46:12 |
oeisdata/seq/A355/A355110.seq
|
0dd4d9ece39255bc320af35b733b7494
|
A355111
|
Expansion of e.g.f. 3 / (4 - 3*x - exp(3*x)).
|
[
"1",
"2",
"11",
"93",
"1041",
"14541",
"243747",
"4767183",
"106556373",
"2679469065",
"74864397015",
"2300883358995",
"77144051804409",
"2802027511061325",
"109604157405491691",
"4593512301562215783",
"205348466229473678301",
"9753645833118762303249",
"490530576727430107027839",
"26040317900991310393061499"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A003575",
"A006155",
"A032033",
"A255927",
"A343673",
"A355110",
"A355111",
"A355112",
"A355113",
"A355114"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-21T12:46:18 |
oeisdata/seq/A355/A355111.seq
|
0ce5177da3d95ff96ba9b1a87e09dfe8
|
A355112
|
Expansion of e.g.f. 4 / (5 - 4*x - exp(4*x)).
|
[
"1",
"2",
"12",
"112",
"1376",
"21056",
"386688",
"8286720",
"202958848",
"5592199168",
"171203895296",
"5765504860160",
"211811563929600",
"8429932686999552",
"361312700788375552",
"16592261047219388416",
"812749365813312487424",
"42299637489384965537792",
"2330989060564353634271232"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A003576",
"A006155",
"A094417",
"A326324",
"A343674",
"A355110",
"A355111",
"A355112",
"A355113",
"A355114"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-21T12:46:24 |
oeisdata/seq/A355/A355112.seq
|
afaf46ecdda72d7aca5c2108afaa74a5
|
A355113
|
Expansion of e.g.f. 5 / (6 - 5*x - exp(5*x)).
|
[
"1",
"2",
"13",
"133",
"1779",
"29565",
"589705",
"13728695",
"365295695",
"10934634985",
"363678872325",
"13305294463275",
"531030788556475",
"22960273845453725",
"1069101897816615425",
"53336480697298243375",
"2838300249311563302375",
"160480124820425410172625",
"9607441647405962075600125"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A003577",
"A006155",
"A094418",
"A355110",
"A355111",
"A355112",
"A355113",
"A355114"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-21T12:46:30 |
oeisdata/seq/A355/A355113.seq
|
28075dcb29ae9b1e1b4043583eefd4e6
|
A355114
|
Expansion of e.g.f. 6 / (7 - 6*x - exp(6*x)).
|
[
"1",
"2",
"14",
"156",
"2256",
"40416",
"869040",
"21817440",
"626063616",
"20210176512",
"724888631808",
"28599923045376",
"1230970377166848",
"57397448756994048",
"2882187551571941376",
"155065468075097960448",
"8898907099302329647104",
"542609247778976191610880",
"35031706496702707368591360"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A003578",
"A006155",
"A094419",
"A355110",
"A355111",
"A355112",
"A355113",
"A355114"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-21T12:45:58 |
oeisdata/seq/A355/A355114.seq
|
d7440439638787e70cd1af067c326b2f
|
A355115
|
a(n) = index of n^2 in A355159.
|
[
"1",
"3",
"5",
"9",
"16",
"24",
"29",
"37",
"44",
"53",
"66",
"80",
"94",
"108",
"121",
"135",
"155",
"178",
"197",
"217",
"235",
"256",
"285",
"314",
"337",
"364",
"388",
"416",
"452",
"488",
"522",
"554",
"584",
"619",
"660",
"704",
"743",
"780",
"815",
"854",
"901",
"946",
"990",
"1036",
"1077",
"1120",
"1174",
"1229",
"1283",
"1336",
"1384",
"1434",
"1494"
] |
[
"nonn",
"easy"
] | 12 | 1 | 2 |
[
"A355115",
"A355159"
] | null |
Clark Kimberling, Jun 26 2022
| 2022-07-07T02:20:54 |
oeisdata/seq/A355/A355115.seq
|
270a8798af4b1766caa23ef4a40e5892
|
A355116
|
a(1) = 1; a(n+1) = Sum_{d|n} 3^(n/d - 1) * a(d).
|
[
"1",
"1",
"4",
"13",
"43",
"124",
"388",
"1117",
"3370",
"9967",
"29860",
"88909",
"266896",
"798337",
"2394553",
"7178233",
"21533029",
"64579750",
"193738672",
"581159161",
"1743472426",
"5230263235",
"15690765067",
"47071824676",
"141215472685",
"423645012649",
"1270934954221",
"3812800839124",
"11438402333398",
"34315194788359"
] |
[
"nonn"
] | 6 | 1 | 3 |
[
"A003238",
"A351405",
"A355116",
"A355117"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-24T08:30:48 |
oeisdata/seq/A355/A355116.seq
|
da512edc79e55f878b7c8372a8661490
|
A355117
|
a(1) = 1; a(n+1) = Sum_{d|n} 4^(n/d - 1) * a(d).
|
[
"1",
"1",
"5",
"21",
"89",
"345",
"1405",
"5501",
"22033",
"87649",
"350405",
"1398981",
"5596345",
"22373561",
"89492141",
"357930301",
"1431711857",
"5726679153",
"22906712645",
"91626189381",
"366504720137",
"1466016390873",
"5864065352173",
"23456251396589",
"93825005578001",
"375299982311441",
"1501199928316661"
] |
[
"nonn"
] | 5 | 1 | 3 |
[
"A003238",
"A351405",
"A355116",
"A355117"
] | null |
Ilya Gutkovskiy, Jun 19 2022
| 2022-06-24T08:30:39 |
oeisdata/seq/A355/A355117.seq
|
dfa55208bced3276ed60db911b4b0ef3
|
A355118
|
The number of nonequivalent root ancestral configurations in a recursively defined family of gene trees and species trees with at least n = 9 leaves, in which for n >= 12 leaves, 3-leaf trees are successively added at the root of the tree with n-3 leaves.
|
[
"23",
"33",
"47",
"69",
"99",
"141",
"207",
"297",
"423",
"621",
"891",
"1269",
"1863",
"2673",
"3807",
"5589",
"8019",
"11421",
"16767",
"24057",
"34263",
"50301",
"72171",
"102789",
"150903",
"216513",
"308367",
"452709",
"649539",
"925101",
"1358127",
"1948617",
"2775303",
"4074381",
"5845851",
"8325909",
"12223143",
"17537553"
] |
[
"nonn"
] | 14 | 9 | 1 | null | null |
Noah A Rosenberg, Jun 19 2022
| 2022-06-21T19:22:51 |
oeisdata/seq/A355/A355118.seq
|
f034a7ace4d5fabf5bdcdffda039a1f4
|
A355119
|
a(n) is the number of order-n magic triangles composed of the numbers from 1 to n(n+1)/2 in which the sum of the k-th row and the (n-k+1)-st row is the same for all k and all three directions, counted up to rotations and reflections.
|
[
"1",
"1",
"0",
"0",
"7584",
"5546793216"
] |
[
"nonn",
"more"
] | 38 | 1 | 5 |
[
"A000217",
"A006052",
"A008586",
"A342467",
"A355119",
"A356643",
"A356808"
] | null |
Donghwi Park, Jun 19 2022
| 2024-01-30T16:05:18 |
oeisdata/seq/A355/A355119.seq
|
1feb2a5d04dbd1400038e6334e47e3a7
|
A355120
|
E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2 * log(1+x)).
|
[
"1",
"1",
"3",
"26",
"654",
"45084",
"7934924",
"3381663872",
"3365978050576",
"7632454575648720",
"38732162420625498608",
"434139952882119137261024",
"10640704036253473615712677216",
"565765176687479152385624223741568",
"64834956096893473256448986077914291328"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A354728",
"A355084",
"A355096",
"A355120",
"A355133"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:10 |
oeisdata/seq/A355/A355120.seq
|
f80dbbf5f30778425cfa6ea9cbb6e2b7
|
A355121
|
E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(-2 * log(1-x)).
|
[
"1",
"1",
"5",
"74",
"2778",
"248244",
"51212444",
"23984832416",
"25218677193200",
"59000757443457072",
"304720138059811544048",
"3449059394896458379058208",
"84991203371449537414272981856",
"4532232538284485346856696552505728",
"520204832574009673696495358635072488576"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A135750",
"A355086",
"A355098",
"A355121"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:15 |
oeisdata/seq/A355/A355121.seq
|
7814ee69c16cbd6827ab43163c219d87
|
A355122
|
E.g.f. A(x) satisfies A(x) = 1 + (exp(x) - 1) * A(2 * (exp(x) - 1)).
|
[
"1",
"1",
"5",
"73",
"2725",
"242921",
"50068197",
"23441365641",
"24644653272869",
"57655911504114985",
"297771560486880287589",
"3370400630994211122517705",
"83052841013576647141181337509",
"4428866659075152490151174819022697",
"508340576698412171558866359984025695205"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A213357",
"A352860",
"A355083",
"A355122"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:19 |
oeisdata/seq/A355/A355122.seq
|
4a75bc93d79d1504f9514cae452f6875
|
A355123
|
E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(2 * (1 - exp(-x))).
|
[
"1",
"1",
"3",
"25",
"611",
"41721",
"7326115",
"3120454233",
"3105527125475",
"7041597540281017",
"35733375744777784867",
"400526056950063657595929",
"9816824637930442994222501475",
"521959475771315485798501882623609",
"59814953381855591853355367174623538851"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A353177",
"A355093",
"A355123"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:23 |
oeisdata/seq/A355/A355123.seq
|
15cf43ef8520c3304bd6c9408d462ea3
|
A355124
|
E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * log(1+x)).
|
[
"1",
"1",
"4",
"42",
"1168",
"84180",
"15107328",
"6495857312",
"6492989426432",
"14753072834027424",
"74941835564789489280",
"840421638561217307501632",
"20603672787268830442103493120",
"1095629510349075557617215030858112",
"125563465926494619940863277689861766144"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A354729",
"A355104",
"A355124",
"A355133"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:27 |
oeisdata/seq/A355/A355124.seq
|
1598f97686c2684a73dabbe6c184e0d1
|
A355125
|
Positions of nonzero terms in A354883.
|
[
"3",
"8",
"13",
"16",
"21",
"26",
"34",
"39",
"44"
] |
[
"nonn",
"hard",
"more"
] | 5 | 1 | 1 |
[
"A354883",
"A355125"
] | null |
Markus Sigg, Jun 20 2022
| 2022-06-22T12:23:20 |
oeisdata/seq/A355/A355125.seq
|
1885fe706d91f4f80fbe3fb771e997f7
|
A355126
|
E.g.f. A(x) satisfies: A(x) = 1 + x * A(-2 * log(1-x)).
|
[
"1",
"1",
"4",
"54",
"1936",
"168780",
"34360128",
"15979581632",
"16740281020160",
"39091514910283872",
"201702609432140369280",
"2281926772696486970224192",
"56217269029941735581289119232",
"2997472083791372184890466743907712",
"344025706673467887482938899075885442048"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A354730",
"A355106",
"A355126",
"A355134"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:31 |
oeisdata/seq/A355/A355126.seq
|
d1b71ace1e74c22d46ad07e23e6a9507
|
A355127
|
a(n) is the number of different (n-1)-move routes for a king on an empty n X n chessboard.
|
[
"1",
"12",
"200",
"2880",
"37680",
"455224",
"5186888",
"56471040",
"593296160",
"6057160296",
"60407414256",
"590807590672",
"5684125083000",
"53924502344880",
"505415790232592",
"4687367714152128",
"43070861665247616",
"392532002390446600",
"3551337773634149120",
"31920035670120464496"
] |
[
"nonn",
"walk"
] | 56 | 1 | 2 |
[
"A086346",
"A086347",
"A151331",
"A323562",
"A355127"
] | null |
Frank Hollstein, Jun 20 2022
| 2022-09-11T00:48:03 |
oeisdata/seq/A355/A355127.seq
|
fc6801b2e639255180858d44f9ae0c5e
|
A355128
|
E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (exp(x) - 1)).
|
[
"1",
"1",
"4",
"54",
"1928",
"167770",
"34128972",
"15867798142",
"16621680303888",
"38813463431274402",
"200266228576991017940",
"2265670919773168963168454",
"55816752493202168837392763544",
"2976116188645489878229876218205674",
"341574630434025162744892242114482410332"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A048801",
"A355100",
"A355128",
"A355131"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:04 |
oeisdata/seq/A355/A355128.seq
|
a205f58750f9e37aaa6af01a08638207
|
A355129
|
a(n) is the number of integer sequences b(0..n) of length n+1, with 0 <= b(k) <= k! and monotonic b(k) <= b(k+1).
|
[
"2",
"3",
"7",
"40",
"856",
"91821",
"60080136",
"279276911843",
"10503211888973754",
"3585680755683196123365",
"12323227994417456429490342865",
"468378989392773003347310901356953089",
"214565221409985003242070442557341938941878313",
"1282499669290042152350268651085002913530161723080398635"
] |
[
"nonn"
] | 65 | 0 | 1 |
[
"A000108",
"A005269",
"A005270",
"A008934",
"A016121",
"A128094",
"A242105",
"A355129"
] | null |
Thomas Scheuerle, Aug 04 2022
| 2022-08-06T08:05:36 |
oeisdata/seq/A355/A355129.seq
|
971c214486e69312538236ae0d118da1
|
A355130
|
E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (1 - exp(-x))).
|
[
"1",
"1",
"4",
"42",
"1160",
"83270",
"14923212",
"6414048354",
"6410464368912",
"14565079937500542",
"73986188807621474900",
"829702542906852010728090",
"20340869993779258576653846936",
"1081654382501102944417336793863094",
"123961854316018592747078219803021082332"
] |
[
"nonn"
] | 11 | 0 | 3 |
[
"A354574",
"A355102",
"A355130",
"A355132"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:35 |
oeisdata/seq/A355/A355130.seq
|
6eadc78ed440b516c36afc68aa469535
|
A355131
|
E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(2 * (exp(x) - 1)).
|
[
"1",
"2",
"18",
"482",
"33554",
"5688162",
"2266828306",
"2077710037986",
"4312607047919378",
"20026622857699101794",
"205970083615742633015314",
"4651396041100180736449396962",
"228932014511191529094605862938898",
"24398187888144654481778017293891600738"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A355122",
"A355128",
"A355131"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:39 |
oeisdata/seq/A355/A355131.seq
|
dfaa9fc3f725005a00decfc9131c5506
|
A355132
|
E.g.f. A(x) satisfies A(x) = 1 + 2 * (1 - exp(-x)) * A(2 * (1 - exp(-x))).
|
[
"1",
"2",
"14",
"290",
"16654",
"2487202",
"916292622",
"801308046114",
"1618342215277838",
"7398618880762147490",
"75427503900622910066190",
"1695072499481604881387820578",
"83204183269315611109025907220238",
"8854418165429899481934158557358648738"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A355123",
"A355130",
"A355132"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:43 |
oeisdata/seq/A355/A355132.seq
|
e1b557450f5ea5a1b6b9a9bf2dd98153
|
A355133
|
E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(2 * log(1+x)).
|
[
"1",
"2",
"14",
"292",
"16836",
"2517888",
"927979616",
"811623678304",
"1639230314891936",
"7494183556478948928",
"76401967141928846136512",
"1716972732272402536841957760",
"84279193103775042893631925450624",
"8968818994749615710061662692132983296"
] |
[
"nonn"
] | 9 | 0 | 2 |
[
"A354728",
"A355120",
"A355124",
"A355133"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:47 |
oeisdata/seq/A355/A355133.seq
|
32e37caad377ce8ea5e4bb1821ff835b
|
A355134
|
E.g.f. A(x) satisfies A(x) = 1 - 2 * log(1-x) * A(-2 * log(1-x)).
|
[
"1",
"2",
"18",
"484",
"33756",
"5726688",
"2282797376",
"2092535127520",
"4343501656698208",
"20170260943214036928",
"207447888426953360929472",
"4684772419161811298440759936",
"230574775676259398837728211069824",
"24573264762390563391638492791134674432"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A355121",
"A355126",
"A355134"
] | null |
Seiichi Manyama, Jun 20 2022
| 2022-06-20T08:36:53 |
oeisdata/seq/A355/A355134.seq
|
a6632ae6b881c8e2711ff7b4044eb93a
|
A355135
|
The indices where A355072(n) = 1.
|
[
"1",
"2",
"5",
"8",
"11",
"14",
"17",
"21",
"25",
"28",
"36",
"40",
"48",
"56",
"63",
"67",
"72",
"76",
"79",
"84",
"88",
"96",
"99",
"104",
"108",
"113",
"126",
"133",
"137",
"141",
"145",
"149",
"153",
"158",
"177",
"182",
"186",
"194",
"206",
"222",
"225",
"232",
"235",
"239",
"246",
"251",
"255",
"261",
"264",
"267",
"270",
"273",
"276",
"279",
"282",
"285",
"288",
"291",
"295",
"299",
"303",
"307",
"325",
"329",
"333"
] |
[
"nonn"
] | 8 | 0 | 2 |
[
"A355072",
"A355135"
] | null |
Scott R. Shannon, Jun 20 2022
| 2022-06-22T07:41:38 |
oeisdata/seq/A355/A355135.seq
|
d2139545d2dfbd13c21de618e5521e7c
|
A355136
|
The fixed points of A355072.
|
[
"3",
"9",
"20",
"29",
"49",
"54",
"59",
"116",
"148",
"150",
"178",
"2618",
"2683",
"2699",
"2941",
"3035",
"3041",
"3043",
"3196",
"3198",
"3200",
"3202",
"3204",
"3208",
"3212",
"3216",
"3220",
"3224",
"3228",
"3297",
"3358",
"3400",
"3416",
"3448",
"3464",
"3507",
"3728",
"3736",
"3738",
"3802",
"3926",
"3928",
"3942",
"3984",
"3986",
"3988",
"4014",
"4070",
"4330",
"4338",
"4340",
"4342"
] |
[
"nonn"
] | 7 | 0 | 1 |
[
"A355072",
"A355136"
] | null |
Scott R. Shannon, Jun 20 2022
| 2022-06-22T07:41:33 |
oeisdata/seq/A355/A355136.seq
|
ff323a42d595d1a354936affe3f1ab3d
|
A355137
|
Indices of primes in the sequence A000296.
|
[
"5",
"6",
"41",
"119",
"5118"
] |
[
"nonn",
"more"
] | 11 | 1 | 1 |
[
"A000296",
"A051130",
"A355137"
] | null |
Vaclav Kotesovec, Jun 20 2022
| 2022-06-24T01:10:21 |
oeisdata/seq/A355/A355137.seq
|
3cdf2ff7ed609d08b2f8331307a3d1a4
|
A355138
|
The products of consecutive terms in A355061.
|
[
"2",
"12",
"90",
"525",
"490",
"84",
"198",
"1815",
"550",
"60",
"126",
"735",
"350",
"120",
"252",
"1617",
"1694",
"132",
"234",
"2535",
"650",
"140",
"294",
"315",
"150",
"220",
"726",
"495",
"300",
"280",
"882",
"945",
"600",
"560",
"1078",
"2541",
"396",
"168",
"1274",
"3549",
"468",
"240",
"700",
"2205",
"378",
"156",
"1690",
"975",
"180",
"264",
"1210",
"825",
"270",
"504",
"980",
"1575",
"540",
"312"
] |
[
"nonn"
] | 8 | 1 | 1 |
[
"A355061",
"A355138",
"A355139"
] | null |
Scott R. Shannon, Jun 20 2022
| 2022-06-21T10:28:23 |
oeisdata/seq/A355/A355138.seq
|
9635072c7206585e1fd07a2383165cf5
|
A355139
|
The indices where A355061(n) = 6.
|
[
"3",
"7",
"11",
"19",
"46",
"75",
"113",
"138",
"169",
"186",
"227",
"240",
"287",
"374",
"382",
"481",
"528",
"536",
"672",
"713",
"722",
"760",
"836",
"922",
"972",
"1015",
"1031",
"1052",
"1077",
"1122",
"1144",
"1235",
"1244",
"1371",
"1392",
"1466",
"1549",
"1613",
"1669",
"1859",
"1938",
"2059",
"2109",
"2118",
"2127",
"2391",
"2557",
"2661",
"2730",
"2739",
"2765",
"2798",
"2949",
"2962"
] |
[
"nonn"
] | 8 | 1 | 1 |
[
"A355061",
"A355138",
"A355139"
] | null |
Scott R. Shannon, Jun 20 2022
| 2022-06-21T10:28:12 |
oeisdata/seq/A355/A355139.seq
|
755e8393816f64e001d58a09ace341c8
|
A355140
|
n/d(n) rounded to the nearest integer, where d(n) is the number of divisors of n (A000005).
|
[
"1",
"1",
"2",
"1",
"3",
"2",
"4",
"2",
"3",
"3",
"6",
"2",
"7",
"4",
"4",
"3",
"9",
"3",
"10",
"3",
"5",
"6",
"12",
"3",
"8",
"7",
"7",
"5",
"15",
"4",
"16",
"5",
"8",
"9",
"9",
"4",
"19",
"10",
"10",
"5",
"21",
"5",
"22",
"7",
"8",
"12",
"24",
"5",
"16",
"8",
"13",
"9",
"27",
"7",
"14",
"7",
"14",
"15",
"30",
"5",
"31",
"16",
"11",
"9",
"16",
"8",
"34",
"11",
"17",
"9",
"36",
"6",
"37",
"19",
"13",
"13",
"19"
] |
[
"nonn"
] | 12 | 1 | 3 |
[
"A000005",
"A078709",
"A090387",
"A090395",
"A334762",
"A355140"
] | null |
Sameer Khan, Jun 20 2022
| 2022-12-22T13:18:03 |
oeisdata/seq/A355/A355140.seq
|
0d974f09f8f6efad67e092a23e3a3093
|
A355141
|
a(0)=1, a(1)=a(2)=0; for n > 2, a(n) = a(n-1) + s if n is odd, a(n-1) - s if n is even, where s = a(n-1) + a(n-2) + a(n-3).
|
[
"1",
"0",
"0",
"1",
"0",
"1",
"-1",
"-1",
"0",
"-2",
"1",
"0",
"1",
"3",
"-1",
"2",
"-2",
"-3",
"0",
"-5",
"3",
"1",
"2",
"8",
"-3",
"4",
"-5",
"-9",
"1",
"-12",
"8",
"5",
"4",
"21",
"-9",
"7",
"-12",
"-26",
"5",
"-28",
"21",
"19",
"7",
"54",
"-26",
"9",
"-28",
"-73",
"19",
"-63",
"54",
"64",
"9",
"136",
"-73",
"-1",
"-63",
"-200",
"64",
"-135",
"136",
"201",
"-1",
"335",
"-200",
"-66"
] |
[
"sign",
"easy"
] | 52 | 0 | 10 | null | null |
Nate Shaw, Jun 20 2022
| 2022-06-22T11:46:48 |
oeisdata/seq/A355/A355141.seq
|
4f6fc02fb71a70344668c0d3e871639c
|
A355142
|
a(n) = 33648*3^n - 1.
|
[
"33647",
"100943",
"302831",
"908495",
"2725487",
"8176463",
"24529391",
"73588175",
"220764527",
"662293583",
"1986880751",
"5960642255",
"17881926767",
"53645780303",
"160937340911",
"482812022735",
"1448436068207",
"4345308204623",
"13035924613871",
"39107773841615",
"117323321524847",
"351969964574543"
] |
[
"nonn",
"easy"
] | 32 | 0 | 1 |
[
"A016789",
"A052333",
"A354747",
"A354748",
"A355142"
] | null |
Felix Fröhlich, Jun 20 2022
| 2023-03-03T16:26:49 |
oeisdata/seq/A355/A355142.seq
|
b4f6334cc5d98e15bf319aa37d1d63de
|
A355143
|
Product of middle divisors of n, or 0 if there are no middle divisors of n.
|
[
"1",
"1",
"0",
"2",
"0",
"6",
"0",
"2",
"3",
"0",
"0",
"12",
"0",
"0",
"15",
"4",
"0",
"3",
"0",
"20",
"0",
"0",
"0",
"24",
"5",
"0",
"0",
"28",
"0",
"30",
"0",
"4",
"0",
"0",
"35",
"6",
"0",
"0",
"0",
"40",
"0",
"42",
"0",
"0",
"45",
"0",
"0",
"48",
"7",
"5",
"0",
"0",
"0",
"54",
"0",
"56",
"0",
"0",
"0",
"60",
"0",
"0",
"63",
"8",
"0",
"66",
"0",
"0",
"0",
"70",
"0",
"432",
"0",
"0",
"0",
"0",
"77",
"0",
"0",
"80"
] |
[
"nonn"
] | 28 | 1 | 4 |
[
"A007955",
"A067742",
"A071090",
"A071561",
"A071562",
"A299761",
"A320142",
"A347950",
"A355143"
] | null |
Omar E. Pol, Jun 20 2022
| 2022-08-24T09:48:54 |
oeisdata/seq/A355/A355143.seq
|
be763cc910cca73e67a9d5ce13dc9ec9
|
A355144
|
Number T(n,k) of partitions of [n] having exactly k blocks of size at least three; triangle T(n,k), n>=0, 0<=k<=floor(n/3), read by rows.
|
[
"1",
"1",
"2",
"4",
"1",
"10",
"5",
"26",
"26",
"76",
"117",
"10",
"232",
"540",
"105",
"764",
"2445",
"931",
"2620",
"11338",
"6909",
"280",
"9496",
"53033",
"48546",
"4900",
"35696",
"253826",
"324753",
"64295",
"140152",
"1235115",
"2131855",
"691075",
"15400",
"568504",
"6142878",
"13792779",
"6739876",
"400400",
"2390480",
"31126539",
"88890880",
"61274213",
"7217210"
] |
[
"nonn",
"tabf"
] | 22 | 0 | 3 |
[
"A000085",
"A000110",
"A025035",
"A048993",
"A124324",
"A124503",
"A288785",
"A355144"
] | null |
Alois P. Heinz, Jun 20 2022
| 2022-06-25T12:54:40 |
oeisdata/seq/A355/A355144.seq
|
a57ff4011162e5f844e5934434b8dd72
|
A355145
|
Triangle read by rows: T(n,k) is the number of primitive subsets of {1,...,n} of cardinality k; n>=0, 0<=k<=ceiling(n/2).
|
[
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"1",
"1",
"4",
"2",
"1",
"5",
"5",
"2",
"1",
"6",
"7",
"3",
"1",
"7",
"12",
"10",
"3",
"1",
"8",
"16",
"15",
"5",
"1",
"9",
"22",
"26",
"13",
"2",
"1",
"10",
"28",
"38",
"22",
"4",
"1",
"11",
"37",
"66",
"60",
"26",
"4",
"1",
"12",
"43",
"80",
"76",
"35",
"6",
"1",
"13",
"54",
"123",
"156",
"111",
"41",
"6",
"1",
"14",
"64",
"161",
"227",
"180",
"74",
"12"
] |
[
"nonn",
"tabf"
] | 37 | 0 | 5 |
[
"A000012",
"A000027",
"A051026",
"A087077",
"A087086",
"A161664",
"A174094",
"A192298",
"A355145"
] | null |
Marcel K. Goh, Jun 20 2022
| 2022-06-27T23:34:59 |
oeisdata/seq/A355/A355145.seq
|
a6fbed6d08c34a2652b8ecb56690198e
|
A355146
|
Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n).
|
[
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"3",
"1",
"1",
"4",
"5",
"2",
"1",
"5",
"9",
"7",
"2",
"1",
"6",
"11",
"8",
"2",
"1",
"7",
"17",
"19",
"10",
"2",
"1",
"8",
"21",
"25",
"14",
"3",
"1",
"9",
"27",
"37",
"24",
"6",
"1",
"10",
"31",
"42",
"26",
"6",
"1",
"11",
"41",
"73",
"68",
"32",
"6",
"1",
"12",
"45",
"79",
"72",
"33",
"6",
"1",
"13",
"57",
"124",
"151",
"105",
"39",
"6",
"1",
"14",
"63",
"138",
"167",
"114",
"41",
"6"
] |
[
"nonn",
"tabf"
] | 16 | 0 | 5 |
[
"A000720",
"A036234",
"A084422",
"A186974",
"A320436",
"A355146"
] | null |
Marcel K. Goh, Jun 27 2022
| 2022-07-06T17:42:50 |
oeisdata/seq/A355/A355146.seq
|
86cf53db18ec386d7f5c6e7b7576ffd4
|
A355147
|
Triangle read by rows: T(n,k) is the number of product-free subsets of {1,...,n} with cardinality k; n >= 0, 0 <= k <= A028391(n).
|
[
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"2",
"1",
"4",
"5",
"2",
"1",
"5",
"9",
"6",
"1",
"1",
"6",
"14",
"15",
"7",
"1",
"1",
"7",
"20",
"29",
"22",
"8",
"1",
"1",
"8",
"26",
"43",
"38",
"17",
"3",
"1",
"9",
"34",
"68",
"76",
"47",
"15",
"2",
"1",
"10",
"43",
"102",
"144",
"123",
"62",
"17",
"2",
"1",
"11",
"53",
"143",
"234",
"238",
"149",
"55",
"11",
"1",
"1",
"12",
"64",
"196",
"377",
"472",
"387",
"204",
"66",
"12",
"1"
] |
[
"nonn",
"tabf"
] | 13 | 0 | 6 |
[
"A028391",
"A326489",
"A355147"
] | null |
Marcel K. Goh, Jun 28 2022
| 2022-07-06T17:43:27 |
oeisdata/seq/A355/A355147.seq
|
fe0805b7ae27bcdaea31b3c68966b94a
|
A355148
|
Numbers that are the concatenation of two palindromes and that have exactly two palindromic factors, all with the same number of decimal digits.
|
[
"12",
"14",
"15",
"16",
"18",
"21",
"24",
"25",
"27",
"28",
"32",
"35",
"36",
"42",
"45",
"48",
"49",
"54",
"56",
"63",
"64",
"72",
"81",
"3388",
"7744",
"101787",
"101808",
"111888",
"151848",
"212565",
"212898",
"232656",
"313464",
"313575",
"353868",
"383595",
"383838",
"414585",
"434676",
"454545",
"505808",
"515595",
"525252",
"555888"
] |
[
"base",
"nonn"
] | 60 | 1 | 1 | null | null |
Nicolas Bělohoubek, Jun 21 2022
| 2024-06-10T19:30:23 |
oeisdata/seq/A355/A355148.seq
|
5d93d88f8a9193846b6c4f08157e662f
|
A355149
|
Partial sums of A351743.
|
[
"1",
"2",
"4",
"5",
"10",
"12",
"15",
"20",
"24",
"27",
"28",
"56",
"57",
"114",
"116",
"145",
"150",
"156",
"169",
"170",
"340",
"341",
"682",
"684",
"855",
"860",
"1032",
"1035",
"1150",
"1152",
"1161",
"1204",
"1232",
"1243",
"1356",
"1368",
"1387",
"1460",
"1480",
"1517",
"1558",
"1596",
"1617",
"1628",
"1776",
"1779",
"2372",
"2376",
"2673",
"2674"
] |
[
"nonn"
] | 11 | 1 | 2 |
[
"A351743",
"A355149"
] | null |
Michael De Vlieger, Rémy Sigrist and David James Sycamore, Jun 21 2022
| 2022-11-17T16:54:42 |
oeisdata/seq/A355/A355149.seq
|
a839cbb933fae0049c88091ab0288277
|
A355150
|
The Hamming weight of A354169, a(n) = A000120(A354169(n)).
|
[
"0",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1"
] |
[
"nonn"
] | 114 | 0 | 6 |
[
"A000120",
"A354169",
"A354767",
"A354798",
"A355150"
] | null |
Thomas Scheuerle, Jun 21 2022
| 2023-12-10T09:28:38 |
oeisdata/seq/A355/A355150.seq
|
516c12046c79a46ceaf236677de7f28c
|
A355151
|
G.f. A(x) satisfies: (1 - x)/(1 + x) = Sum_{n=-oo..+oo} (-1)^n * A(x)^(n^2).
|
[
"1",
"-1",
"1",
"0",
"-3",
"9",
"-15",
"6",
"56",
"-222",
"456",
"-322",
"-1562",
"7604",
"-18062",
"18544",
"46676",
"-293986",
"797456",
"-1066316",
"-1265854",
"11945620",
"-36984046",
"60359006",
"20788743",
"-493365441",
"1756737971",
"-3368998030",
"835358767",
"20230816709",
"-84341891481",
"185935403556"
] |
[
"sign"
] | 15 | 1 | 5 |
[
"A354651",
"A355151"
] | null |
Paul D. Hanna, Jun 21 2022
| 2025-02-16T08:34:03 |
oeisdata/seq/A355/A355151.seq
|
ae12d9299f087383d005ff746db465a9
|
A355152
|
G.f. A(x) satisfies: 0 = Sum_{n=-oo..+oo} x^(n^2) * (x^n - (-1)^n*A(x))^(n+1).
|
[
"1",
"2",
"6",
"21",
"77",
"310",
"1308",
"5710",
"25605",
"117232",
"545719",
"2575126",
"12289906",
"59218913",
"287699288",
"1407690851",
"6930731921",
"34311193558",
"170691635544",
"852874403933",
"4278234997610",
"21537155141117",
"108771673373067",
"550966271295019",
"2798396004637028",
"14248670155477872"
] |
[
"nonn"
] | 6 | 0 | 2 |
[
"A355152",
"A355153"
] | null |
Paul D. Hanna, Jun 21 2022
| 2022-06-22T02:30:18 |
oeisdata/seq/A355/A355152.seq
|
78ab8255c74529c981cc50754917fab4
|
A355153
|
G.f. A(x) satisfies: 0 = Sum_{n=-oo..+oo} x^(n*(n+1)/2) * (x^n - (-1)^n*2*A(x))^(n+1).
|
[
"1",
"2",
"10",
"49",
"272",
"1617",
"10082",
"65101",
"431635",
"2921557",
"20104828",
"140240820",
"989366180",
"7046832503",
"50604822586",
"365995915453",
"2663552184585",
"19490777248544",
"143322830835474",
"1058514890796268",
"7848460747315854",
"58400364116985559",
"435963301942052908"
] |
[
"nonn"
] | 6 | 0 | 2 |
[
"A355152",
"A355153"
] | null |
Paul D. Hanna, Jun 21 2022
| 2022-06-22T02:25:03 |
oeisdata/seq/A355/A355153.seq
|
1af8d68f10788ff47b7bddaf2975ea2b
|
A355154
|
G.f. A(x) satisfies: 1 = Sum_{n=-oo..+oo} (-x)^((n+1)^2) * ((1+x)^n - A(x))^n.
|
[
"1",
"3",
"10",
"47",
"248",
"1354",
"7832",
"46672",
"285136",
"1775728",
"11232028",
"71959338",
"465981585",
"3045116666",
"20055877798",
"132995908915",
"887220714352",
"5950074234287",
"40092205226021",
"271289342487845",
"1842724189708458",
"12559944025175681",
"85877738644538351"
] |
[
"nonn"
] | 6 | 1 | 2 | null | null |
Paul D. Hanna, Jun 21 2022
| 2022-06-22T02:43:10 |
oeisdata/seq/A355/A355154.seq
|
1d4021ae0fe0f727bf49ff27d5a49862
|
A355155
|
G.f. A(x) satisfies: 2 = Sum_{n=-oo..+oo} (-x)^(n*(n+1)/2) * ((1+x)^(n+1) - 2*A(x))^n.
|
[
"1",
"1",
"7",
"28",
"184",
"1024",
"6676",
"42367",
"282765",
"1897203",
"13004369",
"89991470",
"630242521",
"4450613382",
"31683411117",
"227041605009",
"1636747514265",
"11860982110191",
"86356914006201",
"631382010617369",
"4633749074928932",
"34124201919637479",
"252086975581304199"
] |
[
"nonn"
] | 6 | 1 | 3 |
[
"A355155",
"A355156"
] | null |
Paul D. Hanna, Jun 21 2022
| 2022-06-22T02:55:08 |
oeisdata/seq/A355/A355155.seq
|
92320d8436e48203dfec71fe7b463799
|
A355156
|
G.f. A(x) satisfies: 2 = Sum_{n=-oo..+oo} (-x)^(n*(n+1)/2) * ((1+x)^n + 2*A(x))^(n+1).
|
[
"1",
"3",
"7",
"34",
"156",
"635",
"2966",
"14327",
"66047",
"314700",
"1560159",
"7710390",
"38251395",
"192549444",
"974601369",
"4952273462",
"25349634715",
"130414412847",
"673028519274",
"3487306501970",
"18139905710007",
"94640387701755",
"495160150021161",
"2597800048395361",
"13661957722514619"
] |
[
"nonn"
] | 6 | 1 | 2 |
[
"A355155",
"A355156"
] | null |
Paul D. Hanna, Jun 21 2022
| 2022-06-22T02:56:28 |
oeisdata/seq/A355/A355156.seq
|
9593170a8855f4c60cbb5e9c7e9526b0
|
A355157
|
E.g.f.: exp(-x*tan(x)/2).
|
[
"1",
"-1",
"-1",
"-3",
"81",
"5815",
"367791",
"26531589",
"2231306849",
"213451322031",
"21883750567455",
"2048495154903373",
"38238322254619953",
"-84508521173113956633",
"-48971496478118456699569",
"-23204642085706390327411755",
"-10849535606183313563987736639",
"-5259600981361065001871911307681",
"-2687430634156750207499977165012161"
] |
[
"sign"
] | 4 | 0 | 4 |
[
"A009273",
"A354245",
"A355157"
] | null |
Paul D. Hanna, Jun 21 2022
| 2022-06-30T10:39:07 |
oeisdata/seq/A355/A355157.seq
|
1416416dfa00370a327f02663a11cb9a
|
A355158
|
Number of partitions of n that contain more nonprime parts than prime parts.
|
[
"0",
"1",
"1",
"1",
"3",
"4",
"5",
"8",
"12",
"16",
"24",
"29",
"42",
"57",
"74",
"97",
"132",
"165",
"217",
"279",
"355",
"453",
"576",
"717",
"908",
"1135",
"1408",
"1751",
"2169",
"2664",
"3283",
"4022",
"4909",
"5990",
"7282",
"8814",
"10681",
"12885",
"15506",
"18643",
"22362",
"26739",
"31970",
"38100",
"45340",
"53878",
"63908",
"75639",
"89476",
"105580",
"124445"
] |
[
"nonn"
] | 38 | 0 | 5 |
[
"A000040",
"A000041",
"A000607",
"A002095",
"A002096",
"A018252",
"A155515",
"A355158",
"A355225",
"A355306"
] | null |
Omar E. Pol, Jun 24 2022
| 2022-06-30T14:42:49 |
oeisdata/seq/A355/A355158.seq
|
94e2b1cb51b17babf2d009c156147cc6
|
A355159
|
Numbers k such that (fractional part of k^(3/2)) < 1/2.
|
[
"0",
"1",
"3",
"4",
"5",
"9",
"11",
"14",
"15",
"16",
"17",
"18",
"20",
"21",
"22",
"23",
"25",
"27",
"28",
"29",
"30",
"32",
"34",
"35",
"36",
"37",
"38",
"42",
"47",
"49",
"51",
"56",
"57",
"59",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"69",
"71",
"79",
"81",
"83",
"87",
"91",
"92",
"94",
"97",
"98",
"99",
"100",
"101",
"102",
"103",
"106",
"108",
"111",
"112",
"113",
"114",
"115"
] |
[
"nonn",
"easy"
] | 19 | 0 | 3 |
[
"A000093",
"A355159",
"A355160"
] | null |
Clark Kimberling, Jun 22 2022
| 2022-08-03T18:57:19 |
oeisdata/seq/A355/A355159.seq
|
8342fdad7888e86a033cc142c46139fe
|
A355160
|
Numbers k such that (fractional part of k^(3/2)) > 1/2.
|
[
"2",
"6",
"7",
"8",
"10",
"12",
"13",
"19",
"24",
"26",
"31",
"33",
"39",
"40",
"41",
"43",
"44",
"45",
"46",
"48",
"50",
"52",
"53",
"54",
"55",
"58",
"60",
"68",
"70",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"80",
"82",
"84",
"85",
"86",
"88",
"89",
"90",
"93",
"95",
"96",
"104",
"105",
"107",
"109",
"110",
"117",
"118",
"120",
"122",
"124",
"125",
"132",
"133",
"135",
"137"
] |
[
"nonn",
"easy"
] | 19 | 1 | 1 |
[
"A000093",
"A355159",
"A355160"
] | null |
Clark Kimberling, Jun 23 2022
| 2022-08-03T18:57:08 |
oeisdata/seq/A355/A355160.seq
|
9e71b5bee1e163aecb4cf0329563bd8f
|
A355161
|
Primes p such that p - prevprime(p) is not a power of 2.
|
[
"29",
"37",
"53",
"59",
"67",
"79",
"89",
"127",
"137",
"149",
"157",
"163",
"173",
"179",
"191",
"211",
"223",
"239",
"251",
"257",
"263",
"269",
"277",
"293",
"307",
"331",
"337",
"347",
"359",
"373",
"379",
"389",
"419",
"431",
"439",
"449",
"479",
"509",
"521",
"541",
"547",
"557",
"563",
"569",
"577",
"587",
"593",
"599",
"607",
"613"
] |
[
"nonn"
] | 38 | 1 | 1 |
[
"A000079",
"A031925",
"A031931",
"A130796",
"A151800",
"A355161"
] | null |
Reed Michael Upson, Jun 21 2022
| 2022-08-23T09:41:21 |
oeisdata/seq/A355/A355161.seq
|
49f7b270858f46262bd87e33f856cd0d
|
A355162
|
a(n) = exp(-1) * Sum_{k>=0} (4*k + 2)^n / k!.
|
[
"1",
"6",
"52",
"568",
"7312",
"107360",
"1760576",
"31760256",
"623137024",
"13179872768",
"298391335936",
"7189153167360",
"183428957442048",
"4935794590572544",
"139571328018628608",
"4134634425826115584",
"127966201403431518208",
"4127825849826169716736",
"138477447400991610896384",
"4822002684952714247929856"
] |
[
"nonn"
] | 10 | 0 | 2 |
[
"A000110",
"A005493",
"A126390",
"A284859",
"A284864",
"A285064",
"A355162",
"A355163"
] | null |
Ilya Gutkovskiy, Jun 22 2022
| 2022-06-27T03:18:56 |
oeisdata/seq/A355/A355162.seq
|
79bcfd8bfc6c86326ce1d72c44e21682
|
A355163
|
a(n) = exp(-1) * Sum_{k>=0} (4*k + 3)^n / k!.
|
[
"1",
"7",
"65",
"743",
"9921",
"150151",
"2526593",
"46615783",
"933072513",
"20093861895",
"462440842177",
"11310514854375",
"292627518129985",
"7976748158144647",
"228308400790500097",
"6840702405678586343",
"214000748166439723265",
"6973447420429351808007",
"236204029044752265931585",
"8300724166287243795922151"
] |
[
"nonn"
] | 9 | 0 | 2 |
[
"A000110",
"A005494",
"A126390",
"A284859",
"A284864",
"A285064",
"A355162",
"A355163"
] | null |
Ilya Gutkovskiy, Jun 22 2022
| 2022-06-27T02:50:56 |
oeisdata/seq/A355/A355163.seq
|
0dee0bc80fe274a020d5686b6c6ccc84
|
A355164
|
a(n) = exp(-1/3) * Sum_{k>=0} (3*k + 2)^n / (3^k * k!).
|
[
"1",
"3",
"12",
"63",
"405",
"3024",
"25515",
"239355",
"2465478",
"27600669",
"333051669",
"4303119330",
"59202612693",
"863285928327",
"13288589222508",
"215177742933579",
"3654114236490393",
"64902307993517160",
"1202782377224829015",
"23207417212751493327",
"465302639045308247262",
"9677171073270491712513",
"208434297638273958963225"
] |
[
"nonn"
] | 15 | 0 | 2 |
[
"A003575",
"A004212",
"A284864",
"A355164",
"A355165",
"A355167"
] | null |
Ilya Gutkovskiy, Jun 22 2022
| 2023-06-27T11:33:00 |
oeisdata/seq/A355/A355164.seq
|
207e89174ecb01c13d65a80c77a37d84
|
A355165
|
a(n) = exp(-1/4) * Sum_{k>=0} (4*k + 2)^n / (4^k * k!).
|
[
"1",
"3",
"13",
"79",
"601",
"5339",
"53861",
"607527",
"7560625",
"102637235",
"1506225085",
"23726435583",
"398852249097",
"7120170905995",
"134408217821205",
"2673140092099543",
"55832167947587425",
"1221199519275467107",
"27902127744298836845",
"664446811342185649583",
"16457968670922936733113",
"423242969435491221774907"
] |
[
"nonn"
] | 9 | 0 | 2 |
[
"A003576",
"A004213",
"A285064",
"A355164",
"A355165",
"A355167"
] | null |
Ilya Gutkovskiy, Jun 22 2022
| 2022-06-27T02:58:19 |
oeisdata/seq/A355/A355165.seq
|
27b994372c965c33b5177ec6e39559e8
|
A355166
|
Lexicographically earliest sequence of distinct positive integers such for any n > 0, n and a(n) are coprime and have no common 1-bits in their binary expansions.
|
[
"2",
"1",
"4",
"3",
"8",
"17",
"16",
"5",
"20",
"21",
"32",
"19",
"18",
"33",
"64",
"7",
"6",
"13",
"12",
"9",
"10",
"41",
"40",
"35",
"34",
"37",
"68",
"65",
"66",
"97",
"96",
"11",
"14",
"25",
"24",
"67",
"26",
"73",
"80",
"23",
"22",
"85",
"84",
"81",
"82",
"129",
"128",
"71",
"72",
"69",
"76",
"75",
"74",
"137",
"136",
"131",
"70",
"133",
"132",
"193",
"130",
"257",
"256",
"15",
"28"
] |
[
"nonn",
"base"
] | 8 | 1 | 1 |
[
"A065190",
"A238757",
"A352633",
"A355166"
] | null |
Rémy Sigrist, Jun 22 2022
| 2022-06-23T08:11:36 |
oeisdata/seq/A355/A355166.seq
|
7f624cb1ad6308a5efa890ba416c3489
|
A355167
|
a(n) = exp(-1/4) * Sum_{k>=0} (4*k + 3)^n / (4^k * k!).
|
[
"1",
"4",
"20",
"128",
"1008",
"9280",
"96704",
"1120768",
"14274816",
"197833728",
"2958521344",
"47415508992",
"809838505984",
"14670950907904",
"280760761434112",
"5655835404271616",
"119561580162646016",
"2645030742360588288",
"61087848487323959296",
"1469652941137655103488",
"36758243982057508175872",
"954111239026567129595904"
] |
[
"nonn"
] | 12 | 0 | 2 |
[
"A003576",
"A004213",
"A285064",
"A355164",
"A355165",
"A355167"
] | null |
Ilya Gutkovskiy, Jun 22 2022
| 2023-06-27T11:35:26 |
oeisdata/seq/A355/A355167.seq
|
782292f9b591a61e89d2ebe9bddcc66c
|
A355168
|
Numerators of best lower approximates h/k to sqrt(k); complement of A355169.
|
[
"1",
"5",
"8",
"11",
"27",
"36",
"52",
"58",
"64",
"70",
"76",
"89",
"96",
"103",
"110",
"125",
"140",
"148",
"156",
"164",
"181",
"198",
"207",
"216",
"225",
"234",
"272",
"322",
"343",
"364",
"419",
"430",
"453",
"476",
"488",
"500",
"512",
"524",
"536",
"548",
"573",
"598",
"702",
"729",
"756",
"811",
"868",
"882",
"911",
"955",
"970",
"985",
"1000",
"1015"
] |
[
"nonn",
"easy"
] | 5 | 1 | 2 |
[
"A355115",
"A355159",
"A355160",
"A355168",
"A355169"
] | null |
Clark Kimberling, Jun 26 2022
| 2022-07-10T16:43:54 |
oeisdata/seq/A355/A355168.seq
|
dd1ad5ae516870542a2a0301d491518d
|
A355169
|
Numbers h such that (h+1)/k is closer to sqrt(k) than h/k is, where h is the greatest integer j such that j/k < sqrt(k); complement of A355168.
|
[
"2",
"14",
"18",
"22",
"31",
"41",
"46",
"82",
"117",
"132",
"172",
"189",
"243",
"252",
"262",
"281",
"291",
"301",
"311",
"332",
"353",
"374",
"385",
"396",
"407",
"441",
"464",
"560",
"585",
"610",
"623",
"636",
"649",
"662",
"675",
"688",
"715",
"742",
"769",
"783",
"797",
"825",
"839",
"853",
"896",
"925",
"940",
"1060",
"1075",
"1106",
"1137",
"1153"
] |
[
"nonn",
"easy"
] | 4 | 1 | 1 |
[
"A355115",
"A355159",
"A355160",
"A355168",
"A355169"
] | null |
Clark Kimberling, Jun 26 2022
| 2022-07-10T16:44:04 |
oeisdata/seq/A355/A355169.seq
|
6a0890a623a7b80fd22de58c050e30dd
|
A355170
|
The composite numbers in order of appearance in A173395.
|
[
"4",
"6",
"8",
"9",
"10",
"12",
"15",
"16",
"14",
"18",
"20",
"21",
"24",
"25",
"28",
"30",
"27",
"32",
"35",
"36",
"22",
"40",
"42",
"33",
"45",
"48",
"49",
"26",
"44",
"50",
"54",
"56",
"39",
"55",
"60",
"63",
"64",
"52",
"66",
"70",
"72",
"65",
"77",
"80",
"81",
"34",
"78",
"84",
"88",
"90",
"51",
"75",
"91",
"96",
"99",
"100",
"38",
"68",
"98",
"104",
"108",
"110",
"57",
"85",
"105"
] |
[
"nonn",
"easy"
] | 10 | 1 | 1 |
[
"A173395",
"A257471",
"A355170"
] | null |
Denver Massey, Jun 22 2022
| 2022-06-22T21:32:15 |
oeisdata/seq/A355/A355170.seq
|
e4d11832a46e65bfc3b50707ef384893
|
A355171
|
a(n) = Sum_{k=0..n} binomial(n, k + 1)*k!*(n + 1)!/(k + 2)!.
|
[
"0",
"1",
"7",
"50",
"406",
"3804",
"41028",
"506064",
"7084656",
"111690720",
"1967421600",
"38425449600",
"825970435200",
"19404363283200",
"495012834489600",
"13632039812966400",
"403120633444300800",
"12740557701389414400",
"428546132879432601600",
"15284163618598275072000",
"576073025410937628672000"
] |
[
"nonn"
] | 24 | 0 | 3 |
[
"A001705",
"A066667",
"A103213",
"A355171"
] | null |
Peter Luschny, Jun 22 2022
| 2024-02-17T04:50:21 |
oeisdata/seq/A355/A355171.seq
|
d6c768b39eafa6b188c9deaf8b2aa9b1
|
A355172
|
The Fuss-Catalan triangle of order 2, read by rows. Related to ternary trees.
|
[
"1",
"0",
"1",
"0",
"1",
"3",
"0",
"1",
"5",
"12",
"0",
"1",
"7",
"25",
"55",
"0",
"1",
"9",
"42",
"130",
"273",
"0",
"1",
"11",
"63",
"245",
"700",
"1428",
"0",
"1",
"13",
"88",
"408",
"1428",
"3876",
"7752",
"0",
"1",
"15",
"117",
"627",
"2565",
"8379",
"21945",
"43263",
"0",
"1",
"17",
"150",
"910",
"4235",
"15939",
"49588",
"126500",
"246675"
] |
[
"nonn",
"tabl"
] | 28 | 0 | 6 |
[
"A001764",
"A005408",
"A006629",
"A071355",
"A102594",
"A102893",
"A123110",
"A143603",
"A230547",
"A355172",
"A355173",
"A355174",
"A355262"
] | null |
Peter Luschny, Jun 25 2022
| 2025-03-22T20:43:00 |
oeisdata/seq/A355/A355172.seq
|
c64fd8cb1a40ba00e40814b7be533ea2
|
A355173
|
The Fuss-Catalan triangle of order 1, read by rows. Related to binary trees.
|
[
"1",
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"3",
"5",
"0",
"1",
"4",
"9",
"14",
"0",
"1",
"5",
"14",
"28",
"42",
"0",
"1",
"6",
"20",
"48",
"90",
"132",
"0",
"1",
"7",
"27",
"75",
"165",
"297",
"429",
"0",
"1",
"8",
"35",
"110",
"275",
"572",
"1001",
"1430",
"0",
"1",
"9",
"44",
"154",
"429",
"1001",
"2002",
"3432",
"4862",
"0",
"1",
"10",
"54",
"208",
"637",
"1638",
"3640",
"7072",
"11934",
"16796"
] |
[
"nonn",
"tabl"
] | 36 | 0 | 6 |
[
"A000027",
"A000096",
"A000108",
"A000245",
"A000344",
"A000588",
"A000958",
"A002057",
"A009766",
"A030237",
"A071724",
"A115144",
"A115145",
"A115147",
"A115148",
"A123110",
"A130020",
"A262394",
"A355172",
"A355173",
"A355174",
"A355262"
] | null |
Peter Luschny, Jun 25 2022
| 2025-03-22T20:42:54 |
oeisdata/seq/A355/A355173.seq
|
2ce668b05632159756f389d4b2c5b188
|
A355174
|
The Fuss-Catalan triangle of order 3, read by rows. Related to quartic trees.
|
[
"1",
"0",
"1",
"0",
"1",
"4",
"0",
"1",
"7",
"22",
"0",
"1",
"10",
"49",
"140",
"0",
"1",
"13",
"85",
"357",
"969",
"0",
"1",
"16",
"130",
"700",
"2695",
"7084",
"0",
"1",
"19",
"184",
"1196",
"5750",
"20930",
"53820",
"0",
"1",
"22",
"247",
"1872",
"10647",
"47502",
"166257",
"420732",
"0",
"1",
"25",
"319",
"2755",
"17980",
"93496",
"395560",
"1344904",
"3362260"
] |
[
"nonn",
"tabl"
] | 21 | 0 | 6 |
[
"A002293",
"A016777",
"A123110",
"A196678",
"A233658",
"A233667",
"A355172",
"A355173",
"A355174",
"A355262"
] | null |
Peter Luschny, Jun 25 2022
| 2025-03-22T20:42:50 |
oeisdata/seq/A355/A355174.seq
|
5e479ff5eeb3593065dc4c77990f7547
|
A355175
|
Determinant of the n X n matrix [(i-j)^2 + d(i,j)]_{1<=i,j<=n}, where d(i,j) is 1 or 0 according as i = j or not.
|
[
"1",
"0",
"-9",
"45",
"931",
"6392",
"29205",
"104497",
"315469",
"838696",
"2018523",
"4482765",
"9314943",
"18301648",
"34277321",
"61592769",
"106738105",
"179155504",
"292282207",
"464869581",
"722629755",
"1100267400",
"1643960605",
"2414361521",
"3490194501",
"4972536856",
"6989875075",
"9704037421",
"13317112215",
"18079469856",
"24299015697",
"32351810305",
"42694203377",
"55876637664"
] |
[
"sign"
] | 31 | 1 | 3 |
[
"A000290",
"A079034",
"A355175"
] | null |
Zhi-Wei Sun, Jun 28 2022
| 2022-06-29T10:15:48 |
oeisdata/seq/A355/A355175.seq
|
965a9f78ba16c0e9f4fd4c7beb3c41b6
|
A355176
|
a(n) is the smallest index k such that prime(n) divides both A090252(k) and A090252(2*k+1).
|
[
"2",
"3",
"14",
"32",
"60",
"96",
"120",
"128",
"132",
"244",
"264",
"388",
"480",
"484",
"488",
"2064",
"1056",
"571",
"776",
"960",
"968",
"976",
"980",
"2112",
"2128",
"1143",
"1536",
"1552",
"1556",
"1920",
"3872",
"1937",
"3904",
"3920",
"1961",
"4128",
"4256",
"3104",
"6224",
"3113",
"3844",
"3848",
"7808",
"7824",
"7840",
"8256",
"8448",
"8452"
] |
[
"nonn"
] | 43 | 1 | 1 |
[
"A000040",
"A090252",
"A355176"
] | null |
Thomas Scheuerle, Jun 22 2022
| 2022-06-24T05:29:44 |
oeisdata/seq/A355/A355176.seq
|
833d09a91bf808038b3b8a6863601a52
|
A355177
|
Numbers k such that omega(k^2 - 1) = omega(k) where omega(k) = A001221(k).
|
[
"2",
"3",
"6",
"10",
"12",
"15",
"18",
"24",
"26",
"28",
"33",
"48",
"63",
"66",
"70",
"72",
"78",
"80",
"82",
"84",
"90",
"105",
"108",
"110",
"114",
"120",
"130",
"132",
"140",
"156",
"165",
"170",
"174",
"182",
"190",
"192",
"195",
"222",
"234",
"238",
"242",
"252",
"258",
"264",
"273",
"276",
"280",
"290",
"294",
"306",
"308",
"310",
"315",
"318",
"336",
"342",
"345",
"350",
"354",
"357",
"366",
"372",
"374",
"378",
"380",
"385",
"396",
"399"
] |
[
"nonn",
"easy"
] | 9 | 1 | 1 |
[
"A001221",
"A082863",
"A190789",
"A355177"
] | null |
Juri-Stepan Gerasimov, Jun 22 2022
| 2022-07-01T20:09:23 |
oeisdata/seq/A355/A355177.seq
|
af5c4cf028d693a56a9cdecb7fd968ec
|
A355178
|
Decimal expansion of 2^(-2/3)/L, where L is the conjectured Landau's constant A081760.
|
[
"1",
"1",
"5",
"9",
"5",
"9",
"5",
"2",
"6",
"6",
"9",
"6",
"3",
"9",
"2",
"8",
"3",
"6",
"5",
"7",
"6",
"9",
"9",
"9",
"2",
"0",
"5",
"1",
"5",
"7",
"0",
"0",
"2",
"0",
"8",
"8",
"1",
"9",
"4",
"5",
"1",
"6",
"5",
"2",
"6",
"3",
"4",
"3",
"9",
"7",
"8",
"2",
"8",
"5",
"5",
"2",
"6",
"3",
"1",
"0",
"5",
"0",
"5",
"9",
"7",
"4",
"7",
"9",
"7",
"3",
"7",
"5",
"7",
"2",
"0",
"5",
"2",
"8",
"6",
"2",
"5",
"8",
"6",
"5",
"8",
"0",
"8",
"5",
"2",
"5"
] |
[
"nonn",
"cons"
] | 29 | 1 | 3 |
[
"A002580",
"A073005",
"A081760",
"A175379",
"A203145",
"A235362",
"A355178",
"A357318"
] | null |
Stefano Spezia, Sep 23 2022
| 2023-08-02T13:49:42 |
oeisdata/seq/A355/A355178.seq
|
791651d32565829e19ff9f37aeb30171
|
A355179
|
Expansion of e.g.f. -LambertW(x^2 * (1 - exp(x)))/2.
|
[
"0",
"0",
"0",
"3",
"6",
"10",
"375",
"2541",
"11788",
"317556",
"4238685",
"37921015",
"909616026",
"18283276518",
"261259582675",
"6360432558585",
"164704011195480",
"3332419310132776",
"88606184592031353",
"2713050497589230763",
"71412977041725823750",
"2144089948615678382970"
] |
[
"nonn"
] | 28 | 0 | 4 |
[
"A048802",
"A355179",
"A355180",
"A357267"
] | null |
Seiichi Manyama, Sep 24 2022
| 2025-02-16T08:34:03 |
oeisdata/seq/A355/A355179.seq
|
520e54cf76eed5bc733e4a14337c1135
|
A355180
|
Expansion of e.g.f. -LambertW(x^3 * (1 - exp(x)))/6.
|
[
"0",
"0",
"0",
"0",
"4",
"10",
"20",
"35",
"6776",
"60564",
"352920",
"1663365",
"126625180",
"2361079006",
"27334747804",
"245495250455",
"11174333090480",
"328952158255400",
"6245314009946736",
"90576650639967369",
"3209305759254634740",
"122557203047084965810",
"3365068665450300234580"
] |
[
"nonn"
] | 18 | 0 | 5 |
[
"A048802",
"A355179",
"A355180",
"A357267"
] | null |
Seiichi Manyama, Sep 24 2022
| 2025-02-16T08:34:03 |
oeisdata/seq/A355/A355180.seq
|
e1a7b6dee439281e89a6ce1a3676f701
|
A355181
|
Expansion of e.g.f. -LambertW(x^2/2 * (1 - exp(x))).
|
[
"0",
"0",
"0",
"3",
"6",
"10",
"195",
"1281",
"5908",
"90756",
"1098765",
"9605035",
"147947646",
"2496239538",
"33836915203",
"588360763095",
"12104789358600",
"223722576473896",
"4578806487368313",
"108875473376842467",
"2519418390663035170",
"60831875074927797750",
"1640260621340460494991"
] |
[
"nonn"
] | 15 | 0 | 4 |
[
"A048802",
"A355181",
"A355308",
"A357267"
] | null |
Seiichi Manyama, Sep 24 2022
| 2025-02-16T08:34:03 |
oeisdata/seq/A355/A355181.seq
|
1c86645b07bb37bb110d149075183964
|
A355182
|
a(n) = t(n) - s(n) where s(n) = n*(n-1)/2 is the sum of the first n nonnegative integers and t(n) is the smallest sum of consecutive integers starting from n such that t(n) > s(n).
|
[
"1",
"1",
"4",
"3",
"1",
"6",
"3",
"10",
"6",
"1",
"10",
"4",
"15",
"8",
"21",
"13",
"4",
"19",
"9",
"26",
"15",
"3",
"22",
"9",
"30",
"16",
"1",
"24",
"8",
"33",
"16",
"43",
"25",
"6",
"35",
"15",
"46",
"25",
"3",
"36",
"13",
"48",
"24",
"61",
"36",
"10",
"49",
"22",
"63",
"35",
"6",
"49",
"19",
"64",
"33",
"1",
"48",
"15",
"64",
"30",
"81",
"46",
"10",
"63",
"26",
"81",
"43",
"4",
"61",
"21",
"80",
"39",
"100",
"58",
"15",
"78",
"34",
"99"
] |
[
"nonn"
] | 49 | 1 | 3 |
[
"A000217",
"A001477",
"A093001",
"A288998",
"A355182"
] | null |
Andrea La Rosa, Jun 23 2022
| 2022-07-20T22:37:52 |
oeisdata/seq/A355/A355182.seq
|
1ff232dd671316450e9abec31bc59dc5
|
A355183
|
Decimal expansion of the area of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.
|
[
"2",
"1",
"8",
"9",
"5",
"1",
"4",
"1",
"6",
"4",
"9",
"7",
"4",
"6",
"0",
"0",
"6",
"5",
"0",
"6",
"8",
"9",
"1",
"8",
"2",
"9",
"8",
"9",
"4",
"6",
"2",
"6",
"4",
"1",
"0",
"4",
"7",
"5",
"9",
"5",
"6",
"2",
"5",
"0",
"0",
"5",
"0",
"2",
"5",
"9",
"7",
"4",
"3",
"0",
"9",
"0",
"2",
"2",
"3",
"9",
"6",
"5",
"0",
"6",
"5",
"4",
"3",
"0",
"9",
"9",
"7",
"1",
"2",
"8",
"2",
"8",
"0",
"9",
"3",
"8",
"5",
"1",
"3",
"3",
"8",
"5",
"0",
"0",
"4",
"5",
"7",
"7",
"0",
"1",
"8",
"8",
"7",
"6",
"3",
"6",
"4",
"6",
"6",
"8",
"5"
] |
[
"nonn",
"cons"
] | 9 | 0 | 1 |
[
"A021058",
"A103712",
"A244921",
"A254140",
"A352453",
"A355183",
"A355184",
"A355185"
] | null |
Amiram Eldar, Jun 23 2022
| 2022-06-23T13:49:07 |
oeisdata/seq/A355/A355183.seq
|
030e6dee9daa8225de3ab5cb4f9f37fb
|
A355184
|
Decimal expansion of the perimeter of the region that represents the set of points in a unit square that are closer to the center of the square than to the closest edge.
|
[
"1",
"7",
"0",
"3",
"0",
"8",
"2",
"4",
"9",
"6",
"6",
"5",
"8",
"9",
"5",
"3",
"2",
"2",
"7",
"8",
"3",
"5",
"8",
"4",
"9",
"1",
"2",
"2",
"7",
"4",
"9",
"2",
"0",
"3",
"1",
"5",
"7",
"1",
"9",
"8",
"0",
"3",
"4",
"4",
"2",
"2",
"9",
"5",
"0",
"4",
"9",
"7",
"7",
"1",
"2",
"1",
"2",
"1",
"6",
"6",
"0",
"3",
"7",
"8",
"4",
"2",
"1",
"7",
"2",
"6",
"9",
"2",
"4",
"5",
"5",
"2",
"3",
"3",
"5",
"0",
"4",
"9",
"0",
"3",
"5",
"1",
"6",
"3",
"3",
"3",
"3",
"1",
"2",
"3",
"5",
"3",
"4",
"0",
"2",
"3",
"8",
"9",
"5",
"7",
"0"
] |
[
"nonn",
"cons"
] | 5 | 1 | 2 |
[
"A103712",
"A244921",
"A254140",
"A352453",
"A355183",
"A355184"
] | null |
Amiram Eldar, Jun 23 2022
| 2022-06-23T13:49:16 |
oeisdata/seq/A355/A355184.seq
|
ecdafd822092084eb30cec5982575160
|
A355185
|
Decimal expansion of the volume of the region that represents the set of points in a unit cube that are closer to the center of the cube than to the closest face.
|
[
"8",
"6",
"8",
"4",
"1",
"0",
"0",
"4",
"8",
"8",
"2",
"4",
"6",
"1",
"3",
"5",
"4",
"3",
"9",
"7",
"2",
"8",
"3",
"7",
"1",
"1",
"6",
"2",
"5",
"7",
"6",
"9",
"3",
"0",
"8",
"2",
"3",
"8",
"6",
"3",
"6",
"4",
"3",
"9",
"3",
"0",
"7",
"0",
"9",
"8",
"2",
"4",
"8",
"6",
"8",
"0",
"9",
"5",
"3",
"2",
"9",
"6",
"1",
"9",
"3",
"5",
"2",
"9",
"4",
"5",
"7",
"5",
"4",
"9",
"1",
"5",
"2",
"2",
"0",
"7",
"9",
"4",
"0",
"7",
"1",
"9",
"2",
"4",
"6",
"2",
"3",
"3",
"6",
"2",
"4",
"6",
"1",
"9",
"3",
"6",
"0",
"4",
"5",
"7",
"6"
] |
[
"nonn",
"cons"
] | 5 | -1 | 1 |
[
"A093066",
"A097047",
"A355183",
"A355185"
] | null |
Amiram Eldar, Jun 23 2022
| 2022-06-23T13:49:23 |
oeisdata/seq/A355/A355185.seq
|
cd615b83aac8221d919b071b07ce9db7
|
A355186
|
Decimal expansion of 2*log(sqrt(2)+1)/Pi.
|
[
"5",
"6",
"1",
"0",
"9",
"9",
"8",
"5",
"2",
"3",
"3",
"9",
"1",
"8",
"0",
"1",
"2",
"7",
"1",
"3",
"5",
"7",
"1",
"9",
"5",
"8",
"8",
"9",
"3",
"5",
"2",
"3",
"9",
"6",
"9",
"2",
"8",
"0",
"8",
"8",
"7",
"2",
"4",
"2",
"4",
"6",
"2",
"8",
"0",
"9",
"9",
"9",
"2",
"5",
"8",
"9",
"9",
"5",
"5",
"9",
"3",
"1",
"2",
"6",
"7",
"0",
"5",
"5",
"5",
"8",
"5",
"5",
"7",
"8",
"8",
"0",
"5",
"6",
"3",
"6",
"3",
"0",
"5",
"3",
"9",
"4",
"5",
"3",
"8",
"8",
"1",
"1",
"6",
"0",
"7",
"0",
"0",
"8",
"2",
"9",
"2",
"3",
"0",
"2",
"7"
] |
[
"nonn",
"cons"
] | 6 | 0 | 1 |
[
"A019669",
"A060294",
"A091648",
"A345653",
"A355186"
] | null |
Amiram Eldar, Jun 23 2022
| 2022-06-23T13:49:35 |
oeisdata/seq/A355/A355186.seq
|
0bc17c73e1f92aa1e6001bc580b40ea2
|
A355187
|
Number of Collatz trajectories (A070165) for all positive integers <= 10^n that contain 2^4 as the greatest power of 2 within its trajectory.
|
[
"6",
"89",
"933",
"9401",
"93744",
"937712",
"9379078",
"93773848"
] |
[
"nonn",
"more"
] | 22 | 1 | 1 |
[
"A070165",
"A135282",
"A355187"
] | null |
Frank M Jackson, Jun 23 2022
| 2022-07-04T04:38:08 |
oeisdata/seq/A355/A355187.seq
|
ab5db3b366b1d25adebccc4d366d4858
|
A355188
|
Primes p such that (2^p+p^2)/3 is prime.
|
[
"5",
"7",
"17",
"43",
"61",
"73",
"241",
"739",
"1297",
"4211",
"98519"
] |
[
"nonn",
"more"
] | 24 | 1 | 1 |
[
"A242929",
"A355188"
] | null |
J. M. Bergot and Robert Israel, Jun 23 2022
| 2024-10-31T16:26:16 |
oeisdata/seq/A355/A355188.seq
|
b72bafe2682f436a4e320e8dfc8347bf
|
A355189
|
Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of x.
|
[
"1",
"1",
"1",
"1",
"2",
"4",
"8",
"14",
"32",
"70",
"140",
"324",
"768",
"1800",
"4368",
"10800",
"27300",
"70560",
"184800",
"494208",
"1343680",
"3704400",
"10388250",
"29560960",
"85250880",
"249318000",
"738720000",
"2216160000",
"6729074352",
"20675655000",
"64245312000",
"201819656500",
"640760440320"
] |
[
"nonn"
] | 10 | 0 | 5 |
[
"A060776",
"A060777",
"A060795",
"A060796",
"A061030",
"A061031",
"A061032",
"A061033",
"A200743",
"A200744",
"A355189",
"A355190",
"A355191",
"A355192"
] | null |
Max Alekseyev, Jun 23 2022
| 2022-06-25T21:56:44 |
oeisdata/seq/A355/A355189.seq
|
91c7a2b752f3f4e86267de4bdb8a7645
|
A355190
|
Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of y.
|
[
"1",
"1",
"1",
"2",
"3",
"5",
"9",
"18",
"35",
"72",
"160",
"350",
"770",
"1848",
"4455",
"10920",
"27648",
"70720",
"185895",
"496125",
"1344000",
"3706560",
"10395840",
"29568000",
"85299200",
"249356800",
"738840960",
"2216522880",
"6730407936",
"20678434920",
"64253314125",
"201847852800",
"640813814784",
"2055410286592",
"6658705461408",
"21780889600000"
] |
[
"nonn"
] | 8 | 0 | 4 |
[
"A060776",
"A060777",
"A060795",
"A060796",
"A061030",
"A061031",
"A061032",
"A061033",
"A200743",
"A200744",
"A355189",
"A355190",
"A355191",
"A355192"
] | null |
Max Alekseyev, Jun 23 2022
| 2022-06-25T21:56:52 |
oeisdata/seq/A355/A355190.seq
|
4a9a4918eda8ca5c93447690950f9e83
|
A355191
|
Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of z.
|
[
"1",
"1",
"2",
"3",
"4",
"6",
"10",
"20",
"36",
"72",
"162",
"352",
"810",
"1872",
"4480",
"11088",
"27720",
"71280",
"186368",
"496128",
"1347192",
"3720960",
"10407936",
"29576988",
"85322160",
"249500160",
"738904320",
"2216712960",
"6732000000",
"20680540160",
"64257392640",
"201852518400",
"640832000000",
"2055425699250",
"6658777165824",
"21781337550336"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A060776",
"A060777",
"A060795",
"A060796",
"A061030",
"A061031",
"A061032",
"A061033",
"A200743",
"A200744",
"A355189",
"A355190",
"A355191",
"A355192"
] | null |
Max Alekseyev, Jun 23 2022
| 2022-06-25T21:57:02 |
oeisdata/seq/A355/A355191.seq
|
c483848a0c0f347ccc85460c680a625e
|
A355192
|
Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of z-x.
|
[
"0",
"0",
"1",
"2",
"2",
"2",
"2",
"6",
"4",
"2",
"22",
"28",
"42",
"72",
"112",
"288",
"420",
"720",
"1568",
"1920",
"3512",
"16560",
"19686",
"16028",
"71280",
"182160",
"184320",
"552960",
"2925648",
"4885160",
"12080640",
"32861900",
"71559680",
"77631750",
"217165824",
"604653336",
"368858880",
"4069377144",
"7919402400",
"17537715360",
"87352688640",
"127718553600"
] |
[
"nonn"
] | 9 | 0 | 4 |
[
"A060776",
"A060777",
"A060795",
"A060796",
"A061030",
"A061031",
"A061032",
"A061033",
"A200743",
"A200744",
"A355189",
"A355190",
"A355191",
"A355192"
] | null |
Max Alekseyev, Jun 23 2022
| 2022-06-25T21:57:10 |
oeisdata/seq/A355/A355192.seq
|
bace5b94f0878edac6ba76b7485a9dfa
|
A355193
|
Number of partitions of n that contain at least one odd prime as a part.
|
[
"0",
"0",
"0",
"1",
"1",
"3",
"4",
"8",
"10",
"17",
"22",
"35",
"45",
"67",
"86",
"123",
"156",
"216",
"273",
"369",
"463",
"613",
"765",
"997",
"1236",
"1587",
"1958",
"2485",
"3049",
"3830",
"4677",
"5823",
"7077",
"8740",
"10576",
"12971",
"15629",
"19046",
"22862",
"27701",
"33125",
"39928",
"47579",
"57078",
"67788",
"80963",
"95852",
"114023"
] |
[
"nonn"
] | 24 | 0 | 6 |
[
"A000041",
"A065091",
"A235945",
"A353188",
"A355193",
"A355195"
] | null |
Omar E. Pol, Jun 23 2022
| 2022-10-12T17:16:06 |
oeisdata/seq/A355/A355193.seq
|
d4cc10d5045177745d80a66d1fa0a96c
|
A355194
|
The number of evenly tagged partitions: partitions of n elements together with an involution defined on the set of classes which has at most one fixed point, such that a class and its image have the same number of elements.
|
[
"1",
"1",
"2",
"4",
"13",
"41",
"176",
"722",
"3774",
"18958",
"116302",
"687182",
"4812226",
"32541874",
"255274826",
"1938568634",
"16798483589",
"141220228149",
"1337121257864",
"12305678519102",
"126208299343263",
"1260257489267963",
"13901541357573146",
"149520289244078172",
"1763398965493327476"
] |
[
"nonn"
] | 36 | 0 | 3 |
[
"A350291",
"A355194"
] | null |
Eddie Nijholt, Jun 23 2022
| 2025-03-22T20:42:40 |
oeisdata/seq/A355/A355194.seq
|
0ef2f140f35028dab236f667b3bf8fb8
|
A355195
|
Number of partitions of n that do not contain odd primes as parts.
|
[
"1",
"1",
"2",
"2",
"4",
"4",
"7",
"7",
"12",
"13",
"20",
"21",
"32",
"34",
"49",
"53",
"75",
"81",
"112",
"121",
"164",
"179",
"237",
"258",
"339",
"371",
"478",
"525",
"669",
"735",
"927",
"1019",
"1272",
"1403",
"1734",
"1912",
"2348",
"2591",
"3153",
"3484",
"4213",
"4655",
"5595",
"6183",
"7387",
"8171",
"9706",
"10731",
"12692",
"14035",
"16515",
"18266"
] |
[
"nonn"
] | 27 | 0 | 3 |
[
"A000041",
"A065091",
"A353188",
"A355193",
"A355195"
] | null |
Omar E. Pol, Jun 23 2022
| 2022-06-24T17:12:38 |
oeisdata/seq/A355/A355195.seq
|
910b3920f0356ad9877aac27ed3718f8
|
A355196
|
Sum of the largest parts of the partitions of n into exactly 3 prime parts.
|
[
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"3",
"3",
"8",
"5",
"12",
"12",
"12",
"7",
"23",
"18",
"38",
"24",
"31",
"24",
"59",
"30",
"73",
"47",
"71",
"49",
"113",
"55",
"115",
"40",
"102",
"59",
"171",
"48",
"168",
"100",
"191",
"102",
"220",
"50",
"265",
"89",
"246",
"120",
"322",
"109",
"383",
"136",
"348",
"181",
"477",
"158",
"516",
"117",
"468",
"199",
"605",
"133",
"574",
"170",
"600",
"252",
"751",
"133"
] |
[
"nonn"
] | 6 | 0 | 7 |
[
"A010051",
"A068307",
"A355196",
"A355197",
"A355198",
"A355199"
] | null |
Wesley Ivan Hurt, Jun 23 2022
| 2022-06-25T01:21:01 |
oeisdata/seq/A355/A355196.seq
|
3b97771d7bad32c8a5f8e16da6d384fa
|
A355197
|
Sum of the middle parts of the partitions of n into exactly 3 prime parts.
|
[
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"2",
"3",
"5",
"3",
"5",
"8",
"8",
"5",
"12",
"10",
"17",
"8",
"15",
"12",
"26",
"10",
"24",
"19",
"33",
"23",
"48",
"23",
"57",
"16",
"54",
"31",
"80",
"16",
"71",
"36",
"93",
"42",
"112",
"26",
"122",
"31",
"120",
"48",
"145",
"23",
"148",
"48",
"160",
"59",
"190",
"42",
"218",
"39",
"196",
"71",
"240",
"35",
"246",
"62",
"252",
"108",
"310",
"53",
"366",
"59",
"340",
"96"
] |
[
"nonn"
] | 5 | 0 | 7 |
[
"A010051",
"A068307",
"A355196",
"A355197",
"A355198",
"A355199"
] | null |
Wesley Ivan Hurt, Jun 23 2022
| 2022-06-25T01:21:08 |
oeisdata/seq/A355/A355197.seq
|
c261e63399035d47d32c38b1010301f3
|
A355198
|
Sum of the smallest parts of the partitions of n into exactly 3 prime parts.
|
[
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"2",
"2",
"5",
"2",
"5",
"4",
"6",
"2",
"10",
"4",
"13",
"4",
"11",
"4",
"20",
"4",
"18",
"6",
"21",
"6",
"28",
"6",
"31",
"4",
"30",
"6",
"46",
"4",
"41",
"8",
"49",
"8",
"58",
"4",
"64",
"6",
"64",
"8",
"73",
"6",
"80",
"8",
"80",
"10",
"98",
"8",
"114",
"6",
"106",
"10",
"124",
"6",
"124",
"8",
"124",
"12",
"136",
"6",
"172",
"10",
"164",
"12",
"170",
"4",
"193",
"10",
"183",
"12",
"189"
] |
[
"nonn"
] | 5 | 0 | 7 |
[
"A010051",
"A068307",
"A355196",
"A355197",
"A355198",
"A355199"
] | null |
Wesley Ivan Hurt, Jun 23 2022
| 2022-06-25T01:21:17 |
oeisdata/seq/A355/A355198.seq
|
5a13d37668dc7014eed1816f0e18ca8b
|
A355199
|
Sum of all the parts in the partitions of n into exactly 3 prime parts.
|
[
"0",
"0",
"0",
"0",
"0",
"0",
"6",
"7",
"8",
"18",
"10",
"22",
"24",
"26",
"14",
"45",
"32",
"68",
"36",
"57",
"40",
"105",
"44",
"115",
"72",
"125",
"78",
"189",
"84",
"203",
"60",
"186",
"96",
"297",
"68",
"280",
"144",
"333",
"152",
"390",
"80",
"451",
"126",
"430",
"176",
"540",
"138",
"611",
"192",
"588",
"250",
"765",
"208",
"848",
"162",
"770",
"280",
"969",
"174",
"944",
"240",
"976",
"372"
] |
[
"nonn"
] | 4 | 0 | 7 |
[
"A010051",
"A068307",
"A355196",
"A355197",
"A355198",
"A355199"
] | null |
Wesley Ivan Hurt, Jun 23 2022
| 2022-06-25T01:21:25 |
oeisdata/seq/A355/A355199.seq
|
9f5c0a163a7f15e1d6b104e56d889810
|
A355200
|
Numbers k that can be written as the sum of 3 divisors of k (not necessarily distinct).
|
[
"3",
"4",
"6",
"8",
"9",
"12",
"15",
"16",
"18",
"20",
"21",
"24",
"27",
"28",
"30",
"32",
"33",
"36",
"39",
"40",
"42",
"44",
"45",
"48",
"51",
"52",
"54",
"56",
"57",
"60",
"63",
"64",
"66",
"68",
"69",
"72",
"75",
"76",
"78",
"80",
"81",
"84",
"87",
"88",
"90",
"92",
"93",
"96",
"99",
"100",
"102",
"104",
"105",
"108",
"111",
"112",
"114",
"116",
"117",
"120",
"123",
"124",
"126",
"128",
"129",
"132",
"135"
] |
[
"nonn",
"easy",
"changed"
] | 52 | 1 | 1 |
[
"A000027",
"A002966",
"A005843",
"A008585",
"A008586",
"A008588",
"A134667",
"A299174",
"A348536",
"A354591",
"A355200",
"A355641",
"A356609",
"A356635",
"A356657",
"A356659",
"A356660"
] | null |
Wesley Ivan Hurt, Jun 23 2022
| 2025-07-17T07:55:46 |
oeisdata/seq/A355/A355200.seq
|
5649eac1e68ee9fc9628d5de71982789
|
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