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| sequence_name
stringlengths 4
573
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listlengths 1
348
| keywords
listlengths 1
8
| score
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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
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| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A356801 | a(n) is the least semiprime p*q such that p*q+i*(p+q) is prime for i from 1 to n but not n+1. | [
"4",
"6",
"15",
"155",
"35",
"851",
"34601",
"474869",
"15157931",
"1467715961"
]
| [
"nonn",
"more",
"hard"
]
| 20 | 0 | 1 | [
"A001358",
"A034386",
"A356801",
"A356825"
]
| null | J. M. Bergot and Robert Israel, Aug 28 2022 | 2024-04-16T13:41:35 | oeisdata/seq/A356/A356801.seq | 169d68524ee0d0f3237fdc1accabf768 |
A356802 | A refinement of the Mahonian numbers (non-canonical ordering). | [
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"3",
"5",
"3",
"3",
"5",
"3",
"1",
"1",
"4",
"9",
"6",
"9",
"16",
"4",
"11",
"11",
"4",
"16",
"9",
"6",
"9",
"4",
"1",
"1",
"5",
"14",
"10",
"19",
"35",
"14",
"26",
"40",
"5",
"10",
"61",
"19",
"35",
"26",
"40",
"40",
"26",
"35",
"19",
"61",
"10",
"5",
"40",
"26",
"14",
"35",
"19",
"10",
"14",
"5",
"1"
]
| [
"nonn",
"tabf"
]
| 30 | 1 | 5 | [
"A008302",
"A356802",
"A357611"
]
| null | Denis K. Sunko, Aug 28 2022 | 2023-03-18T08:49:14 | oeisdata/seq/A356/A356802.seq | f538bcba14f97161b52aba8fc257bd8c |
A356803 | a(n) = product of prohibited prime factors of A354790(n). | [
"1",
"1",
"2",
"6",
"15",
"105",
"385",
"2310",
"6006",
"102102",
"277134",
"6374082",
"16804398",
"520936338",
"3038795305",
"66853496710",
"190275336790",
"7420738134810",
"17897074325130",
"769574195980590",
"1903683537425670",
"100895227483560510",
"258818192240437830",
"15787909726666707630",
"36475515575402393490"
]
| [
"nonn"
]
| 11 | 1 | 3 | [
"A354790",
"A355057",
"A356803"
]
| null | Michael De Vlieger, Sep 06 2022 | 2022-09-08T01:34:57 | oeisdata/seq/A356/A356803.seq | c5b7359b02ecc0b209e84e4fde5d23dd |
A356804 | a(n) is a binary encoded version of A356803(n). | [
"0",
"0",
"1",
"3",
"6",
"14",
"28",
"31",
"59",
"123",
"243",
"499",
"995",
"2019",
"2028",
"2045",
"4061",
"4095",
"8127",
"16319",
"32575",
"65343",
"130623",
"261695",
"523327",
"1047615",
"2095167",
"4192319",
"8386611",
"8386679",
"16775270",
"16775279",
"33550447",
"67104879",
"134213709",
"134213727",
"268427359",
"536862815"
]
| [
"nonn",
"base"
]
| 9 | 1 | 4 | [
"A354790",
"A356803",
"A356804"
]
| null | Michael De Vlieger, Sep 06 2022 | 2022-09-08T01:35:01 | oeisdata/seq/A356/A356804.seq | fe97b2a09105cf9b674db7ba1deb9f84 |
A356805 | Decimal expansion of the unique positive real root of the equation x^x^(x - 1) = x + 1. | [
"1",
"8",
"5",
"5",
"6",
"6",
"0",
"2",
"3",
"1",
"9",
"6",
"1",
"7",
"3",
"1",
"1",
"1",
"2",
"6",
"7",
"8",
"8",
"3",
"9",
"3",
"7",
"4",
"4",
"4",
"3",
"4",
"8",
"0",
"8",
"7",
"7",
"9",
"0",
"3",
"4",
"8",
"4",
"1",
"9",
"2",
"8",
"0",
"0",
"3",
"4",
"4",
"9",
"5",
"5",
"1",
"8",
"0",
"8",
"8",
"5",
"2",
"3",
"4",
"5",
"2",
"8",
"5",
"5",
"9",
"6",
"7",
"9",
"7",
"3",
"8",
"7",
"3",
"8",
"5",
"8",
"3",
"4",
"7",
"4",
"8",
"9"
]
| [
"cons",
"nonn"
]
| 13 | 1 | 2 | [
"A124930",
"A356562",
"A356805"
]
| null | Marco Ripà and Flavio Niccolò Baglioni, Aug 28 2022 | 2022-09-05T09:10:16 | oeisdata/seq/A356/A356805.seq | 88ebb86867d56de1db2f2a5bc0e2750f |
A356806 | a(n) = Sum_{k=0..n} (k*n-1)^(n-k) * binomial(n,k). | [
"1",
"0",
"4",
"27",
"448",
"10625",
"344736",
"14437213",
"753991680",
"47974773393",
"3650824000000",
"326917384798301",
"33956137832546304",
"4041303651931462969",
"545552768347831566336",
"82828479894303251953125",
"14040577418634835164921856",
"2640293357854435329683551265"
]
| [
"nonn"
]
| 18 | 0 | 3 | [
"A052506",
"A351736",
"A351737",
"A356806",
"A356811",
"A356814",
"A356817"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-09-01T09:31:30 | oeisdata/seq/A356/A356806.seq | 2f5b2b53cf1b2d9a19a9e299e0b99e2c |
A356807 | Tetranacci sequence beginning with 3, 7, 12, 24. | [
"3",
"7",
"12",
"24",
"46",
"89",
"171",
"330",
"636",
"1226",
"2363",
"4555",
"8780",
"16924",
"32622",
"62881",
"121207",
"233634",
"450344",
"868066",
"1673251",
"3225295",
"6216956",
"11983568",
"23099070",
"44524889",
"85824483",
"165432010",
"318880452",
"614661834",
"1184798779",
"2283773075",
"4402114140",
"8485347828"
]
| [
"nonn",
"easy"
]
| 34 | 1 | 1 | [
"A022120",
"A100683",
"A356807"
]
| null | Greg Dresden and Hangyu Liang, Aug 29 2022 | 2024-08-30T09:53:10 | oeisdata/seq/A356/A356807.seq | f05bfa5ed53793b8d82adb803004d480 |
A356808 | Number of n-level magic triangles. | [
"1",
"4",
"96",
"238536576"
]
| [
"nonn",
"hard",
"more"
]
| 5 | 1 | 2 | null | null | Michel Marcus, Aug 29 2022 | 2022-08-29T10:22:42 | oeisdata/seq/A356/A356808.seq | 7267ec456c7da6a775377e47dce329d5 |
A356809 | Fibonacci numbers which are not the sum of two squares. | [
"3",
"21",
"55",
"987",
"2584",
"6765",
"17711",
"46368",
"317811",
"832040",
"2178309",
"5702887",
"14930352",
"102334155",
"267914296",
"701408733",
"1836311903",
"4807526976",
"12586269025",
"32951280099",
"86267571272",
"225851433717",
"591286729879",
"1548008755920",
"10610209857723"
]
| [
"nonn"
]
| 24 | 1 | 1 | [
"A000045",
"A001481",
"A022340",
"A022544",
"A124132",
"A124134",
"A236264",
"A356809"
]
| null | Ctibor O. Zizka, Aug 29 2022 | 2023-01-10T18:19:28 | oeisdata/seq/A356/A356809.seq | 36bd88000d7bd5545a85c9d633a439d9 |
A356810 | Decimal expansion of the unique root of the equation x^(x^(((log(x))^(x-1) - 1)/(log(x) - 1))) = x+1 for x in the interval [1,2]. | [
"1",
"8",
"4",
"4",
"1",
"6",
"2",
"9",
"7",
"4",
"9",
"0",
"1",
"6",
"0",
"9",
"2",
"5",
"8",
"5",
"2",
"9",
"3",
"4",
"7",
"2",
"0",
"8",
"8",
"4",
"8",
"0",
"6",
"3",
"2",
"5",
"5",
"5",
"8",
"0",
"4",
"7",
"6",
"6",
"4",
"5",
"6",
"4",
"4",
"5",
"0",
"9",
"0",
"7",
"1",
"3",
"9",
"8",
"0",
"4",
"3",
"8",
"3",
"0",
"2",
"7",
"5",
"0",
"8",
"0",
"2",
"1",
"1",
"3",
"9",
"1",
"5",
"8",
"0",
"9",
"5",
"8",
"3",
"8",
"4",
"2",
"1",
"8",
"9",
"1",
"8",
"7",
"8",
"6",
"0",
"3",
"1",
"7"
]
| [
"cons",
"nonn"
]
| 31 | 1 | 2 | [
"A356805",
"A356810"
]
| null | Flavio Niccolò Baglioni and Marco Ripà, Aug 29 2022 | 2022-10-01T01:17:58 | oeisdata/seq/A356/A356810.seq | 6096b8ade78a7ea163e7efea8044d36d |
A356811 | a(n) = Sum_{k=0..n} (k*n+1)^(n-k) * binomial(n,k). | [
"1",
"2",
"8",
"71",
"1040",
"22457",
"676000",
"26861977",
"1347932416",
"82873789793",
"6114540967424",
"532596023373713",
"53990083205042176",
"6289985311473281329",
"833180470332123750400",
"124356049859476364116193",
"20754548375601491155681280",
"3847574240184742568296430273"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A080108",
"A240165",
"A245834",
"A356806",
"A356811",
"A356814",
"A356817"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-09-01T09:31:08 | oeisdata/seq/A356/A356811.seq | 949df4a7b218adb9ac9328bb008ea1f2 |
A356812 | Expansion of e.g.f. exp(x * (1 - exp(2*x))). | [
"1",
"0",
"-4",
"-12",
"16",
"400",
"2208",
"-448",
"-131840",
"-1357056",
"-4820480",
"71120896",
"1537308672",
"14006460416",
"3075702784",
"-2224350781440",
"-41354996154368",
"-359660395495424",
"1675436608585728",
"121894823709900800",
"2317859245604208640",
"20543311167964053504"
]
| [
"sign"
]
| 26 | 0 | 3 | [
"A292893",
"A351736",
"A356812",
"A356813",
"A356815",
"A356819"
]
| null | Seiichi Manyama, Aug 29 2022 | 2023-10-04T15:07:59 | oeisdata/seq/A356/A356812.seq | 10cb93223ceeaedc0442fc5aec402b2f |
A356813 | Expansion of e.g.f. exp(x * (1 - exp(3*x))). | [
"1",
"0",
"-6",
"-27",
"0",
"1215",
"12312",
"45927",
"-657072",
"-15857937",
"-167699160",
"-266960529",
"29356170984",
"700068823623",
"8419188469104",
"-1491045413265",
"-2856006296224992",
"-79065447339366945",
"-1162293393139510824",
"-744123842820101745",
"538503788896323210360"
]
| [
"sign"
]
| 20 | 0 | 3 | [
"A292893",
"A351737",
"A356812",
"A356813",
"A356816"
]
| null | Seiichi Manyama, Aug 29 2022 | 2023-02-23T18:03:42 | oeisdata/seq/A356/A356813.seq | d43d3cea4e8c6cc337889eaeb6e1924a |
A356814 | a(n) = Sum_{k=0..n} (-1)^k * (k*n+1)^(n-k) * binomial(n,k). | [
"1",
"0",
"-4",
"-27",
"-64",
"4375",
"199584",
"6739607",
"169934848",
"-1012395105",
"-709624000000",
"-86599643309201",
"-8221227668471808",
"-638169258399740977",
"-27617164284655812608",
"3853095093357099609375",
"1568756883209662050074624",
"360407172063462944082773311"
]
| [
"sign"
]
| 12 | 0 | 3 | [
"A292893",
"A320258",
"A356806",
"A356811",
"A356812",
"A356813",
"A356814",
"A356817"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-08-29T16:35:56 | oeisdata/seq/A356/A356814.seq | 903650e5fffb06324f9845e3d133f52b |
A356815 | Expansion of e.g.f. exp(-x * (exp(2*x) + 1)). | [
"1",
"-2",
"0",
"4",
"32",
"48",
"-608",
"-6400",
"-24064",
"163072",
"3567104",
"28394496",
"6535168",
"-3250745344",
"-50725740544",
"-344530853888",
"2476610551808",
"110057610608640",
"1655672654135296",
"9616664975114240",
"-195178079811272704",
"-6998474114188967936",
"-110894925369151848448"
]
| [
"sign"
]
| 17 | 0 | 2 | [
"A240165",
"A351736",
"A356812",
"A356815",
"A356816",
"A356818"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-08-31T09:09:47 | oeisdata/seq/A356/A356815.seq | 48ee4e9a6e692b251beb259f7b4a5974 |
A356816 | Expansion of e.g.f. exp(-x * (exp(3*x) + 1)). | [
"1",
"-2",
"-2",
"1",
"88",
"583",
"676",
"-35597",
"-519392",
"-3359393",
"19013884",
"896435395",
"13640180896",
"85591357135",
"-1527872118356",
"-61100053650053",
"-1076294742932288",
"-7610985095240513",
"200631806070276988",
"9284475508083767059",
"200226297062313730816",
"1940767272243466116463"
]
| [
"sign"
]
| 14 | 0 | 2 | [
"A351737",
"A356813",
"A356815",
"A356816",
"A356818"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-08-31T09:09:38 | oeisdata/seq/A356/A356816.seq | c81b68bf622a5e256fde4a452128e3b3 |
A356817 | a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k). | [
"1",
"-2",
"0",
"1",
"144",
"4143",
"110368",
"2535475",
"13299968",
"-5169863825",
"-639341093376",
"-59073970497885",
"-4677854594527232",
"-276406098219258425",
"2399871442122924032",
"5163244810691492730907",
"1331213942683118587674624",
"262517264591996332314037215"
]
| [
"sign"
]
| 11 | 0 | 2 | [
"A356806",
"A356811",
"A356814",
"A356815",
"A356816",
"A356817",
"A356818"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-08-29T16:36:01 | oeisdata/seq/A356/A356817.seq | b92f3c36953725ae11f5149eb240e577 |
A356818 | Expansion of e.g.f. exp(-x * (exp(x) + 1)). | [
"1",
"-2",
"2",
"1",
"0",
"-17",
"-32",
"103",
"976",
"2287",
"-12816",
"-143585",
"-481016",
"2339335",
"39769720",
"209863327",
"-397553376",
"-16949434913",
"-142681662368",
"-233212601153",
"9138353475736",
"128343346833463",
"702261255539496",
"-4251314594919617",
"-135331386127555856"
]
| [
"sign"
]
| 12 | 0 | 2 | [
"A356815",
"A356816",
"A356818"
]
| null | Seiichi Manyama, Aug 29 2022 | 2022-08-31T09:09:42 | oeisdata/seq/A356/A356818.seq | 959170000b87a0ea47a48800cef31c21 |
A356819 | Expansion of e.g.f. exp(-x * exp(2*x)). | [
"1",
"-1",
"-3",
"-1",
"41",
"239",
"229",
"-8401",
"-87151",
"-324577",
"3238541",
"70271519",
"601086265",
"142860431",
"-81504662539",
"-1393683935281",
"-10777424809951",
"63537986981183",
"3552608426329117",
"60283510555017023",
"441644419610814281",
"-6191820436867600081"
]
| [
"sign"
]
| 13 | 0 | 3 | [
"A216689",
"A292952",
"A356812",
"A356819",
"A356820"
]
| null | Seiichi Manyama, Aug 29 2022 | 2023-02-23T18:03:22 | oeisdata/seq/A356/A356819.seq | abc85046c3f31107dcccc1454cb875ac |
A356820 | Expansion of e.g.f. exp(-x * exp(3*x)). | [
"1",
"-1",
"-5",
"-10",
"73",
"1004",
"5473",
"-15562",
"-746447",
"-9174088",
"-41916959",
"823985546",
"24629093641",
"335144105828",
"1248594602305",
"-67564407472426",
"-2160461588461343",
"-34957074099518608",
"-154556217713939903",
"10500560586914149250",
"409146670525578079801"
]
| [
"sign"
]
| 14 | 0 | 3 | [
"A292952",
"A356813",
"A356819",
"A356820"
]
| null | Seiichi Manyama, Aug 29 2022 | 2025-03-13T14:36:06 | oeisdata/seq/A356/A356820.seq | 5d2a5e0b1e29f41008e65d00ac7640dc |
A356821 | Lucas-Carmichael numbers k that have an abundancy index sigma(k)/k that is larger than the abundancy indices of all smaller Lucas-Carmichael numbers. | [
"399",
"6304359999",
"408598269695",
"517270926095",
"20203946790335"
]
| [
"nonn",
"hard",
"more"
]
| 14 | 1 | 1 | [
"A000203",
"A004394",
"A006972",
"A328691",
"A329460",
"A356821"
]
| null | Amiram Eldar and Daniel Suteu, Aug 29 2022 | 2023-07-30T09:04:17 | oeisdata/seq/A356/A356821.seq | 6ff85676c78a611b176fb5a7ccf95c8a |
A356822 | Irregular triangle read by rows where row n starts with n and each further term is the sum of the distinct palindromes in the concatenation of the decimal digits of preceding terms. | [
"1",
"1",
"12",
"125",
"463",
"476",
"483",
"491",
"500",
"500",
"6055",
"6170",
"2",
"2",
"24",
"250",
"497",
"513",
"517",
"3",
"3",
"36",
"375",
"750",
"2082",
"2112",
"4258",
"4504",
"4504",
"4548",
"5002",
"4",
"4",
"48",
"500",
"505",
"6065",
"62742",
"63407",
"63410",
"63411",
"63422",
"63444",
"5",
"5",
"60",
"66",
"738",
"756"
]
| [
"nonn",
"tabf",
"look",
"base"
]
| 50 | 1 | 3 | null | null | Neal Gersh Tolunsky, Sep 17 2022 | 2023-09-26T19:16:11 | oeisdata/seq/A356/A356822.seq | 636f77c849d094cf04a5d7b0bf5ecddc |
A356823 | Tribternary numbers. | [
"0",
"1",
"3",
"4",
"9",
"10",
"12",
"27",
"28",
"30",
"31",
"36",
"37",
"81",
"82",
"84",
"85",
"90",
"91",
"93",
"108",
"109",
"111",
"112",
"243",
"244",
"246",
"247",
"252",
"253",
"255",
"270",
"271",
"273",
"274",
"279",
"280",
"324",
"325",
"327",
"328",
"333",
"334",
"336",
"729",
"730",
"732",
"733",
"738",
"739",
"741",
"756",
"757",
"759",
"760",
"765",
"766",
"810",
"811",
"813",
"814",
"819"
]
| [
"nonn",
"base"
]
| 9 | 1 | 3 | [
"A003714",
"A003726",
"A005836",
"A060140",
"A356823"
]
| null | Tanya Khovanova and PRIMES STEP Senior group, Aug 29 2022 | 2022-08-30T13:42:41 | oeisdata/seq/A356/A356823.seq | d844e33fef11192826fd07356fbcb32c |
A356824 | Palindromes that can be written as the sum of two palindromic primes. | [
"4",
"5",
"6",
"7",
"8",
"9",
"22",
"202",
"232",
"252",
"262",
"282",
"292",
"414",
"444",
"454",
"464",
"474",
"484",
"494",
"626",
"666",
"686",
"696",
"808",
"828",
"858",
"878",
"888",
"898",
"20002",
"20602",
"20802",
"20902",
"21612",
"21712",
"21812",
"21912",
"22622",
"22722",
"22822",
"22922",
"23632",
"23732",
"23832",
"23932",
"24642",
"24742",
"24842",
"24942"
]
| [
"nonn",
"base"
]
| 17 | 1 | 1 | [
"A002113",
"A002385",
"A261906",
"A356824"
]
| null | Tanya Khovanova, Aug 29 2022 | 2022-09-04T12:46:24 | oeisdata/seq/A356/A356824.seq | d23f1fda9b5729571cfa25115b7de981 |
A356825 | a(n) is the least semiprime p*q such that p*q-i*(p+q) is prime for i from 1 to n but not n+1. | [
"4",
"9",
"33",
"65",
"77",
"161",
"371",
"38981",
"2561",
"568181"
]
| [
"nonn",
"more"
]
| 10 | 0 | 1 | [
"A001358",
"A356801",
"A356825"
]
| null | J. M. Bergot and Robert Israel, Aug 29 2022 | 2022-09-04T12:53:28 | oeisdata/seq/A356/A356825.seq | d9fb3ba08dd1344cdc059aee9dacdf6a |
A356826 | Numbers k such that 2^k - 29 is prime. | [
"5",
"8",
"104",
"212",
"79316",
"102272",
"225536",
"340688"
]
| [
"nonn",
"more"
]
| 26 | 1 | 1 | [
"A000043",
"A050414",
"A057220",
"A059608",
"A059609",
"A059610",
"A059611",
"A059612",
"A096502",
"A096817",
"A096818",
"A096819",
"A096820",
"A356826"
]
| null | Craig J. Beisel, Aug 29 2022 | 2023-12-10T09:17:13 | oeisdata/seq/A356/A356826.seq | dc46508bec3407ed880c8f8a8d97f0fa |
A356827 | Expansion of e.g.f. exp(x * exp(3*x)). | [
"1",
"1",
"7",
"46",
"361",
"3436",
"37729",
"463366",
"6280369",
"93015352",
"1491337441",
"25684077706",
"472217487625",
"9221588527204",
"190441412508481",
"4143470377262806",
"94663498086222049",
"2264440394856702832",
"56570146384760433217",
"1472545685988162638722"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A000248",
"A003725",
"A216689",
"A277456",
"A295552",
"A336951",
"A351737",
"A355501",
"A356820",
"A356827"
]
| null | Seiichi Manyama, Aug 29 2022 | 2023-12-04T06:29:10 | oeisdata/seq/A356/A356827.seq | e5bd3e4a05d4960be0226a9296dcdb7f |
A356828 | Number of vertex cuts in the n-ladder graph P_2 x P_n. | [
"0",
"2",
"23",
"147",
"748",
"3414",
"14719",
"61495",
"252364",
"1024938",
"4137207",
"16639339",
"66775964",
"267631726",
"1071801407",
"4290282671",
"17168559452",
"68692172578",
"274811988823",
"1099352487299",
"4397662311948",
"17591258505542",
"70366504900671",
"281469570617703",
"1125886855379628"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 2 | [
"A059020",
"A356828"
]
| null | Eric W. Weisstein, Aug 30 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356828.seq | 3a59f759bd0fb9e1d95cc7ccb9ea41fc |
A356829 | Number of vertex cuts in the n-Möbius ladder. | [
"0",
"0",
"8",
"82",
"512",
"2644",
"12364",
"54598",
"232772",
"970520",
"3988624",
"16239066",
"65709256",
"264814140",
"1064414100",
"4271035662",
"17118683020",
"68563527616",
"274481537112",
"1098506723042",
"4395504614544",
"17585769696164",
"70352578566620",
"281434319454038",
"1125797816327892"
]
| [
"nonn"
]
| 16 | 1 | 3 | [
"A286185",
"A356829"
]
| null | Eric W. Weisstein, Aug 30 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356829.seq | 38ef413086288b28a7da04f459b13e7c |
A356830 | Number of vertex cuts in the n-prism graph. | [
"0",
"2",
"12",
"88",
"520",
"2654",
"12376",
"54612",
"232788",
"970538",
"3988644",
"16239088",
"65709280",
"264814166",
"1064414128",
"4271035692",
"17118683052",
"68563527650",
"274481537148",
"1098506723080",
"4395504614584",
"17585769696206",
"70352578566664",
"281434319454084",
"1125797816327940"
]
| [
"nonn"
]
| 25 | 1 | 2 | [
"A000129",
"A002203",
"A286182",
"A356830"
]
| null | Eric W. Weisstein, Aug 30 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356830.seq | 1b94f4c7ac881afe9b35db0e0f7a261f |
A356831 | Size of the automorphism group for the underlying graph of the divisibility graph of size n. | [
"1",
"2",
"2",
"2",
"4",
"2",
"4",
"4",
"4",
"2",
"4",
"2",
"6",
"4",
"2",
"4",
"12",
"12",
"48",
"48",
"48",
"12",
"48",
"24",
"24",
"12",
"12",
"12",
"48",
"48",
"240",
"480",
"240",
"96",
"96",
"96",
"480",
"288",
"192",
"192",
"960",
"960",
"5760",
"2880",
"2880",
"1440",
"8640",
"4320",
"4320",
"4320",
"2880",
"2880",
"20160",
"20160",
"10080",
"10080",
"10080",
"2880",
"20160",
"20160",
"161280",
"60480",
"60480",
"120960",
"241920",
"120960"
]
| [
"nonn"
]
| 25 | 1 | 2 | null | null | Nils Gaute Voll, Aug 30 2022 | 2024-12-19T11:45:36 | oeisdata/seq/A356/A356831.seq | cd1c25ee89bb8ad459ea5cc1de38f448 |
A356832 | Number of permutations p of [n] such that at most one element of {p(1),...,p(i-1)} is between p(i) and p(i+1) for all i < n and n = 0 or p(n) < 3. | [
"1",
"1",
"2",
"4",
"10",
"26",
"72",
"206",
"608",
"1834",
"5636",
"17578",
"55516",
"177192",
"570700",
"1852572",
"6055080",
"19910730",
"65823752",
"218654100",
"729459552",
"2443051214",
"8210993364",
"27685671844",
"93625082140",
"317470233150",
"1079183930828",
"3676951654520",
"12554734605496",
"42952566314236"
]
| [
"nonn"
]
| 20 | 0 | 3 | [
"A000142",
"A102407",
"A216837",
"A291683",
"A356692",
"A356832"
]
| null | Alois P. Heinz, Aug 30 2022 | 2022-09-03T22:09:43 | oeisdata/seq/A356/A356832.seq | 64757b184a66620df3441a2e36d76520 |
A356833 | Primes p such that the minimum number of divisors among the numbers between p and NextPrime(p) is a square. | [
"5",
"13",
"19",
"31",
"37",
"43",
"53",
"61",
"67",
"73",
"79",
"83",
"89",
"103",
"109",
"127",
"131",
"139",
"151",
"157",
"163",
"173",
"181",
"193",
"199",
"211",
"223",
"233",
"241",
"251",
"257",
"263",
"269",
"271",
"277",
"293",
"307",
"311",
"313",
"317",
"331",
"337",
"353",
"367",
"373",
"379",
"383",
"389",
"397",
"401",
"409",
"421",
"433",
"443",
"449",
"457",
"461",
"463",
"467",
"479"
]
| [
"nonn",
"easy"
]
| 50 | 1 | 1 | [
"A000005",
"A000040",
"A000290",
"A036436",
"A061112",
"A353284",
"A353285",
"A353286",
"A356833",
"A357170",
"A357175"
]
| null | Claude H. R. Dequatre, Sep 16 2022 | 2022-11-02T07:51:34 | oeisdata/seq/A356/A356833.seq | 882ee297e1152d98741df4f14f873dcf |
A356834 | a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^n/(n - 2*k)!. | [
"1",
"1",
"4",
"33",
"448",
"8105",
"192576",
"5946913",
"226097152",
"10389920913",
"571788928000",
"36818407010561",
"2741300619657216",
"234014330510734969",
"22620660476040331264",
"2457467449742570271105",
"298061856229112792743936",
"40058727579693211737837857"
]
| [
"nonn"
]
| 39 | 0 | 3 | [
"A256016",
"A352082",
"A356834",
"A357146",
"A357174"
]
| null | Seiichi Manyama, Sep 16 2022 | 2022-09-16T12:13:56 | oeisdata/seq/A356/A356834.seq | 4759a45ae4eeeba9f86913d3fcdad665 |
A356835 | Coordination sequence of the {4,3,5} hyperbolic honeycomb. | [
"1",
"6",
"30",
"126",
"498",
"1982",
"7854",
"31014",
"122562",
"484422",
"1914254",
"7564542",
"29893554",
"118131966",
"466827678",
"1844789414",
"7290156162",
"28808903814",
"113845717662",
"449890341534",
"1777856189330",
"7025651266782",
"27763649373966",
"109715127592326",
"433567254075330",
"1713351367231142",
"6770744053574286"
]
| [
"nonn"
]
| 20 | 0 | 2 | [
"A247308",
"A356835"
]
| null | Eryk Kopczynski, Aug 31 2022 | 2022-11-06T08:52:51 | oeisdata/seq/A356/A356835.seq | 9242d6190af9956ab4ffd4fa3fc42816 |
A356836 | Coordination sequence of the {5,3,4} hyperbolic honeycomb. | [
"1",
"12",
"102",
"812",
"6402",
"50412",
"396902",
"3124812",
"24601602",
"193688012",
"1524902502",
"12005532012",
"94519353602",
"744149296812",
"5858675020902",
"46125250870412",
"363143331942402",
"2859021404668812",
"22509027905408102",
"177213201838596012",
"1395196586803360002",
"10984359492588284012"
]
| [
"nonn"
]
| 18 | 0 | 2 | [
"A076765",
"A095004",
"A356835",
"A356836"
]
| null | Eryk Kopczynski, Aug 31 2022 | 2022-11-06T08:58:24 | oeisdata/seq/A356/A356836.seq | 21e9cd51e8398920b156106b8a26e7ab |
A356837 | Coordination sequence of the {3,5,3} hyperbolic honeycomb. | [
"1",
"20",
"260",
"3212",
"39470",
"484760",
"5953532",
"73117640",
"897985850",
"11028509072",
"135445355180",
"1663456422080",
"20429547136382",
"250903113935780",
"3081437496506420",
"37844317258279532",
"464780593592780450",
"5708148959489987900",
"70103969470537620692",
"860973771077827270580"
]
| [
"nonn"
]
| 14 | 0 | 2 | null | null | Eryk Kopczynski, Aug 31 2022 | 2022-11-06T09:03:40 | oeisdata/seq/A356/A356837.seq | 3a1b1371c70ca1c8d598ff756f64b081 |
A356838 | The smallest of the most common prime factors of n. | [
"2",
"3",
"2",
"5",
"2",
"7",
"2",
"3",
"2",
"11",
"2",
"13",
"2",
"3",
"2",
"17",
"3",
"19",
"2",
"3",
"2",
"23",
"2",
"5",
"2",
"3",
"2",
"29",
"2",
"31",
"2",
"3",
"2",
"5",
"2",
"37",
"2",
"3",
"2",
"41",
"2",
"43",
"2",
"3",
"2",
"47",
"2",
"7",
"5",
"3",
"2",
"53",
"3",
"5",
"2",
"3",
"2",
"59",
"2",
"61",
"2",
"3",
"2",
"5",
"2",
"67",
"2",
"3",
"2",
"71",
"2",
"73",
"2",
"5",
"2",
"7",
"2",
"79",
"2",
"3",
"2",
"83",
"2",
"5",
"2",
"3",
"2",
"89"
]
| [
"nonn",
"easy"
]
| 47 | 2 | 1 | [
"A020639",
"A051903",
"A356838",
"A356840",
"A356862"
]
| null | Jens Ahlström, Aug 31 2022 | 2022-09-13T04:06:42 | oeisdata/seq/A356/A356838.seq | 581b335da6dd07f9734fc92f521491a5 |
A356839 | a(n) = A005132(2*n) + A005132(2*n+1). | [
"1",
"9",
"9",
"33",
"33",
"33",
"33",
"33",
"33",
"105",
"105",
"59",
"59",
"59",
"59",
"59",
"125",
"191",
"191",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"381",
"381",
"381",
"381",
"381",
"227",
"227",
"227",
"227",
"227",
"227",
"227",
"227",
"227",
"227",
"227",
"227",
"429",
"631",
"631",
"631",
"631",
"191",
"417",
"873",
"873"
]
| [
"nonn"
]
| 31 | 0 | 2 | [
"A005132",
"A356839"
]
| null | Paul Curtz, Aug 31 2022 | 2022-09-16T02:10:49 | oeisdata/seq/A356/A356839.seq | 28da45a7cbd20c34059bd34c58ad0dac |
A356840 | Largest most common prime factor of n. | [
"2",
"3",
"2",
"5",
"3",
"7",
"2",
"3",
"5",
"11",
"2",
"13",
"7",
"5",
"2",
"17",
"3",
"19",
"2",
"7",
"11",
"23",
"2",
"5",
"13",
"3",
"2",
"29",
"5",
"31",
"2",
"11",
"17",
"7",
"3",
"37",
"19",
"13",
"2",
"41",
"7",
"43",
"2",
"3",
"23",
"47",
"2",
"7",
"5",
"17",
"2",
"53",
"3",
"11",
"2",
"19",
"29",
"59",
"2",
"61",
"31",
"3",
"2",
"13",
"11",
"67",
"2",
"23",
"7",
"71",
"2",
"73",
"37",
"5",
"2",
"11",
"13",
"79",
"2",
"3",
"41",
"83"
]
| [
"nonn",
"easy"
]
| 38 | 2 | 1 | [
"A051903",
"A356838",
"A356840",
"A356862"
]
| null | Jens Ahlström, Aug 31 2022 | 2022-09-13T04:06:34 | oeisdata/seq/A356/A356840.seq | d2e97924c56b0e2dcbe6b3bab44633f0 |
A356841 | Numbers k such that the k-th composition in standard order covers an interval of positive integers (gapless). | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"10",
"11",
"13",
"14",
"15",
"16",
"18",
"20",
"21",
"22",
"23",
"26",
"27",
"29",
"30",
"31",
"32",
"36",
"37",
"38",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"50",
"52",
"53",
"54",
"55",
"58",
"59",
"61",
"62",
"63",
"64",
"68",
"72",
"74",
"75",
"77",
"78",
"82",
"83",
"84",
"85",
"86",
"87",
"89",
"90",
"91",
"92",
"93",
"94",
"95",
"101"
]
| [
"nonn"
]
| 11 | 1 | 3 | [
"A053251",
"A055932",
"A073491",
"A073492",
"A073493",
"A107428",
"A132747",
"A137921",
"A286470",
"A356224",
"A356225",
"A356230",
"A356233",
"A356603",
"A356841",
"A356842",
"A356843",
"A356844",
"A356845"
]
| null | Gus Wiseman, Aug 31 2022 | 2022-09-01T19:48:36 | oeisdata/seq/A356/A356841.seq | 657ae95ee181fcee3b64f35afae8edcc |
A356842 | Numbers k such that the k-th composition in standard order does not cover an interval of positive integers (not gapless). | [
"9",
"12",
"17",
"19",
"24",
"25",
"28",
"33",
"34",
"35",
"39",
"40",
"48",
"49",
"51",
"56",
"57",
"60",
"65",
"66",
"67",
"69",
"70",
"71",
"73",
"76",
"79",
"80",
"81",
"88",
"96",
"97",
"98",
"99",
"100",
"103",
"104",
"112",
"113",
"115",
"120",
"121",
"124",
"129",
"130",
"131",
"132",
"133",
"134",
"135",
"137",
"138",
"139",
"140",
"141",
"142",
"143",
"144",
"145"
]
| [
"nonn"
]
| 4 | 1 | 1 | [
"A053251",
"A055932",
"A073491",
"A073492",
"A073493",
"A107428",
"A132747",
"A137921",
"A286470",
"A333217",
"A356224",
"A356225",
"A356230",
"A356233",
"A356603",
"A356841",
"A356842",
"A356843",
"A356844",
"A356845"
]
| null | Gus Wiseman, Sep 01 2022 | 2022-09-01T19:48:31 | oeisdata/seq/A356/A356842.seq | ec12d0067daa13a74ab85f374b09c8f6 |
A356843 | Numbers k such that the k-th composition in standard order covers an interval of positive integers (gapless) but contains no 1's. | [
"2",
"4",
"8",
"10",
"16",
"18",
"20",
"32",
"36",
"42",
"64",
"68",
"72",
"74",
"82",
"84",
"128",
"136",
"146",
"148",
"164",
"170",
"256",
"264",
"272",
"274",
"276",
"290",
"292",
"296",
"298",
"324",
"328",
"330",
"338",
"340",
"512",
"528",
"548",
"580",
"584",
"586",
"594",
"596",
"658",
"660",
"676",
"682",
"1024",
"1040",
"1056",
"1092",
"1096",
"1098"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A022340",
"A053251",
"A055932",
"A073491",
"A073492",
"A073493",
"A107428",
"A137921",
"A251729",
"A333217",
"A356224",
"A356225",
"A356230",
"A356233",
"A356603",
"A356841",
"A356842",
"A356843",
"A356844",
"A356845",
"A356846"
]
| null | Gus Wiseman, Sep 01 2022 | 2022-09-01T19:48:26 | oeisdata/seq/A356/A356843.seq | a273ad4be9d88059100d95993219a3d6 |
A356844 | Numbers k such that the k-th composition in standard order contains at least one 1. Numbers that are odd or whose binary expansion contains at least two adjacent 1's. | [
"1",
"3",
"5",
"6",
"7",
"9",
"11",
"12",
"13",
"14",
"15",
"17",
"19",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"33",
"35",
"37",
"38",
"39",
"41",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"65",
"67",
"69",
"70",
"71",
"73",
"75",
"76",
"77",
"78",
"79",
"81",
"83",
"85",
"86",
"87"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A004754",
"A004760",
"A004780",
"A005408",
"A022340",
"A055932",
"A073492",
"A073493",
"A099036",
"A132747",
"A212804",
"A333217",
"A356843",
"A356844",
"A356845"
]
| null | Gus Wiseman, Sep 02 2022 | 2022-09-03T12:20:22 | oeisdata/seq/A356/A356844.seq | b41bd4c0b55714dc278d501065b37926 |
A356845 | Odd numbers with gapless prime indices. | [
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"23",
"25",
"27",
"29",
"31",
"35",
"37",
"41",
"43",
"45",
"47",
"49",
"53",
"59",
"61",
"67",
"71",
"73",
"75",
"77",
"79",
"81",
"83",
"89",
"97",
"101",
"103",
"105",
"107",
"109",
"113",
"121",
"125",
"127",
"131",
"135",
"137",
"139",
"143",
"149",
"151",
"157",
"163",
"167",
"169",
"173",
"175",
"179",
"181",
"191"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A001221",
"A001222",
"A001414",
"A003963",
"A034296",
"A055932",
"A056239",
"A073491",
"A073493",
"A107428",
"A112798",
"A136107",
"A251729",
"A264396",
"A287170",
"A289508",
"A294674",
"A325160",
"A356069",
"A356224",
"A356225",
"A356230",
"A356231",
"A356233",
"A356234",
"A356603",
"A356841",
"A356843",
"A356845"
]
| null | Gus Wiseman, Sep 03 2022 | 2022-09-03T12:19:58 | oeisdata/seq/A356/A356845.seq | adb5205b052b0b433174be64d310623f |
A356846 | Number of integer compositions of n into parts not covering an interval of positive integers. | [
"0",
"0",
"0",
"0",
"2",
"5",
"11",
"25",
"57",
"115",
"236",
"482",
"978",
"1986",
"4003",
"8033",
"16150",
"32402",
"64943",
"130207",
"260805",
"522123",
"1045168",
"2091722",
"4185431",
"8374100",
"16753538",
"33515122",
"67042865",
"134106640",
"268246886",
"536549760",
"1073194999",
"2146553011",
"4293391411",
"8587283895"
]
| [
"nonn"
]
| 8 | 0 | 5 | [
"A000009",
"A000041",
"A001227",
"A011782",
"A034296",
"A053251",
"A055932",
"A060142",
"A066208",
"A073491",
"A073492",
"A080259",
"A107428",
"A107429",
"A188575",
"A239327",
"A239955",
"A356604",
"A356605",
"A356841",
"A356842",
"A356846"
]
| null | Gus Wiseman, Sep 03 2022 | 2022-09-03T12:19:49 | oeisdata/seq/A356/A356846.seq | e05302714babc2a1b9fd4d7736e78971 |
A356847 | Greedily choose a(n) to be the least prime p > a(n-1) such that all sums a(i) + a(j) - 1, 1 <= i < j, are also prime. | [
"5",
"7",
"13",
"67",
"97",
"9337",
"28657",
"516157",
"2193637",
"1725215287",
"5858906527",
"10845974467",
"311697041437",
"2748104242057",
"478834469031547",
"30509330585363257"
]
| [
"nonn",
"more"
]
| 31 | 1 | 1 | null | null | Jeffrey Shallit, Feb 23 2023 | 2023-03-05T13:30:45 | oeisdata/seq/A356/A356847.seq | eda76496aa62ef3e153c980121fe6482 |
A356848 | Expansion of g.f. A(x) satisfying A(x) = x * Sum_{n>=0} d^n/dx^n x^(2*n-1) * A(x)^n / n!. | [
"1",
"1",
"5",
"37",
"353",
"4061",
"54221",
"820205",
"13829377",
"256853629",
"5208050365",
"114465346733",
"2711004465185",
"68846143222013",
"1866577974450733",
"53824099877628077",
"1645120108520147713",
"53135285623703158429",
"1808560829585046118685",
"64707781796679229092045",
"2428043851750587122468513"
]
| [
"nonn"
]
| 16 | 0 | 3 | [
"A356848",
"A360579"
]
| null | Paul D. Hanna, Feb 23 2023 | 2025-03-23T20:52:57 | oeisdata/seq/A356/A356848.seq | 8792d7eb197a4765f2ad2656151b8f3c |
A356849 | a(n) = a(n-1) - a(n-2) + 3*a(n-3) with a(0) = 1, a(1) = 2 and a(2) = 4. | [
"1",
"2",
"4",
"5",
"7",
"14",
"22",
"29",
"49",
"86",
"124",
"185",
"319",
"506",
"742",
"1193",
"1969",
"3002",
"4612",
"7517",
"11911",
"18230",
"28870",
"46373",
"72193",
"112430",
"179356",
"283505",
"441439",
"696002",
"1105078",
"1733393",
"2716321",
"4298162",
"6782020",
"10632821",
"16745287",
"26458526",
"41611702",
"65389037"
]
| [
"nonn",
"easy"
]
| 19 | 0 | 2 | null | null | Giorgos Kalogeropoulos, Aug 31 2022 | 2022-10-12T11:13:54 | oeisdata/seq/A356/A356849.seq | 7f8e450ad1671db9c075edac87478867 |
A356850 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that a(n) is coprime to the previous Omega(a(n)) terms. | [
"1",
"2",
"3",
"5",
"4",
"7",
"9",
"10",
"11",
"13",
"6",
"17",
"19",
"14",
"15",
"23",
"22",
"21",
"25",
"26",
"29",
"27",
"31",
"8",
"33",
"35",
"34",
"37",
"39",
"38",
"41",
"43",
"45",
"28",
"47",
"51",
"46",
"49",
"53",
"55",
"12",
"59",
"61",
"57",
"20",
"67",
"69",
"58",
"65",
"71",
"62",
"63",
"73",
"74",
"77",
"75",
"79",
"52",
"83",
"85",
"81",
"44",
"89",
"87",
"82",
"91",
"93",
"86",
"95",
"97",
"94",
"99",
"101",
"103",
"50",
"107"
]
| [
"nonn"
]
| 31 | 1 | 2 | [
"A000040",
"A001222",
"A093714",
"A336957",
"A356850",
"A356851",
"A356903"
]
| null | Scott R. Shannon, Aug 31 2022 | 2025-05-07T13:16:04 | oeisdata/seq/A356/A356850.seq | 024a87ac12a0b6f1dff5fbfbd65ce9a2 |
A356851 | a(1) = 1, a(2) = 2, a(3) = 4; for n > 3, a(n) is the smallest positive number not occurring earlier such that a(n) shares a factor with the previous Omega(a(n)) terms. | [
"1",
"2",
"4",
"6",
"3",
"9",
"12",
"15",
"5",
"10",
"20",
"14",
"7",
"21",
"28",
"35",
"30",
"25",
"40",
"45",
"50",
"18",
"22",
"8",
"16",
"24",
"26",
"13",
"39",
"52",
"65",
"78",
"60",
"33",
"11",
"44",
"55",
"66",
"70",
"34",
"17",
"51",
"68",
"85",
"102",
"90",
"38",
"19",
"57",
"76",
"95",
"114",
"110",
"46",
"23",
"69",
"92",
"115",
"138",
"130",
"58",
"29",
"87",
"116",
"145",
"174",
"150",
"62",
"31",
"93",
"124",
"155",
"186"
]
| [
"nonn"
]
| 18 | 1 | 2 | [
"A000040",
"A001222",
"A064413",
"A093714",
"A336957",
"A356850",
"A356851"
]
| null | Scott R. Shannon, Aug 31 2022 | 2023-05-07T19:33:09 | oeisdata/seq/A356/A356851.seq | 80dffff16c71b44a8fd875c8faa7fd30 |
A356852 | Minimum over all order two bases for the interval [1, n] of the maximum number of ways some number in the interval [1, n] can be written as a sum of at most two elements of the basis. | [
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3"
]
| [
"nonn"
]
| 17 | 1 | 6 | [
"A001212",
"A265262",
"A356852"
]
| null | Javier Múgica, Aug 31 2022 | 2022-10-15T10:28:19 | oeisdata/seq/A356/A356852.seq | b5cf408a40b1facc3ce3845452bf05d5 |
A356853 | Number of permutations p of [2n+1] such that at most one element of {p(1),...,p(i-1)} is between p(i) and p(i+1) for all i <= 2n and p(2n+1) = n+1. | [
"1",
"2",
"20",
"216",
"2720",
"36228",
"503216",
"7171404",
"104142520",
"1533200656",
"22811374568",
"342216338652",
"5168324302672",
"78483423004680",
"1197266739443160",
"18335055482658748",
"281714880491273736",
"4340894020114398672",
"67055152953864109240",
"1038097819961270208088"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A356692",
"A356853"
]
| null | Alois P. Heinz, Aug 31 2022 | 2022-09-03T22:10:51 | oeisdata/seq/A356/A356853.seq | e0af33352d325b1ea3b45890d4a0a0fb |
A356854 | Palindromes that can be written in more than one way as the sum of two distinct palindromic primes. | [
"282",
"484",
"858",
"888",
"21912",
"22722",
"23832",
"24642",
"25752",
"26662",
"26762",
"26862",
"26962",
"27672",
"27772",
"27872",
"27972",
"28482",
"28782",
"28882",
"28982",
"29692",
"29792",
"29892",
"29992",
"40704",
"41514",
"41614",
"41814",
"42624",
"42824",
"42924",
"43434",
"43734",
"43834",
"43934",
"44744",
"44844",
"44944",
"45354"
]
| [
"nonn",
"base"
]
| 11 | 1 | 1 | [
"A356824",
"A356854"
]
| null | Tanya Khovanova and Massimo Kofler, Aug 31 2022 | 2022-09-04T12:46:38 | oeisdata/seq/A356/A356854.seq | 79cd48ea2d84f1c35458c674b95f1004 |
A356855 | a(n) is the least number m such that u defined by u(i) = bigomega(m + 2i) satisfies u(i) = u(0) for 0 <= i < n and u(n) != u(0), or -1 if no such number exists. | [
"1",
"4",
"3",
"215",
"213",
"1383",
"3091",
"8129",
"151403",
"151401",
"2560187",
"33396293",
"33396291",
"56735777",
"1156217487",
"2514196079"
]
| [
"nonn",
"more"
]
| 110 | 1 | 2 | [
"A001222",
"A073093",
"A091304",
"A113752",
"A356855",
"A356893"
]
| null | Jean-Marc Rebert, Sep 04 2022 | 2022-10-24T00:09:29 | oeisdata/seq/A356/A356855.seq | 0545f18d14f565893d49065e3298e722 |
A356856 | Primes p such that the least positive primitive root of p (A001918) divides p-1. | [
"2",
"3",
"5",
"7",
"11",
"13",
"19",
"29",
"31",
"37",
"43",
"53",
"59",
"61",
"67",
"71",
"79",
"83",
"101",
"107",
"109",
"127",
"131",
"139",
"149",
"151",
"163",
"173",
"179",
"181",
"191",
"197",
"199",
"211",
"223",
"227",
"229",
"239",
"269",
"271",
"283",
"293",
"317",
"331",
"347",
"349",
"367",
"373",
"379",
"389",
"419",
"421",
"443",
"461",
"463",
"467",
"487"
]
| [
"nonn"
]
| 13 | 1 | 1 | [
"A001918",
"A006093",
"A356856"
]
| null | Giorgos Kalogeropoulos, Aug 31 2022 | 2023-08-31T14:58:48 | oeisdata/seq/A356/A356856.seq | 32979ba8df3337b9a451179c87c6ae5c |
A356857 | Triangle of numbers T(n,k) = (-1)^(n-k)*(n+1)!*Stirling2(n,k)/(k+1). | [
"1",
"-3",
"2",
"12",
"-24",
"6",
"-60",
"280",
"-180",
"24",
"360",
"-3600",
"4500",
"-1440",
"120",
"-2520",
"52080",
"-113400",
"65520",
"-12600",
"720",
"20160",
"-846720",
"3034080",
"-2822400",
"940800",
"-120960",
"5040",
"-181440",
"15361920",
"-87635520",
"123451776",
"-63504000",
"13789440",
"-1270080",
"40320"
]
| [
"sign",
"tabl"
]
| 26 | 1 | 2 | [
"A019538",
"A356857"
]
| null | Samuel Gantner, Aug 31 2022 | 2025-06-02T15:26:04 | oeisdata/seq/A356/A356857.seq | 6607548655ffb2a6b4b409675d6f5fa7 |
A356858 | a(n) is the product of the first n numbers not divisible by 5. | [
"1",
"1",
"2",
"6",
"24",
"144",
"1008",
"8064",
"72576",
"798336",
"9580032",
"124540416",
"1743565824",
"27897053184",
"474249904128",
"8536498274304",
"162193467211776",
"3406062811447296",
"74933381851840512",
"1723467782592331776",
"41363226782215962624",
"1075443896337615028224",
"29036985201115605762048"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A000142",
"A000351",
"A002266",
"A047201",
"A356858",
"A356859",
"A356860",
"A356861"
]
| null | Stefano Spezia, Sep 01 2022 | 2024-11-03T16:13:42 | oeisdata/seq/A356/A356858.seq | bf46900b713d41efb456c777ec56ac7c |
A356859 | a(n) is the number of zero digits in the product of the first n numbers not divisible by 5. | [
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"1",
"0",
"0",
"2",
"1",
"0",
"1",
"1",
"1",
"0",
"2",
"1",
"0",
"0",
"2",
"4",
"1",
"2",
"2",
"2",
"6",
"5",
"2",
"3",
"5",
"4",
"2",
"5",
"3",
"4",
"6",
"4",
"3",
"8",
"3",
"3",
"4",
"8",
"9",
"6",
"3",
"5",
"9",
"6",
"10",
"9",
"7",
"4",
"11",
"10",
"10",
"8",
"13",
"9",
"5",
"8",
"8",
"11",
"7",
"8",
"10",
"13",
"11",
"10",
"12",
"11",
"13",
"13",
"16",
"6",
"16",
"10",
"21",
"17"
]
| [
"nonn",
"base"
]
| 6 | 0 | 7 | [
"A047201",
"A055641",
"A356858",
"A356859",
"A356860",
"A356861"
]
| null | Stefano Spezia, Sep 01 2022 | 2022-09-04T12:38:30 | oeisdata/seq/A356/A356859.seq | f1ac815be80967ba6336d98fc0deecb0 |
A356860 | a(n) is the number of digits in the product of the first n numbers not divisible by 5. | [
"1",
"1",
"1",
"1",
"2",
"3",
"4",
"4",
"5",
"6",
"7",
"9",
"10",
"11",
"12",
"13",
"15",
"16",
"17",
"19",
"20",
"22",
"23",
"24",
"26",
"27",
"29",
"30",
"32",
"33",
"35",
"37",
"38",
"40",
"41",
"43",
"45",
"46",
"48",
"50",
"51",
"53",
"55",
"57",
"58",
"60",
"62",
"64",
"65",
"67",
"69",
"71",
"73",
"74",
"76",
"78",
"80",
"82",
"84",
"85",
"87",
"89",
"91",
"93",
"95",
"97",
"99",
"101",
"103"
]
| [
"nonn",
"base"
]
| 6 | 0 | 5 | [
"A047201",
"A055642",
"A356858",
"A356859",
"A356860",
"A356861"
]
| null | Stefano Spezia, Sep 01 2022 | 2022-09-04T12:38:41 | oeisdata/seq/A356/A356860.seq | 1d3f73e6bc539e7c3951c0d098f40911 |
A356861 | a(n) is the number of nonzero digits in the product of the first n numbers not divisible by 5. | [
"1",
"1",
"1",
"1",
"2",
"3",
"2",
"3",
"5",
"6",
"5",
"8",
"10",
"10",
"11",
"12",
"15",
"14",
"16",
"19",
"20",
"20",
"19",
"23",
"24",
"25",
"27",
"24",
"27",
"31",
"32",
"32",
"34",
"38",
"36",
"40",
"41",
"40",
"44",
"47",
"43",
"50",
"52",
"53",
"50",
"51",
"56",
"61",
"60",
"58",
"63",
"61",
"64",
"67",
"72",
"67",
"70",
"72",
"76",
"72",
"78",
"84",
"83",
"85",
"84",
"90",
"91",
"91",
"90"
]
| [
"nonn",
"base"
]
| 7 | 0 | 5 | [
"A047201",
"A055640",
"A356858",
"A356859",
"A356860",
"A356861"
]
| null | Stefano Spezia, Sep 01 2022 | 2022-09-04T12:38:51 | oeisdata/seq/A356/A356861.seq | bc6ce54dbd81ecf15cc5d662d2e487b1 |
A356862 | Numbers with a unique largest prime exponent. | [
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"11",
"12",
"13",
"16",
"17",
"18",
"19",
"20",
"23",
"24",
"25",
"27",
"28",
"29",
"31",
"32",
"37",
"40",
"41",
"43",
"44",
"45",
"47",
"48",
"49",
"50",
"52",
"53",
"54",
"56",
"59",
"60",
"61",
"63",
"64",
"67",
"68",
"71",
"72",
"73",
"75",
"76",
"79",
"80",
"81",
"83",
"84",
"88",
"89",
"90",
"92",
"96",
"97",
"98",
"99",
"101",
"103",
"104"
]
| [
"nonn",
"easy"
]
| 53 | 1 | 1 | [
"A000041",
"A001221",
"A001222",
"A002865",
"A027746",
"A051903",
"A056239",
"A070003",
"A102750",
"A112798",
"A124010",
"A246655",
"A247180",
"A283050",
"A319161",
"A327473",
"A356838",
"A356840",
"A356862",
"A359178",
"A362605",
"A362606",
"A362607",
"A362608",
"A362609",
"A362610",
"A362611",
"A362613",
"A362614",
"A362615",
"A376250"
]
| null | Jens Ahlström, Sep 01 2022 | 2024-09-17T04:02:44 | oeisdata/seq/A356/A356862.seq | 5b09a63f1769da065bcd3b55623e97ba |
A356863 | Numbers that are the product of two palindromes in two or more ways and are the concatenation of two palindromes, with all the palindromes having the same number of decimal digits. | [
"12",
"16",
"18",
"24",
"36",
"113131311886868688",
"153535351846464648",
"182919281817080718",
"183838381816161618",
"185676581814323418",
"192919291807080708",
"193838391806161608",
"283919382716080617",
"293656392403040304",
"293919392706080607",
"365838563634161436",
"385838583614161416",
"387676783612323216",
"567838765432161234",
"587838785412161214"
]
| [
"nonn",
"base"
]
| 18 | 1 | 1 | [
"A002113",
"A355148",
"A356863"
]
| null | Chai Wah Wu, Sep 01 2022 | 2022-09-04T12:45:19 | oeisdata/seq/A356/A356863.seq | d88bbd1ddeb87f0a47d343e2181d0c59 |
A356864 | a(n) is the number of primes p < n such that 2*n-p and p*(2*n-p)+2*n are also prime. | [
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"0",
"0",
"3",
"0",
"2",
"3",
"0",
"3",
"4",
"1",
"1",
"2",
"1",
"2",
"3",
"0",
"0",
"3",
"1",
"3",
"1",
"0",
"5",
"3",
"0",
"2",
"1",
"0",
"3",
"6",
"0",
"1",
"2",
"1",
"1",
"3",
"0",
"2",
"2",
"0",
"2",
"1",
"1",
"4",
"6",
"0",
"2",
"11",
"0",
"3",
"3",
"0",
"2",
"2",
"0",
"0",
"2",
"0",
"4",
"4",
"0",
"1",
"3",
"1",
"5",
"3",
"0",
"2",
"8",
"0",
"2",
"3",
"0",
"1",
"5",
"0",
"0",
"6",
"1",
"4",
"5",
"0",
"3",
"4",
"0",
"3",
"1"
]
| [
"nonn"
]
| 12 | 1 | 11 | [
"A061357",
"A356864"
]
| null | J. M. Bergot and Robert Israel, Sep 01 2022 | 2022-09-06T10:29:20 | oeisdata/seq/A356/A356864.seq | e87779baf7b59cb936db49258ac0e2b3 |
A356865 | Minimal absolute value of determinant of a nonsingular n X n symmetric Toeplitz matrix using the integers 1 to n. | [
"1",
"1",
"3",
"8",
"12",
"3",
"13",
"19",
"5",
"5",
"1",
"3",
"1"
]
| [
"nonn",
"hard",
"more"
]
| 12 | 0 | 3 | [
"A348891",
"A350953",
"A350954",
"A356865"
]
| null | Lucas A. Brown, Sep 01 2022 | 2022-10-11T00:55:10 | oeisdata/seq/A356/A356865.seq | 2270ffef088e41c8946a0358831cda64 |
A356866 | Smallest Carmichael number (A002997) with n prime factors that is also a strong pseudoprime to base 2 (A001262). | [
"15841",
"5310721",
"440707345",
"10761055201",
"5478598723585",
"713808066913201",
"1022751992545146865",
"5993318051893040401",
"120459489697022624089201",
"27146803388402594456683201",
"14889929431153115006659489681"
]
| [
"nonn",
"more"
]
| 61 | 3 | 1 | [
"A001262",
"A002997",
"A006931",
"A063847",
"A180065",
"A356866"
]
| null | Daniel Suteu, Oct 01 2022 | 2022-10-02T13:32:40 | oeisdata/seq/A356/A356866.seq | f20f810c7aa099b6245d7fd3e093ff77 |
A356867 | For n >= 1, write n = 3^m + k, where m >= 0 is the greatest power of 3 <= n, and k is in the range 0 <= k < 3^(m+1) - 3^m, then for n such that k=0, a(n)=n, and for n such that k > 0, a(n) is the smallest prime multiple p*a(k), p != 3, that is not already a term. | [
"1",
"2",
"3",
"5",
"4",
"6",
"10",
"8",
"9",
"7",
"14",
"15",
"25",
"20",
"12",
"50",
"16",
"18",
"35",
"28",
"30",
"125",
"40",
"24",
"100",
"32",
"27",
"11",
"22",
"21",
"55",
"44",
"42",
"70",
"56",
"45",
"49",
"98",
"75",
"175",
"140",
"60",
"250",
"80",
"36",
"245",
"196",
"150",
"625",
"200",
"48",
"500",
"64",
"54",
"77",
"110",
"105",
"275",
"88",
"84",
"350",
"112",
"90",
"343"
]
| [
"nonn",
"look"
]
| 64 | 1 | 2 | [
"A005940",
"A007089",
"A007949",
"A011655",
"A046523",
"A048473",
"A053735",
"A100484",
"A348717",
"A356867",
"A364611",
"A364628",
"A364958",
"A365390",
"A365424",
"A365459",
"A365462",
"A365463",
"A365464",
"A365465",
"A365717",
"A365719",
"A365721",
"A365722"
]
| null | David James Sycamore, Sep 01 2022 | 2025-07-01T10:08:03 | oeisdata/seq/A356/A356867.seq | 34f01bf491068412971f57ac15a78e05 |
A356868 | a(n) = n^2 * prime(n). | [
"2",
"12",
"45",
"112",
"275",
"468",
"833",
"1216",
"1863",
"2900",
"3751",
"5328",
"6929",
"8428",
"10575",
"13568",
"17051",
"19764",
"24187",
"28400",
"32193",
"38236",
"43907",
"51264",
"60625",
"68276",
"75087",
"83888",
"91669",
"101700",
"122047",
"134144",
"149193",
"160684",
"182525",
"195696",
"214933",
"235372",
"254007",
"276800",
"300899"
]
| [
"nonn",
"easy"
]
| 15 | 1 | 1 | [
"A000040",
"A000290",
"A004232",
"A033286",
"A196421",
"A356868"
]
| null | Alex Ratushnyak, Sep 01 2022 | 2022-09-03T22:23:46 | oeisdata/seq/A356/A356868.seq | 0885e63b3ccc21b270ba66dff53a7687 |
A356869 | Decimal expansion of 4 / sqrt(5). | [
"1",
"7",
"8",
"8",
"8",
"5",
"4",
"3",
"8",
"1",
"9",
"9",
"9",
"8",
"3",
"1",
"7",
"5",
"7",
"1",
"2",
"7",
"3",
"3",
"8",
"9",
"3",
"4",
"9",
"8",
"5",
"0",
"2",
"0",
"9",
"8",
"8",
"3",
"5",
"2",
"4",
"9",
"4",
"6",
"8",
"7",
"6",
"8",
"9",
"2",
"2",
"0",
"5",
"7",
"9",
"4",
"1",
"6",
"7",
"1",
"7",
"7",
"9",
"6",
"3",
"2",
"8",
"4",
"1",
"6",
"7",
"4",
"0",
"5",
"1",
"0",
"2",
"4",
"3",
"9",
"1",
"9",
"5",
"3",
"1",
"5",
"3",
"1",
"5",
"2",
"6",
"7",
"0",
"3",
"0",
"2",
"5"
]
| [
"nonn",
"cons",
"easy"
]
| 56 | 1 | 2 | [
"A121570",
"A179290",
"A204188",
"A356869"
]
| null | Michal Paulovic, Sep 01 2022 | 2022-09-09T23:37:48 | oeisdata/seq/A356/A356869.seq | a54e65c73af1ae535074516b507b9e8e |
A356870 | a(n) = (A005132(2*n-1) + A005132(2*n))/4. | [
"1",
"2",
"5",
"8",
"8",
"8",
"8",
"8",
"17",
"26",
"26",
"15",
"15",
"15",
"15",
"15",
"48",
"48",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"29",
"62",
"95",
"95",
"95",
"95",
"95",
"57",
"57",
"57",
"57",
"57",
"57",
"57",
"57",
"57",
"57",
"57",
"57",
"158",
"158",
"158",
"158",
"103",
"48",
"161",
"218",
"218",
"99",
"99",
"99",
"99",
"99",
"35",
"35",
"168",
"100",
"100",
"100"
]
| [
"nonn",
"look"
]
| 53 | 1 | 2 | [
"A005132",
"A356839",
"A356870"
]
| null | Paul Curtz, Sep 02 2022 | 2022-09-16T10:16:07 | oeisdata/seq/A356/A356870.seq | a8fe33ffc8afea4b5ad974ea5e8490ae |
A356871 | Primitive coreful abundant numbers (second definition): coreful abundant numbers (A308053) that are powerful numbers (A001694). | [
"72",
"108",
"144",
"200",
"216",
"288",
"324",
"400",
"432",
"576",
"648",
"784",
"800",
"864",
"900",
"972",
"1000",
"1152",
"1296",
"1568",
"1600",
"1728",
"1764",
"1800",
"1936",
"1944",
"2000",
"2304",
"2592",
"2700",
"2704",
"2744",
"2916",
"3136",
"3200",
"3456",
"3528",
"3600",
"3872",
"3888",
"4000",
"4356",
"4500",
"4608",
"4900",
"5000",
"5184"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A001694",
"A057723",
"A307959",
"A308053",
"A328136",
"A339940",
"A356871"
]
| null | Amiram Eldar, Sep 02 2022 | 2022-09-03T08:49:47 | oeisdata/seq/A356/A356871.seq | dcccf1da0c30a98a6a9b2e48f83215db |
A356872 | a(n) = k is the smallest number such that 3*k+1 contains n distinct prime factors. | [
"1",
"3",
"23",
"303",
"4363",
"56723",
"1077743",
"33410043",
"718854803",
"22284498903",
"824526459423",
"35454637755203",
"1588862487308763",
"68321086954276823",
"4167586304210886223",
"213640038906023626563",
"13032042373267441220363",
"873146839008918561764343",
"63739719247651055008797063"
]
| [
"nonn"
]
| 30 | 1 | 2 | [
"A002110",
"A180278",
"A219108",
"A356872"
]
| null | Alex Ratushnyak, Sep 02 2022 | 2022-09-28T11:16:39 | oeisdata/seq/A356/A356872.seq | 23ccc72479392d784ec83d5794a5ace7 |
A356873 | a(n) is the smallest number k such that 2^k+1 has at least n distinct prime factors. | [
"0",
"5",
"14",
"18",
"30",
"42",
"78",
"78",
"78",
"90",
"150",
"150",
"210",
"210",
"234",
"234",
"270",
"390",
"390",
"390",
"390",
"450",
"510",
"630",
"630",
"630",
"810",
"810",
"810",
"966",
"966",
"1170",
"1170",
"1170",
"1170",
"1170",
"1170",
"1170"
]
| [
"nonn",
"hard",
"more"
]
| 27 | 1 | 2 | [
"A046799",
"A071852",
"A180278",
"A219108",
"A356872",
"A356873"
]
| null | Alex Ratushnyak, Sep 02 2022 | 2022-10-13T09:50:58 | oeisdata/seq/A356/A356873.seq | 5490744430bc557f9fe1c769059b31d8 |
A356874 | Write n as Sum_{i in S} 2^(i-1), where S is a set of positive integers, then a(n) = Sum_{i in S} F_i, where F_i is the i-th Fibonacci number, A000045(i). | [
"0",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"3",
"4",
"4",
"5",
"5",
"6",
"6",
"7",
"5",
"6",
"6",
"7",
"7",
"8",
"8",
"9",
"8",
"9",
"9",
"10",
"10",
"11",
"11",
"12",
"8",
"9",
"9",
"10",
"10",
"11",
"11",
"12",
"11",
"12",
"12",
"13",
"13",
"14",
"14",
"15",
"13",
"14",
"14",
"15",
"15",
"16",
"16",
"17",
"16",
"17",
"17",
"18",
"18",
"19",
"19",
"20",
"13",
"14",
"14",
"15",
"15",
"16",
"16",
"17",
"16",
"17",
"17",
"18",
"18",
"19",
"19",
"20"
]
| [
"nonn",
"base",
"easy"
]
| 20 | 0 | 4 | [
"A000045",
"A000121",
"A000201",
"A022290",
"A022342",
"A287870",
"A356874"
]
| null | Peter Munn, Sep 02 2022 | 2023-08-08T12:10:24 | oeisdata/seq/A356/A356874.seq | a5fa7fd41ae2233283552872fe676c06 |
A356875 | Square array, n >= 0, k >= 0, read by descending antidiagonals. A(n,k) = A022341(n)*2^k. | [
"1",
"2",
"5",
"4",
"10",
"9",
"8",
"20",
"18",
"17",
"16",
"40",
"36",
"34",
"21",
"32",
"80",
"72",
"68",
"42",
"33",
"64",
"160",
"144",
"136",
"84",
"66",
"37",
"128",
"320",
"288",
"272",
"168",
"132",
"74",
"41",
"256",
"640",
"576",
"544",
"336",
"264",
"148",
"82",
"65",
"512",
"1280",
"1152",
"1088",
"672",
"528",
"296",
"164",
"130",
"69",
"1024",
"2560",
"2304",
"2176",
"1344",
"1056",
"592",
"328",
"260",
"138",
"73"
]
| [
"nonn",
"easy",
"tabl"
]
| 8 | 0 | 2 | [
"A000045",
"A003714",
"A022290",
"A022341",
"A035513",
"A054582",
"A287870",
"A356874",
"A356875"
]
| null | Peter Munn, Sep 02 2022 | 2022-09-07T18:58:08 | oeisdata/seq/A356/A356875.seq | a3cf84805c72a6b65012653152ed6d1d |
A356876 | Binary weight of the composite numbers (A002808). | [
"1",
"2",
"1",
"2",
"2",
"2",
"3",
"4",
"1",
"2",
"2",
"3",
"3",
"2",
"3",
"3",
"4",
"3",
"4",
"1",
"2",
"2",
"3",
"2",
"3",
"4",
"2",
"3",
"3",
"4",
"4",
"2",
"3",
"3",
"4",
"3",
"4",
"5",
"3",
"4",
"4",
"4",
"5",
"6",
"1",
"2",
"2",
"2",
"3",
"3",
"2",
"3",
"4",
"3",
"4",
"4",
"2",
"3",
"3",
"3",
"4",
"4",
"5",
"3",
"4",
"5",
"4",
"5",
"5",
"6",
"2",
"3",
"4",
"3",
"4",
"3",
"4",
"4",
"4",
"5",
"6",
"3",
"4",
"5",
"4",
"5",
"5",
"6",
"4",
"5",
"5"
]
| [
"base",
"nonn",
"easy"
]
| 25 | 1 | 2 | [
"A000120",
"A002808",
"A014499",
"A356876"
]
| null | Karl-Heinz Hofmann, Oct 02 2022 | 2022-10-05T15:40:18 | oeisdata/seq/A356/A356876.seq | 99e791257afdf829f3d58476b0fbf051 |
A356877 | a(n) is the least number k such that (the binary weight of k) - (the binary weight of k^2) = n. | [
"0",
"23",
"111",
"479",
"1471",
"6015",
"24319",
"28415",
"114175",
"457727",
"490495",
"1964031",
"6025215",
"8122367",
"32497663",
"98549759",
"132104191",
"528449535",
"1593769983",
"1862205439",
"7448952831",
"25635323903",
"29930291199",
"119721689087",
"411242070015",
"479961546751",
"514321285119",
"2057287237631",
"7687987265535"
]
| [
"nonn",
"base"
]
| 41 | 0 | 2 | [
"A000120",
"A159918",
"A260986",
"A356877",
"A357750"
]
| null | Karl-Heinz Hofmann, Oct 10 2022 | 2022-10-18T01:43:03 | oeisdata/seq/A356/A356877.seq | 99ce8eea3009f1fb886c1aa1038dfb88 |
A356878 | a(n) is the least number of binary zeros of squares with binary weight n. | [
"1",
"0",
"2",
"2",
"4",
"2",
"3",
"4",
"3",
"4",
"5",
"5",
"5",
"2",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"7",
"7",
"7",
"7",
"7",
"7",
"8",
"7",
"6",
"8",
"9",
"6",
"7",
"8",
"9",
"8",
"9",
"9",
"8",
"10",
"9",
"9",
"10",
"9",
"9",
"9",
"9",
"10",
"10",
"10",
"11",
"10"
]
| [
"nonn",
"base",
"hard",
"more"
]
| 31 | 0 | 3 | [
"A000120",
"A164343",
"A164344",
"A356878"
]
| null | Karl-Heinz Hofmann, Sep 30 2022 | 2022-10-13T16:33:35 | oeisdata/seq/A356/A356878.seq | 8985b658d4b7696000b361b97b832008 |
A356879 | Numbers k such that the sum k^x + k^y can be a square with {x, y} >= 0. | [
"0",
"2",
"3",
"8",
"15",
"18",
"24",
"32",
"35",
"48",
"50",
"63",
"72",
"80",
"98",
"99",
"120",
"128",
"143",
"162",
"168",
"195",
"200",
"224",
"242",
"255",
"288",
"323",
"338",
"360",
"392",
"399",
"440",
"450",
"483",
"512",
"528",
"575",
"578",
"624",
"648",
"675",
"722",
"728",
"783",
"800",
"840",
"882",
"899",
"960",
"968",
"1023",
"1058",
"1088",
"1152",
"1155",
"1224"
]
| [
"nonn"
]
| 34 | 0 | 2 | [
"A001105",
"A132411",
"A132592",
"A270473",
"A356879",
"A356880"
]
| null | Karl-Heinz Hofmann, Sep 12 2022 | 2022-10-13T13:58:56 | oeisdata/seq/A356/A356879.seq | 9ac01a7ed9cd841bb7df43899f834234 |
A356880 | Squares that can be expressed as the sum of two powers of two (2^x + 2^y). | [
"4",
"9",
"16",
"36",
"64",
"144",
"256",
"576",
"1024",
"2304",
"4096",
"9216",
"16384",
"36864",
"65536",
"147456",
"262144",
"589824",
"1048576",
"2359296",
"4194304",
"9437184",
"16777216",
"37748736",
"67108864",
"150994944",
"268435456",
"603979776",
"1073741824",
"2415919104",
"4294967296",
"9663676416",
"17179869184"
]
| [
"nonn",
"easy"
]
| 50 | 1 | 1 | [
"A000290",
"A000302",
"A002063",
"A029744",
"A048645",
"A220221",
"A270473",
"A272711",
"A356880"
]
| null | Karl-Heinz Hofmann, Sep 02 2022 | 2022-09-25T09:34:29 | oeisdata/seq/A356/A356880.seq | eb0a604f1e5d14b3250f471d4e1eaeb0 |
A356881 | Palindromes that can be written in more than one way as the sum of two palindromic primes. | [
"202",
"282",
"484",
"858",
"888",
"21912",
"22722",
"23832",
"24642",
"24842",
"25752",
"26662",
"26762",
"26862",
"26962",
"27672",
"27772",
"27872",
"27972",
"28482",
"28682",
"28782",
"28882",
"28982",
"29692",
"29792",
"29892",
"29992",
"40704",
"41514",
"41614",
"41814",
"42624",
"42824",
"42924",
"43434",
"43734"
]
| [
"nonn",
"base"
]
| 11 | 1 | 1 | [
"A356824",
"A356854",
"A356881"
]
| null | Tanya Khovanova, Sep 02 2022 | 2024-02-22T20:11:30 | oeisdata/seq/A356/A356881.seq | 8dc47c2e045eb6d172d31a8a217487c9 |
A356882 | E.g.f. satisfies: A(x) * log(A(x)) = x * (exp(x*A(x)) - 1). | [
"1",
"0",
"2",
"3",
"16",
"125",
"756",
"7567",
"85968",
"994905",
"14373460",
"225366251",
"3800667960",
"72169966453",
"1469546796732",
"32150706096615",
"760806334538656",
"19142440567996721",
"512272692571487652",
"14560087915617858883",
"436598686303562722440",
"13796641165956117509901"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A349560",
"A349588",
"A356785",
"A356788",
"A356789",
"A356882",
"A356883"
]
| null | Seiichi Manyama, Sep 02 2022 | 2022-09-02T18:06:43 | oeisdata/seq/A356/A356882.seq | 5a4cf4903adf857fad5d5629c7e6dff3 |
A356883 | E.g.f. satisfies: A(x)^2 * log(A(x)) = x * (exp(x*A(x)) - 1). | [
"1",
"0",
"2",
"3",
"-8",
"5",
"696",
"2527",
"-40144",
"-178407",
"8337880",
"76134971",
"-1781542344",
"-24938260763",
"691630553264",
"14216543752335",
"-312910463346464",
"-9343318015483471",
"195539694928047144",
"8145971436703039363",
"-142317653823753257560",
"-8498984155838272275459"
]
| [
"sign"
]
| 8 | 0 | 3 | [
"A349560",
"A355763",
"A356785",
"A356788",
"A356789",
"A356882",
"A356883"
]
| null | Seiichi Manyama, Sep 02 2022 | 2022-09-02T18:06:48 | oeisdata/seq/A356/A356883.seq | 4addf1e52ae4538f10cace1b10477856 |
A356884 | E.g.f. satisfies A(x)^A(x) = 1/(1 - x*A(x))^x. | [
"1",
"0",
"2",
"3",
"20",
"150",
"1254",
"14280",
"190000",
"2863728",
"49465080",
"954312480",
"20303200488",
"473604468480",
"12007399511184",
"328671680500800",
"9663415159357440",
"303695188102656000",
"10159173955921651776",
"360424299614544829440",
"13517056067747847719040"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A141209",
"A184949",
"A349559",
"A356786",
"A356787",
"A356884",
"A356885"
]
| null | Seiichi Manyama, Sep 02 2022 | 2022-09-02T18:06:52 | oeisdata/seq/A356/A356884.seq | 86ea4cb372b6068f34e7ce64e3b06f5e |
A356885 | E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x*A(x))^x. | [
"1",
"0",
"2",
"3",
"-4",
"30",
"954",
"6300",
"6432",
"424872",
"18273960",
"260682840",
"1754408424",
"47063118960",
"2314149100704",
"54798086299320",
"773632032345600",
"20746972036284480",
"1072205580591921600",
"36098491880448944640",
"816375193722964932480",
"25160238159364392336000"
]
| [
"sign"
]
| 7 | 0 | 3 | [
"A184949",
"A349559",
"A355767",
"A356786",
"A356787",
"A356884",
"A356885"
]
| null | Seiichi Manyama, Sep 02 2022 | 2022-09-02T18:06:56 | oeisdata/seq/A356/A356885.seq | c40c9e96ccd80db0117f25dbd40daef7 |
A356886 | Write n as 2^m - k, where 2^m is the least power of 2 such that 2^m >= n, and k is a number in the range 0 <= k < 2^(m-1) - 1. Then for n such that k=0, a(n)=n, and for n such that k > 0, a(n) is the smallest odd prime multiple of a(k) that is not already a term. | [
"1",
"2",
"3",
"4",
"9",
"6",
"5",
"8",
"15",
"18",
"27",
"12",
"21",
"10",
"7",
"16",
"35",
"30",
"63",
"36",
"81",
"54",
"45",
"24",
"25",
"42",
"99",
"20",
"33",
"14",
"11",
"32",
"55",
"70",
"165",
"60",
"297",
"126",
"75",
"72",
"135",
"162",
"243",
"108",
"189",
"90",
"105",
"48",
"49",
"50",
"147",
"84",
"351",
"198",
"195",
"40",
"65",
"66",
"117",
"28",
"39",
"22",
"13",
"64",
"91"
]
| [
"nonn"
]
| 37 | 1 | 2 | [
"A005940",
"A356886"
]
| null | David James Sycamore, Sep 02 2022 | 2023-01-12T21:19:43 | oeisdata/seq/A356/A356886.seq | c61a5c13c11bb05206cb002d48f93a24 |
A356887 | Number of n X n matrices over GF(2) whose characteristic polynomial is a single monic irreducible (prime) raised to some power. | [
"1",
"2",
"10",
"176",
"14016",
"4032512",
"6213763072",
"32018926665728",
"870713558978002944",
"89293629194528350011392",
"40675925233031615853327548416",
"72389802739964734146185851566030848",
"563250609270594469597103043401725627072512"
]
| [
"nonn"
]
| 11 | 0 | 2 | null | null | Geoffrey Critzer, Sep 02 2022 | 2025-06-20T20:22:29 | oeisdata/seq/A356/A356887.seq | a172bf7788a6b38defc740f8a4acc166 |
A356888 | a(n) = ((n-1)^2 + 2)*2^(n-2). | [
"1",
"3",
"12",
"44",
"144",
"432",
"1216",
"3264",
"8448",
"21248",
"52224",
"125952",
"299008",
"700416",
"1622016",
"3719168",
"8454144",
"19070976",
"42729472",
"95158272",
"210763776",
"464519168",
"1019215872",
"2227175424",
"4848615424",
"10519314432",
"22749904896",
"49056579584",
"105495134208",
"226291089408"
]
| [
"nonn",
"easy"
]
| 26 | 1 | 2 | [
"A334551",
"A356888"
]
| null | Jack Hanke, Sep 02 2022 | 2024-10-07T03:23:24 | oeisdata/seq/A356/A356888.seq | f9dcb1bbccc0e247394dd45639de8afd |
A356889 | a(n) = (n^2 + 3*n + 10/3)*4^(n-3) - 1/3. | [
"3",
"21",
"125",
"693",
"3669",
"18773",
"93525",
"456021",
"2184533",
"10310997",
"48059733",
"221599061",
"1012225365",
"4585772373",
"20624790869",
"92162839893",
"409453548885",
"1809612887381",
"7960006055253",
"34863681197397",
"152099108509013",
"661172992169301",
"2864594294232405",
"12373170851239253"
]
| [
"nonn",
"easy"
]
| 22 | 2 | 1 | [
"A334551",
"A356889"
]
| null | Jack Hanke, Sep 02 2022 | 2024-01-07T13:34:06 | oeisdata/seq/A356/A356889.seq | 93ee7d5f10886ca4c42d19110420c06d |
A356890 | a(n) is the first twin prime that begins a sequence of exactly n twin primes under the map t -> 3*t+2. | [
"7",
"3",
"19",
"40951819",
"12454922269"
]
| [
"nonn",
"more"
]
| 15 | 1 | 1 | null | null | J. M. Bergot and Robert Israel, Sep 02 2022 | 2022-09-08T08:15:54 | oeisdata/seq/A356/A356890.seq | 1639258a0751089c152ec5b1fea8d685 |
A356891 | a(n) = a(n-1) * a(n-2) + 1 if n is even, otherwise a(n) = a(n-3) + 1, with a(0) = a(1) = 1. | [
"1",
"1",
"2",
"2",
"5",
"3",
"16",
"6",
"97",
"17",
"1650",
"98",
"161701",
"1651",
"266968352",
"161702",
"43169316455105",
"266968353",
"11524841314155180292066",
"43169316455106",
"497519521785644682185076928856988997",
"11524841314155180292067"
]
| [
"nonn"
]
| 26 | 0 | 3 | [
"A007660",
"A356891"
]
| null | J. Conrad, Sep 02 2022 | 2022-11-06T08:40:18 | oeisdata/seq/A356/A356891.seq | b7760341c1cb5c9449057c1314926a19 |
A356892 | E.g.f. satisfies log(A(x)) = x^3 * (exp(x * A(x)) - 1) * A(x). | [
"1",
"0",
"0",
"0",
"24",
"60",
"120",
"210",
"101136",
"1089144",
"7409520",
"39917790",
"4097460840",
"100410712116",
"1474154203704",
"16356956618730",
"786764261166240",
"30867868254267120",
"778327514455987296",
"14658714575197061814",
"522720977799308061240",
"25075479032600008569900"
]
| [
"nonn"
]
| 38 | 0 | 5 | [
"A349557",
"A355508",
"A356785",
"A356892",
"A356963"
]
| null | Seiichi Manyama, Sep 07 2022 | 2022-09-12T03:05:12 | oeisdata/seq/A356/A356892.seq | 89f37067036c34510b66d99410446aa8 |
A356893 | a(n) is the smallest number m such that m, m+1, m+2 and m+3 each have exactly n prime factors (counted with multiplicity). | [
"602",
"4023",
"57967",
"8706123",
"296299374",
"4109290623"
]
| [
"nonn",
"more"
]
| 18 | 3 | 1 | [
"A113752",
"A356893"
]
| null | Zak Seidov, Sep 03 2022 | 2022-09-04T12:37:25 | oeisdata/seq/A356/A356893.seq | 34f6bcf16250687e9ea4554a577d311b |
A356894 | a(n) is the number of 0's in the maximal tribonacci representation of n (A352103). | [
"1",
"0",
"1",
"0",
"2",
"1",
"1",
"0",
"2",
"2",
"1",
"2",
"1",
"1",
"0",
"3",
"2",
"3",
"2",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"0",
"4",
"3",
"3",
"2",
"3",
"3",
"2",
"3",
"2",
"2",
"1",
"3",
"2",
"3",
"2",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"0",
"4",
"4",
"3",
"4",
"3",
"3",
"2",
"4",
"3",
"4",
"3",
"3",
"2",
"3",
"3",
"2",
"3",
"2",
"2",
"1",
"4",
"3",
"3",
"2",
"3",
"3",
"2",
"3",
"2",
"2",
"1",
"3",
"2",
"3",
"2"
]
| [
"nonn",
"base"
]
| 12 | 0 | 5 | [
"A000073",
"A023416",
"A102364",
"A117479",
"A278042",
"A352103",
"A352104",
"A356894",
"A356895"
]
| null | Amiram Eldar, Sep 03 2022 | 2022-09-05T05:24:32 | oeisdata/seq/A356/A356894.seq | e968028eb135bb77022b9cd802f1b730 |
A356895 | a(n) is the length of the maximal tribonacci representation of n (A352103). | [
"1",
"1",
"2",
"2",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"7"
]
| [
"nonn",
"base"
]
| 8 | 0 | 3 | [
"A070939",
"A072649",
"A095791",
"A278044",
"A352103",
"A352104",
"A356894",
"A356895"
]
| null | Amiram Eldar, Sep 03 2022 | 2022-09-05T05:24:36 | oeisdata/seq/A356/A356895.seq | f69e36e2effb48b8550adee237fd4a46 |
A356896 | Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an even number of 1's. | [
"0",
"2",
"3",
"4",
"6",
"9",
"10",
"11",
"13",
"14",
"15",
"16",
"17",
"19",
"22",
"23",
"24",
"26",
"28",
"30",
"33",
"34",
"35",
"37",
"38",
"39",
"40",
"41",
"43",
"46",
"47",
"48",
"50",
"51",
"53",
"54",
"55",
"57",
"58",
"59",
"60",
"61",
"63",
"66",
"67",
"68",
"70",
"72",
"74",
"77",
"78",
"79",
"81",
"82",
"83",
"84",
"85",
"87",
"90",
"91",
"92",
"94",
"96",
"97",
"98",
"100",
"103"
]
| [
"nonn",
"base"
]
| 8 | 1 | 2 | [
"A058265",
"A308197",
"A342051",
"A352103",
"A356896",
"A356897",
"A356898"
]
| null | Amiram Eldar, Sep 03 2022 | 2022-09-05T05:24:46 | oeisdata/seq/A356/A356896.seq | e21b2662ef88bc6a51fc4a611c1ddd97 |
A356897 | Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an odd number of 1's. | [
"1",
"5",
"7",
"8",
"12",
"18",
"20",
"21",
"25",
"27",
"29",
"31",
"32",
"36",
"42",
"44",
"45",
"49",
"52",
"56",
"62",
"64",
"65",
"69",
"71",
"73",
"75",
"76",
"80",
"86",
"88",
"89",
"93",
"95",
"99",
"101",
"102",
"106",
"108",
"110",
"112",
"113",
"117",
"123",
"125",
"126",
"130",
"133",
"137",
"143",
"145",
"146",
"150",
"152",
"154",
"156",
"157",
"161",
"167",
"169"
]
| [
"nonn",
"base"
]
| 8 | 1 | 2 | [
"A001950",
"A058265",
"A308198",
"A342050",
"A352103",
"A356896",
"A356897",
"A356898"
]
| null | Amiram Eldar, Sep 03 2022 | 2022-09-05T05:24:50 | oeisdata/seq/A356/A356897.seq | 8f980f8c32e6d10c08213b6907336445 |
A356898 | a(n) is the number of trailing 1's in the maximal tribonacci representation of n (A352103). | [
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"3",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"0",
"2",
"0",
"1",
"0",
"3",
"1",
"0",
"2",
"0",
"1",
"0",
"5",
"0",
"1",
"0",
"3",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"0",
"2",
"0",
"1",
"0",
"3",
"1",
"0",
"2",
"0",
"1",
"0",
"6",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"0",
"2",
"0",
"1",
"0",
"3",
"1",
"0",
"2",
"0",
"1",
"0",
"5",
"0",
"1",
"0",
"3",
"1",
"0",
"2",
"0",
"1",
"0",
"4",
"0",
"2",
"0",
"1"
]
| [
"nonn",
"base"
]
| 8 | 0 | 4 | [
"A058265",
"A278045",
"A352103",
"A356749",
"A356896",
"A356897",
"A356898"
]
| null | Amiram Eldar, Sep 03 2022 | 2022-09-05T05:24:39 | oeisdata/seq/A356/A356898.seq | 518c3dc949db7ce1e376762cdf0ce8d7 |
A356899 | Nonnegative numbers whose minimal and maximal tribonacci representations are the same. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"11",
"12",
"15",
"16",
"17",
"18",
"19",
"21",
"22",
"23",
"28",
"29",
"30",
"32",
"33",
"34",
"35",
"36",
"39",
"40",
"41",
"42",
"43",
"52",
"53",
"54",
"55",
"56",
"59",
"60",
"61",
"62",
"63",
"65",
"66",
"67",
"72",
"73",
"74",
"76",
"77",
"78",
"79",
"80",
"96",
"97",
"98",
"99",
"100",
"102",
"103",
"104",
"109",
"110",
"111",
"113"
]
| [
"nonn",
"base"
]
| 8 | 1 | 3 | [
"A000071",
"A089068",
"A278038",
"A352103",
"A356899"
]
| null | Amiram Eldar, Sep 03 2022 | 2022-09-05T05:24:42 | oeisdata/seq/A356/A356899.seq | 57cf57e23db7603755c3cca70a7a8b5a |
A356900 | a(n) = P(n, 1/2) where P(n, x) = x^(-n)*Sum_{k=0..n} A241171(n, k)*x^k. | [
"1",
"1",
"8",
"154",
"5552",
"321616",
"27325088",
"3200979664",
"494474723072",
"97390246272256",
"23820397371219968",
"7083386168647642624",
"2516691244849530785792",
"1052914814802404260765696",
"512347915163742179541659648",
"286902390859642414913802102784",
"183187476890368376930869730803712"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A000364",
"A002105",
"A094088",
"A241171",
"A269941",
"A327022",
"A356900"
]
| null | Peter Luschny, Sep 03 2022 | 2022-09-03T08:13:12 | oeisdata/seq/A356/A356900.seq | 08807a62f2e31880e4ff362134198f60 |
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