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| offset_a
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666,262,453B
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
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⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
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stringlengths 29
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stringlengths 32
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A357001 | a(n) = A002729(n) - A357000(n) - 1. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"43",
"0",
"12",
"0",
"0",
"0",
"0",
"0",
"1954",
"8",
"0",
"342",
"0",
"0",
"0",
"0"
]
| [
"nonn",
"more"
]
| 19 | 1 | 16 | [
"A002729",
"A357000",
"A357001",
"A357002"
]
| null | Pontus von Brömssen, Sep 08 2022 | 2023-06-29T09:03:55 | oeisdata/seq/A357/A357001.seq | 4f305527ffb2b3b2bff9339a72ba4a1c |
A357002 | Numbers k such that A357001(k) > 0. | [
"8",
"16",
"18",
"24",
"25",
"27"
]
| [
"nonn",
"more"
]
| 6 | 1 | 1 | [
"A357000",
"A357001",
"A357002"
]
| null | Pontus von Brömssen, Sep 08 2022 | 2022-09-17T08:51:38 | oeisdata/seq/A357/A357002.seq | e4ed046ce00e1ee162ac8d50674b0606 |
A357003 | Number of Hamiltonian cycles in the cyclic Haar graph with index n. | [
"0",
"0",
"1",
"0",
"1",
"1",
"6",
"0",
"1",
"0",
"6",
"1",
"6",
"6",
"72",
"0",
"1",
"1",
"8",
"1",
"8",
"8",
"156",
"1",
"8",
"8",
"156",
"8",
"156",
"156",
"1440",
"0",
"1",
"0",
"8",
"0",
"12",
"12",
"335",
"0",
"12",
"0",
"300",
"12",
"352",
"300",
"4800",
"1",
"8",
"12",
"335",
"12",
"300",
"352",
"4800",
"8",
"335",
"300",
"4800",
"335",
"4800",
"4800",
"43200",
"0",
"1",
"1",
"10",
"1"
]
| [
"nonn"
]
| 8 | 1 | 7 | [
"A010796",
"A291165",
"A357000",
"A357003",
"A357004"
]
| null | Pontus von Brömssen, Sep 08 2022 | 2022-09-17T09:53:54 | oeisdata/seq/A357/A357003.seq | ba6648e415170793a3de4a77b93832c1 |
A357004 | Smallest k for which the cyclic Haar graphs with indices k and n are isomorphic. | [
"1",
"2",
"3",
"4",
"5",
"5",
"7",
"8",
"9",
"10",
"11",
"9",
"11",
"11",
"15",
"16",
"17",
"17",
"19",
"17",
"19",
"19",
"23",
"17",
"19",
"19",
"23",
"19",
"23",
"23",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"37",
"39",
"34",
"37",
"42",
"43",
"37",
"45",
"43",
"47",
"33",
"35",
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"39",
"37",
"43",
"45",
"47",
"35",
"39",
"43",
"47",
"39",
"47",
"47",
"63",
"64",
"65",
"65",
"67",
"65"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A137706",
"A163382",
"A272919",
"A357000",
"A357004",
"A357005"
]
| null | Pontus von Brömssen, Sep 08 2022 | 2023-06-26T22:31:46 | oeisdata/seq/A357/A357004.seq | 238e627ff891034a749dc219961ce322 |
A357005 | Smallest k that is cyclically equivalent (see Comment for definition) to n. | [
"1",
"2",
"3",
"4",
"5",
"5",
"7",
"8",
"9",
"10",
"11",
"9",
"11",
"11",
"15",
"16",
"17",
"17",
"19",
"17",
"19",
"19",
"23",
"17",
"19",
"19",
"23",
"19",
"23",
"23",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"37",
"39",
"34",
"37",
"42",
"43",
"37",
"45",
"43",
"47",
"33",
"35",
"37",
"39",
"37",
"43",
"45",
"47",
"35",
"39",
"43",
"47",
"39",
"47",
"47",
"63",
"64",
"65",
"65",
"67",
"65"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A000120",
"A002729",
"A163382",
"A267508",
"A357004",
"A357005",
"A357006"
]
| null | Pontus von Brömssen, Sep 08 2022 | 2022-09-17T09:53:46 | oeisdata/seq/A357/A357005.seq | 845e85e5a8ea5fcf77b1133a7b9fa549 |
A357006 | Numbers k that are the smallest of all numbers that are cyclically equivalent to k. | [
"1",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"10",
"11",
"15",
"16",
"17",
"19",
"23",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"39",
"42",
"43",
"45",
"47",
"63",
"64",
"65",
"67",
"69",
"71",
"75",
"79",
"95",
"127",
"128",
"129",
"130",
"131",
"133",
"135",
"136",
"137",
"138",
"139",
"141",
"143",
"147",
"151",
"153",
"155",
"159",
"170",
"171",
"175",
"187",
"191",
"255",
"256"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A002729",
"A137706",
"A333764",
"A357005",
"A357006"
]
| null | Pontus von Brömssen, Sep 08 2022 | 2022-09-17T09:53:42 | oeisdata/seq/A357/A357006.seq | 57db892cad3f73db2935d5343a5dc5c9 |
A357007 | Number of vertices in an equilateral triangle when n internal equilateral triangles are drawn between the 3n points that divide each side into n+1 equal parts. | [
"3",
"6",
"15",
"30",
"51",
"66",
"111",
"150",
"171",
"246",
"303",
"312",
"435",
"510",
"543",
"678",
"771",
"765",
"975",
"1059",
"1131",
"1326",
"1455",
"1488",
"1731",
"1878",
"1899",
"2178",
"2355",
"2376",
"2703",
"2886",
"2955",
"3270",
"3444",
"3420",
"3891",
"4110",
"4191",
"4485",
"4803",
"4878",
"5295",
"5526",
"5544",
"6078",
"6351",
"6396",
"6915",
"7206",
"7311",
"7794",
"8115"
]
| [
"nonn"
]
| 23 | 0 | 1 | [
"A091908",
"A092866",
"A333026",
"A344657",
"A356984",
"A357007",
"A357008"
]
| null | Scott R. Shannon, Sep 08 2022 | 2022-09-10T21:05:02 | oeisdata/seq/A357/A357007.seq | 7357eb23a7d84a465b6de60db7390b29 |
A357008 | Number of edges in an equilateral triangle when n internal equilateral triangles are drawn between the 3n points that divide each side into n+1 equal parts. | [
"3",
"9",
"27",
"57",
"99",
"135",
"219",
"297",
"351",
"489",
"603",
"645",
"867",
"1017",
"1107",
"1353",
"1539",
"1575",
"1947",
"2127",
"2295",
"2649",
"2907",
"3021",
"3459",
"3753",
"3855",
"4359",
"4707",
"4821",
"5403",
"5769",
"5967",
"6537",
"6897",
"6957",
"7779",
"8217",
"8451",
"9003",
"9603",
"9837",
"10587",
"11061",
"11211",
"12153",
"12699",
"12897",
"13827",
"14409",
"14715"
]
| [
"nonn"
]
| 19 | 0 | 1 | [
"A274586",
"A332376",
"A333027",
"A344896",
"A356984",
"A357007",
"A357008"
]
| null | Scott R. Shannon, Sep 08 2022 | 2022-09-10T21:04:57 | oeisdata/seq/A357/A357008.seq | 65037e66a4e02171846ad9d96d8f450c |
A357009 | E.g.f. satisfies log(A(x)) = (exp(x) - 1)^2 * A(x). | [
"1",
"0",
"2",
"6",
"50",
"390",
"4322",
"53046",
"782210",
"12920550",
"241747682",
"5000171286",
"113961184130",
"2830240421190",
"76196913418082",
"2209152734071926",
"68655746019566210",
"2276606079902438310",
"80244521295497399522",
"2995966456305973559766",
"118119901491333724203650"
]
| [
"nonn"
]
| 34 | 0 | 3 | [
"A052859",
"A052880",
"A357009",
"A357010",
"A357024"
]
| null | Seiichi Manyama, Sep 09 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357009.seq | a727bf41b434bc7f8d93b33b3ce12e9b |
A357010 | E.g.f. satisfies log(A(x)) = (exp(x) - 1)^3 * A(x). | [
"1",
"0",
"0",
"6",
"36",
"150",
"1620",
"24486",
"293076",
"3843510",
"68254740",
"1311687366",
"25479935316",
"552545882070",
"13437670215060",
"345157499363046",
"9370414233900756",
"274413997443811830",
"8572526271218671380",
"281754864204797848326",
"9767868351458229261396"
]
| [
"nonn"
]
| 27 | 0 | 4 | [
"A052880",
"A353664",
"A357009",
"A357010",
"A357025"
]
| null | Seiichi Manyama, Sep 09 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357010.seq | 06e5a080f86ba825a39db255500e4100 |
A357011 | E.g.f. satisfies A(x) * log(A(x)) = exp(x * A(x)^3) - 1. | [
"1",
"1",
"6",
"74",
"1407",
"36357",
"1190476",
"47254783",
"2205546706",
"118378505742",
"7184030384361",
"486440226752911",
"36358328607088010",
"2973464028723984551",
"264119772408892921774",
"25321946948812001539166",
"2606224408648404660237647",
"286624141573198517220290837"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A216136",
"A349583",
"A349588",
"A349601",
"A356960",
"A356973",
"A357011"
]
| null | Seiichi Manyama, Sep 08 2022 | 2022-09-12T08:28:14 | oeisdata/seq/A357/A357011.seq | a398e957cb3e509176da82ab9ed50bf1 |
A357012 | Triangle read by rows. T(n, k) = [x^k](0^n + 4^n * ((2 - 2*(1 - x)^(1/2)) / x - 1)). | [
"1",
"0",
"1",
"0",
"4",
"2",
"0",
"16",
"8",
"5",
"0",
"64",
"32",
"20",
"14",
"0",
"256",
"128",
"80",
"56",
"42",
"0",
"1024",
"512",
"320",
"224",
"168",
"132",
"0",
"4096",
"2048",
"1280",
"896",
"672",
"528",
"429",
"0",
"16384",
"8192",
"5120",
"3584",
"2688",
"2112",
"1716",
"1430",
"0",
"65536",
"32768",
"20480",
"14336",
"10752",
"8448",
"6864",
"5720",
"4862"
]
| [
"nonn",
"tabl"
]
| 4 | 0 | 5 | [
"A000108",
"A000302",
"A008549",
"A356651",
"A357012"
]
| null | Peter Luschny, Sep 09 2022 | 2022-09-09T04:05:45 | oeisdata/seq/A357/A357012.seq | 0bd2be5194edc37bfdc8af34eea1ae46 |
A357013 | Triangle read by rows. T(n, k) = ((2*n)! * k!) / (n + k)!. | [
"1",
"2",
"1",
"12",
"4",
"2",
"120",
"30",
"12",
"6",
"1680",
"336",
"112",
"48",
"24",
"30240",
"5040",
"1440",
"540",
"240",
"120",
"665280",
"95040",
"23760",
"7920",
"3168",
"1440",
"720",
"17297280",
"2162160",
"480480",
"144144",
"52416",
"21840",
"10080",
"5040",
"518918400",
"57657600",
"11531520",
"3144960",
"1048320",
"403200",
"172800",
"80640",
"40320"
]
| [
"nonn",
"tabl"
]
| 7 | 0 | 2 | [
"A000142",
"A001813",
"A357013"
]
| null | Peter Luschny, Sep 25 2022 | 2022-09-25T11:05:17 | oeisdata/seq/A357/A357013.seq | 8cf7cdf34072505e3c0c1bd930071b54 |
A357014 | Numbers whose sum of exponential divisors (A051377) is odd. | [
"1",
"3",
"5",
"7",
"11",
"13",
"15",
"17",
"19",
"21",
"23",
"29",
"31",
"33",
"35",
"37",
"39",
"41",
"43",
"47",
"51",
"53",
"55",
"57",
"59",
"61",
"65",
"67",
"69",
"71",
"73",
"77",
"79",
"81",
"83",
"85",
"87",
"89",
"91",
"93",
"95",
"97",
"101",
"103",
"105",
"107",
"109",
"111",
"113",
"115",
"119",
"123",
"127",
"129",
"131",
"133",
"137",
"139",
"141",
"143",
"145",
"149"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A000079",
"A028982",
"A049419",
"A051377",
"A056911",
"A197680",
"A357014",
"A357015",
"A357017"
]
| null | Amiram Eldar, Sep 09 2022 | 2022-09-09T06:30:46 | oeisdata/seq/A357/A357014.seq | 3429f879b2cf386a69da2f0760652a26 |
A357015 | Nonsquarefree numbers whose sum of exponential divisors (A051377) is odd. | [
"81",
"405",
"567",
"625",
"891",
"1053",
"1377",
"1539",
"1863",
"1875",
"2349",
"2401",
"2511",
"2835",
"2997",
"3321",
"3483",
"3807",
"4293",
"4375",
"4455",
"4779",
"4941",
"5265",
"5427",
"5751",
"5913",
"6237",
"6399",
"6723",
"6875",
"6885",
"7203",
"7209",
"7371",
"7695",
"7857",
"8125",
"8181",
"8343",
"8667",
"8829",
"9153",
"9315",
"9639"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A005117",
"A013929",
"A051377",
"A056911",
"A185199",
"A357014",
"A357015"
]
| null | Amiram Eldar, Sep 09 2022 | 2022-09-09T06:30:43 | oeisdata/seq/A357/A357015.seq | 59908da59576434a7317f35ffb4608f6 |
A357016 | Decimal expansion of the asymptotic density of numbers whose exponents in their prime factorization are squares (A197680). | [
"6",
"4",
"1",
"1",
"1",
"5",
"1",
"6",
"1",
"3",
"5",
"9",
"3",
"5",
"1",
"4",
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"3",
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"5",
"4",
"2",
"1",
"1",
"8",
"4",
"6",
"7",
"4",
"0",
"0",
"6",
"9",
"3",
"5",
"6",
"3",
"6",
"3",
"5"
]
| [
"nonn",
"cons"
]
| 5 | 0 | 1 | [
"A000290",
"A010052",
"A049419",
"A197680",
"A357016",
"A357017"
]
| null | Amiram Eldar, Sep 09 2022 | 2022-09-09T04:19:00 | oeisdata/seq/A357/A357016.seq | 7f1f03a8421f9a89c7e4f12ee7b5c849 |
A357017 | Decimal expansion of the asymptotic density of odd numbers whose exponents in their prime factorization are squares. | [
"4",
"0",
"9",
"7",
"9",
"7",
"4",
"4",
"6",
"7",
"1",
"3",
"3",
"1",
"9",
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"9",
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]
| [
"nonn",
"cons"
]
| 5 | 0 | 1 | [
"A000290",
"A010052",
"A051377",
"A197680",
"A357014",
"A357016",
"A357017"
]
| null | Amiram Eldar, Sep 09 2022 | 2022-09-09T04:18:47 | oeisdata/seq/A357/A357017.seq | 479533212102a23f55fc9970fc1dde0f |
A357018 | Records in the number of consecutive integers not expressible as sums of 2 squares. | [
"0",
"1",
"2",
"4",
"5",
"6",
"7",
"8",
"10",
"14",
"18",
"19",
"20",
"23",
"24",
"27",
"28",
"30",
"33",
"34",
"35",
"36",
"47",
"48",
"49",
"52",
"55",
"59",
"60",
"62",
"63",
"65",
"67",
"70",
"71",
"73",
"79",
"80",
"81",
"86",
"87",
"104",
"106"
]
| [
"nonn",
"more"
]
| 6 | 1 | 3 | [
"A001481",
"A022544",
"A104271",
"A260157",
"A297350",
"A357018"
]
| null | Hugo Pfoertner, Sep 09 2022 | 2022-09-09T10:02:57 | oeisdata/seq/A357/A357018.seq | 656942fca91d94a0530088efaba35ccd |
A357019 | a(n) is the largest possible x in n = x^2 - x*y + y^2 with integers x > y >= 0, or 0 if n cannot be expressed in this form. | [
"0",
"1",
"0",
"2",
"2",
"0",
"0",
"3",
"0",
"3",
"0",
"0",
"4",
"4",
"0",
"0",
"4",
"0",
"0",
"5",
"0",
"5",
"0",
"0",
"0",
"5",
"0",
"6",
"6",
"0",
"0",
"6",
"0",
"0",
"0",
"0",
"6",
"7",
"0",
"7",
"0",
"0",
"0",
"7",
"0",
"0",
"0",
"0",
"8",
"8",
"0",
"0",
"8",
"0",
"0",
"0",
"0",
"8",
"0",
"0",
"0",
"9",
"0",
"9",
"8",
"0",
"0",
"9",
"0",
"0",
"0",
"0",
"0",
"9",
"0",
"10",
"10",
"0",
"0",
"10",
"0",
"9",
"0",
"0",
"10",
"0"
]
| [
"nonn"
]
| 16 | 0 | 4 | [
"A002324",
"A003136",
"A133388",
"A357019"
]
| null | Hugo Pfoertner, Sep 10 2022 | 2022-09-12T17:14:19 | oeisdata/seq/A357/A357019.seq | efd8b6586adcb90d325738233b7ee5c3 |
A357020 | a(n) is the start of the first run of exactly n consecutive numbers not of the form x^2 + x*y + y^2. | [
"2",
"5",
"22",
"32",
"68",
"85",
"230",
"260",
"352",
"1901",
"950",
"1912",
"1430",
"1502",
"3442",
"10733",
"4310",
"5890",
"23933",
"15101",
"29548",
"101534",
"18698",
"89245",
"38858",
"46774",
"110440",
"173213",
"118772",
"513598",
"705437",
"273485",
"226324",
"269813",
"726929",
"1448005",
"1053830",
"413974",
"1329178",
"1626548",
"648542"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A002324",
"A003136",
"A034020",
"A104271",
"A357020"
]
| null | Hugo Pfoertner, Sep 10 2022 | 2022-09-12T16:09:43 | oeisdata/seq/A357/A357020.seq | 89016c0f6c47654daf6414ea85a0b598 |
A357021 | First coordinate x of points in the triangular lattice, sorted first by the distance from the origin and then by the circumferential angle phi restricted to the sector 0 <= phi < Pi/6. y is given in A357022. | [
"0",
"1",
"2",
"2",
"3",
"3",
"4",
"4",
"4",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"7",
"7",
"7",
"8",
"7",
"8",
"8",
"8",
"9",
"9",
"8",
"9",
"9",
"10",
"10",
"10",
"9",
"10",
"10",
"11",
"11",
"11",
"10",
"11",
"12",
"12",
"11",
"12",
"12",
"11",
"12",
"13",
"13",
"12",
"13",
"13",
"12",
"13",
"14",
"14",
"14",
"14",
"13",
"14",
"13",
"15",
"15",
"14",
"15",
"15",
"14",
"15",
"16",
"16",
"14",
"16",
"15"
]
| [
"nonn"
]
| 9 | 1 | 3 | [
"A003136",
"A280079",
"A280317",
"A305575",
"A305576",
"A355565",
"A355585",
"A357021"
]
| null | Hugo Pfoertner, Sep 10 2022 | 2025-04-01T08:10:08 | oeisdata/seq/A357/A357021.seq | 8359bce715b77180ee6ca5876c5f048c |
A357022 | Second coordinate y of points in the triangular lattice, sorted first by the distance from the origin and then by the circumferential angle phi restricted to the sector 0 <= phi < Pi/6. x is given in A357021. | [
"0",
"0",
"1",
"0",
"1",
"0",
"2",
"1",
"0",
"2",
"1",
"0",
"3",
"2",
"1",
"0",
"3",
"2",
"1",
"4",
"0",
"3",
"2",
"1",
"4",
"3",
"0",
"2",
"1",
"5",
"4",
"3",
"0",
"2",
"1",
"5",
"4",
"3",
"0",
"2",
"6",
"5",
"1",
"4",
"3",
"0",
"2",
"6",
"5",
"1",
"4",
"3",
"0",
"2",
"7",
"6",
"5",
"4",
"1",
"3",
"0",
"7",
"6",
"2",
"5",
"4",
"1",
"3",
"8",
"7",
"0",
"6",
"2",
"5",
"4",
"1",
"3",
"8",
"7",
"6",
"0",
"2",
"5",
"4",
"1",
"9",
"8",
"3"
]
| [
"nonn"
]
| 4 | 1 | 7 | [
"A357021",
"A357022"
]
| null | Hugo Pfoertner, Sep 10 2022 | 2022-09-10T07:35:02 | oeisdata/seq/A357/A357022.seq | a8d7c782d92a47edef04e953962cfc2c |
A357023 | Semiprimes k such that k is congruent to 5 modulo k's index in the sequence of semiprimes. | [
"4",
"185",
"206",
"209",
"27681",
"3066905",
"3067135",
"3067795",
"3067985",
"348933197",
"348933239",
"348933251",
"348933257",
"348933269",
"44690978141",
"44690978162",
"44690978519",
"44690978561",
"44690978617",
"44690978869",
"44690978981",
"44690979457",
"44690979527",
"6553736049293"
]
| [
"nonn",
"hard"
]
| 32 | 1 | 1 | [
"A001358",
"A106130",
"A357023"
]
| null | Lucas A. Brown, Oct 14 2022 | 2022-10-16T03:23:41 | oeisdata/seq/A357/A357023.seq | 6276ae723f33b9543d08657c7401095a |
A357024 | E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2. | [
"1",
"0",
"2",
"6",
"74",
"750",
"11402",
"195006",
"3994202",
"93164910",
"2455754762",
"72098755806",
"2333497474970",
"82569245246670",
"3170700672801482",
"131342693516044926",
"5837883571730770778",
"277151780512413426990",
"13997018265350140886282",
"749304617892345721184286"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A030019",
"A052859",
"A357009",
"A357024",
"A357025",
"A357031"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-12T03:20:05 | oeisdata/seq/A357/A357024.seq | e40a5cbe63e0df6c9a24657da26f4e03 |
A357025 | E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^3. | [
"1",
"0",
"0",
"6",
"36",
"150",
"3060",
"62286",
"867636",
"15591750",
"419764500",
"10834588446",
"277719263316",
"8580282719190",
"297021183388020",
"10459810717672686",
"393932179466738676",
"16351788886638987750",
"717798906181149294420",
"32905220431196072057406"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A030019",
"A353664",
"A357010",
"A357024",
"A357025",
"A357032"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-10T08:51:06 | oeisdata/seq/A357/A357025.seq | 9570c7c14a785d147766170aa8224a9c |
A357026 | E.g.f. satisfies A(x) = (1 - x)^(log(1 - x) * A(x)). | [
"1",
"0",
"2",
"6",
"58",
"460",
"5528",
"70308",
"1098060",
"18910512",
"371480832",
"8022952080",
"191325228576",
"4961955705408",
"139572074260656",
"4224646630879920",
"137077496211066384",
"4744151145076980864",
"174517898073769832448",
"6798949897214608689024",
"279688643858492900930496"
]
| [
"nonn"
]
| 19 | 0 | 3 | [
"A052813",
"A357026",
"A357027"
]
| null | Seiichi Manyama, Sep 09 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357026.seq | f8042ad94d34d8ca98e9fd079e0c98ba |
A357027 | E.g.f. satisfies A(x) = 1/(1 - x)^(log(1 - x)^2 * A(x)). | [
"1",
"0",
"0",
"6",
"36",
"210",
"2430",
"32424",
"426552",
"6575304",
"118916640",
"2328078456",
"49421111256",
"1153979875152",
"29201577206256",
"791744021665344",
"22988121190902720",
"712541051083100160",
"23447653175729566080",
"816434611464004145280",
"30009023179153182132480"
]
| [
"nonn"
]
| 19 | 0 | 4 | [
"A052813",
"A357026",
"A357027"
]
| null | Seiichi Manyama, Sep 09 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357027.seq | 1e98d637c9d2b813b0801f3a614931eb |
A357028 | E.g.f. satisfies A(x) = (1 - x * A(x))^log(1 - x * A(x)). | [
"1",
"0",
"2",
"6",
"82",
"820",
"13568",
"235368",
"5111748",
"123205248",
"3404436312",
"103998026880",
"3516027852456",
"129715202957184",
"5198615642907360",
"224652658604613120",
"10419411912935774736",
"516120552745366247424",
"27198524267826237745824"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A001761",
"A357028",
"A357029",
"A357036"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-12T03:20:32 | oeisdata/seq/A357/A357028.seq | d5ad79450b0d9f8c472ed22cc04ad0ac |
A357029 | E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2). | [
"1",
"0",
"0",
"6",
"36",
"210",
"3870",
"70224",
"1122072",
"23086344",
"586910880",
"15469437456",
"441107126856",
"14206113541152",
"496333927370736",
"18463733657766144",
"739328759822848320",
"31759148433997889280",
"1447876893211813379520",
"69881726567495477445120"
]
| [
"nonn"
]
| 17 | 0 | 4 | [
"A001761",
"A353344",
"A357028",
"A357029",
"A357037"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-12T04:51:25 | oeisdata/seq/A357/A357029.seq | 9db0588afae383444ba4233367ed88ea |
A357030 | a(n) is the number of integers in 0..n having nonincreasing digits. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"12",
"13",
"14",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"15",
"16",
"17",
"18",
"19",
"19",
"19",
"19",
"19",
"19",
"19",
"20",
"21",
"22",
"23",
"24",
"24",
"24",
"24",
"24",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"30",
"30",
"30",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"37",
"37",
"37",
"38",
"39",
"40"
]
| [
"nonn",
"base"
]
| 56 | 0 | 2 | [
"A009996",
"A357030"
]
| null | Osman Mustafa Quddusi, Sep 09 2022 | 2024-03-04T08:51:20 | oeisdata/seq/A357/A357030.seq | 3b264ad60abcf42845d4c0672caa9e7b |
A357031 | E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2 / 2. | [
"1",
"0",
"1",
"3",
"22",
"195",
"2131",
"28623",
"445789",
"7982355",
"161208976",
"3626200743",
"89942239861",
"2438520508515",
"71754865476841",
"2277574224716703",
"77570723071721938",
"2821841221403098995",
"109200125293424385271",
"4479379126010806153143",
"194148151869063307919725"
]
| [
"nonn"
]
| 14 | 0 | 4 | [
"A030019",
"A060311",
"A357024",
"A357031",
"A357032"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-12T05:21:40 | oeisdata/seq/A357/A357031.seq | 29df5a5de8cf48872b0d04751c7d7dc9 |
A357032 | E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^3 / 6. | [
"1",
"0",
"0",
"1",
"6",
"25",
"160",
"1981",
"24906",
"295625",
"4044900",
"68136541",
"1260048086",
"24330807865",
"508029259920",
"11686882860381",
"289532464998146",
"7588430921962825",
"210991834698749020",
"6244230552027963901",
"195584639712483465486",
"6442981074293371848185"
]
| [
"nonn"
]
| 9 | 0 | 5 | [
"A030019",
"A327504",
"A357025",
"A357031",
"A357032"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-10T08:53:25 | oeisdata/seq/A357/A357032.seq | 99b0d95aa2b65914b8b9687104f5b16f |
A357033 | a(n) is the smallest number that has exactly n divisors that are cyclops numbers (A134808). | [
"1",
"101",
"202",
"404",
"606",
"1212",
"2424",
"7272",
"21816",
"41208",
"84048",
"123624",
"144144",
"336336",
"288288",
"504504",
"432432",
"865368",
"864864",
"1009008",
"2378376",
"1729728",
"3459456",
"3027024",
"4756752",
"6054048",
"9081072",
"11099088",
"12108096",
"16648632",
"23207184",
"29405376",
"36324288"
]
| [
"nonn",
"base"
]
| 15 | 0 | 2 | [
"A134808",
"A357033"
]
| null | Marius A. Burtea, Sep 20 2022 | 2022-10-14T08:52:55 | oeisdata/seq/A357/A357033.seq | 9b5383dacd3f87258e6f9b60280f4a62 |
A357034 | a(n) is the smallest number with exactly n divisors that are hoax numbers (A019506). | [
"1",
"22",
"308",
"638",
"3696",
"4212",
"18480",
"26400",
"55080",
"52800",
"73920",
"108108",
"220320",
"216216",
"275400",
"324324",
"432432",
"550800",
"734400",
"1908000",
"1144800",
"1101600",
"1377000",
"1652400",
"3027024",
"2203200",
"4039200",
"2754000",
"3304800",
"5724000",
"6528600",
"9180000",
"8586000",
"5508000"
]
| [
"nonn",
"base"
]
| 12 | 0 | 2 | [
"A019506",
"A357034"
]
| null | Marius A. Burtea, Sep 20 2022 | 2022-10-14T08:52:59 | oeisdata/seq/A357/A357034.seq | 2eba86d73812ece98e468230cfa6f048 |
A357035 | a(n) is the smallest number that has exactly n divisors that are digitally balanced numbers (A031443). | [
"1",
"2",
"10",
"36",
"150",
"180",
"420",
"840",
"900",
"3420",
"2520",
"5040",
"6300",
"7560",
"12600",
"15120",
"18900",
"42840",
"32760",
"37800",
"95760",
"105840",
"69300",
"124740",
"163800",
"138600",
"166320",
"327600",
"249480",
"207900",
"491400",
"622440",
"498960",
"706860",
"415800",
"963900",
"1496880",
"1164240",
"1081080"
]
| [
"nonn",
"base"
]
| 17 | 0 | 2 | [
"A031443",
"A357035"
]
| null | Marius A. Burtea, Sep 20 2022 | 2023-09-27T11:23:05 | oeisdata/seq/A357/A357035.seq | 40864b7accf94d0ee329edf9b68c03bd |
A357036 | E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2). | [
"1",
"0",
"1",
"3",
"26",
"230",
"2794",
"39564",
"663606",
"12712104",
"275171106",
"6632699040",
"176309074644",
"5123121177096",
"161577261004860",
"5497133655605760",
"200683752698028924",
"7825434930630743616",
"324616635150708044796",
"14273994548639305751040",
"663205761925601097418488"
]
| [
"nonn"
]
| 17 | 0 | 4 | [
"A001761",
"A347001",
"A357028",
"A357036",
"A357037"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-12T05:18:33 | oeisdata/seq/A357/A357036.seq | 99bf3632fb59676ebf6b203ed11fd358 |
A357037 | E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6). | [
"1",
"0",
"0",
"1",
"6",
"35",
"295",
"3304",
"42112",
"599724",
"9657330",
"174222576",
"3464835726",
"75208002792",
"1771121398956",
"44998593873024",
"1226723273550720",
"35714547582173280",
"1106012915718532920",
"36304411160854523520",
"1259105580819317636280",
"46007354360033491345920"
]
| [
"nonn"
]
| 17 | 0 | 5 | [
"A001761",
"A347002",
"A357029",
"A357032",
"A357036",
"A357037"
]
| null | Seiichi Manyama, Sep 09 2022 | 2022-09-12T03:04:27 | oeisdata/seq/A357/A357037.seq | dc4939e1a0d6da3cda65743129dd437f |
A357038 | Numbers m such that each of the four consecutive numbers starting at m is the product of 8 prime factors (counting with multiplicity). | [
"4109290623",
"10440390750",
"24239110623",
"63390659373",
"66169625247",
"67492525373",
"72177640623",
"74735721872",
"88651359872",
"97510501023",
"99039940623"
]
| [
"nonn",
"more"
]
| 9 | 1 | 1 | [
"A356893",
"A357038"
]
| null | Zak Seidov, Sep 09 2022 | 2022-10-08T17:31:05 | oeisdata/seq/A357/A357038.seq | c56c4a0fbc3f990a9536f0a39ca34eb3 |
A357039 | Number of integer solutions to x' = 2n, where x' is the arithmetic derivative of x. | [
"0",
"1",
"1",
"1",
"2",
"2",
"2",
"3",
"2",
"2",
"3",
"4",
"3",
"2",
"3",
"4",
"4",
"4",
"2",
"3",
"4",
"4",
"4",
"6",
"4",
"3",
"5",
"4",
"4",
"7",
"3",
"5",
"6",
"3",
"5",
"7",
"5",
"5",
"7",
"6",
"5",
"8",
"5",
"4",
"9",
"6",
"5",
"8",
"3",
"6",
"8",
"5",
"6",
"9",
"6",
"8",
"10",
"6",
"6",
"13",
"4",
"6",
"10",
"4",
"7",
"9",
"6",
"5",
"8",
"9",
"8",
"11",
"6",
"5",
"12",
"5",
"8",
"12",
"5",
"8",
"11",
"6",
"6",
"14",
"9",
"6",
"11",
"9",
"7",
"14",
"6",
"8",
"13",
"7",
"8",
"13",
"7",
"9",
"13",
"8"
]
| [
"nonn"
]
| 20 | 1 | 5 | [
"A003415",
"A099302",
"A357039"
]
| null | Craig J. Beisel, Sep 09 2022 | 2022-09-12T22:49:11 | oeisdata/seq/A357/A357039.seq | 7a57f133b905ff7a5e46a0fdf8d3b63a |
A357040 | Deficient composite numbers whose sum of aliquot divisors as well as product of aliquot divisors is a perfect square. | [
"75",
"76",
"124",
"147",
"153",
"243",
"332",
"363",
"477",
"507",
"524",
"575",
"688",
"867",
"892",
"963",
"1075",
"1083",
"1421",
"1532",
"1573",
"1587",
"1611",
"1916",
"2032",
"2075",
"2224",
"2299",
"2401",
"2421",
"2523",
"2572",
"2883",
"2891",
"3479",
"4107",
"4336",
"4527",
"4961",
"4975"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A005100",
"A064116",
"A357040"
]
| null | Tanya Khovanova, Sep 09 2022 | 2022-09-11T19:03:46 | oeisdata/seq/A357/A357040.seq | aaa31445b656a081cb90eca388a123c9 |
A357041 | a(n) = Sum_{d|n} 2^(d-1) * binomial(d+n/d-1,d). | [
"1",
"4",
"7",
"18",
"21",
"66",
"71",
"196",
"305",
"648",
"1035",
"2526",
"4109",
"8774",
"16875",
"34288",
"65553",
"134860",
"262163",
"531506",
"1051237",
"2109594",
"4194327",
"8425348",
"16779257",
"33611984",
"67123631",
"134350206",
"268435485",
"537178750",
"1073741855",
"2148064768",
"4295048345",
"8591114580"
]
| [
"nonn"
]
| 110 | 1 | 2 | [
"A081543",
"A338682",
"A357041",
"A360797"
]
| null | Seiichi Manyama, Feb 26 2023 | 2023-07-31T02:25:36 | oeisdata/seq/A357/A357041.seq | 8676da5790d1192ddaeab3991513de34 |
A357042 | The sum of the numbers of the central diamond of the multiplication table [1..k] X [1..k] for k=2*n-1. | [
"1",
"20",
"117",
"400",
"1025",
"2196",
"4165",
"7232",
"11745",
"18100",
"26741",
"38160",
"52897",
"71540",
"94725",
"123136",
"157505",
"198612",
"247285",
"304400",
"370881",
"447700",
"535877",
"636480",
"750625",
"879476",
"1024245",
"1186192",
"1366625",
"1566900",
"1788421",
"2032640",
"2301057",
"2595220",
"2916725",
"3267216",
"3648385"
]
| [
"nonn",
"easy"
]
| 77 | 1 | 2 | [
"A000290",
"A000583",
"A001844",
"A003991",
"A015237",
"A357042"
]
| null | Nicolay Avilov, Sep 18 2022 | 2024-10-04T00:27:08 | oeisdata/seq/A357/A357042.seq | 17122c2c5a34c2aa7b1a918f7341b5d4 |
A357043 | Lexicographically earliest infinite sequence of distinct nonnegative integers such that neither a(n) nor a(n+1) share a digit with (a(n)+a(n+1))/2. | [
"0",
"1",
"3",
"5",
"7",
"2",
"4",
"6",
"8",
"10",
"34",
"9",
"20",
"42",
"18",
"30",
"14",
"31",
"13",
"35",
"17",
"33",
"11",
"37",
"15",
"39",
"16",
"38",
"50",
"22",
"40",
"26",
"41",
"19",
"36",
"52",
"24",
"46",
"21",
"45",
"27",
"44",
"28",
"58",
"70",
"23",
"57",
"25",
"47",
"29",
"51",
"73",
"43",
"60",
"82",
"12",
"48",
"62",
"32",
"56",
"84",
"49",
"61",
"83",
"55",
"71",
"53",
"75",
"91",
"63",
"80",
"54",
"72",
"90",
"64",
"81",
"59"
]
| [
"nonn",
"base",
"easy"
]
| 27 | 0 | 3 | null | null | Eric Angelini and M. F. Hasler, Sep 10 2022 | 2024-12-21T20:32:40 | oeisdata/seq/A357/A357043.seq | 16508ff42437b193e3af7160bd22c3d8 |
A357044 | Lexicographic earliest sequence of distinct palindromes (A002113) such that a(n)+a(n+1) is never palindromic. | [
"1",
"9",
"3",
"7",
"5",
"8",
"2",
"11",
"4",
"6",
"22",
"88",
"44",
"66",
"77",
"33",
"99",
"55",
"101",
"909",
"111",
"191",
"121",
"181",
"131",
"171",
"141",
"161",
"151",
"252",
"262",
"242",
"272",
"232",
"282",
"222",
"292",
"212",
"393",
"313",
"494",
"323",
"383",
"333",
"373",
"343",
"363",
"353",
"454",
"464",
"444",
"474",
"434",
"484",
"424"
]
| [
"nonn",
"base"
]
| 21 | 1 | 2 | [
"A002113",
"A029742",
"A262038",
"A357044",
"A357045"
]
| null | Eric Angelini and M. F. Hasler, Sep 14 2022 | 2024-12-21T20:35:54 | oeisdata/seq/A357/A357044.seq | 105b3c9eaf72dd9c50ea3e6daa075267 |
A357045 | Lexicographically earliest sequence of distinct non-palindromic numbers (A029742) such that a(n)+a(n+1) is always a palindrome (A002113). | [
"10",
"12",
"21",
"23",
"32",
"34",
"43",
"45",
"54",
"47",
"19",
"14",
"30",
"25",
"41",
"36",
"52",
"49",
"17",
"16",
"28",
"27",
"39",
"38",
"50",
"51",
"15",
"18",
"26",
"29",
"37",
"40",
"48",
"53",
"13",
"20",
"24",
"31",
"35",
"42",
"46",
"65",
"56",
"75",
"76",
"85",
"86",
"95",
"96",
"106",
"116",
"126",
"136",
"146",
"157",
"105",
"97",
"64",
"57",
"74"
]
| [
"nonn",
"base"
]
| 16 | 1 | 1 | [
"A002113",
"A029742",
"A357044",
"A357045"
]
| null | Eric Angelini and M. F. Hasler, Sep 14 2022 | 2024-12-21T20:37:03 | oeisdata/seq/A357/A357045.seq | 57fe9b025da1c4345c8a2bf83599b7ce |
A357046 | Squares visited by a knight moving on a board covered with horizontal dominoes [m|m], m = 0, 1, 2, ... in a diamond-shaped spiral, when the knight always jumps to the unvisited square with the least number on the corresponding domino. | [
"0",
"11",
"14",
"1",
"4",
"13",
"10",
"3",
"18",
"7",
"2",
"5",
"22",
"9",
"28",
"31",
"60",
"15",
"32",
"29",
"52",
"25",
"8",
"27",
"12",
"53",
"26",
"23",
"6",
"17",
"34",
"59",
"30",
"87",
"126",
"51",
"24",
"45",
"20",
"39",
"16",
"33",
"58",
"55",
"86",
"125",
"50",
"47",
"76",
"21",
"40",
"67",
"36",
"61",
"94",
"57",
"54",
"85",
"176",
"129",
"56",
"93",
"138",
"187",
"92",
"137",
"96",
"35",
"38",
"19"
]
| [
"nonn",
"fini",
"full"
]
| 26 | 0 | 2 | [
"A174344",
"A268038",
"A274641",
"A274923",
"A316328",
"A326922",
"A326924",
"A328908",
"A328909",
"A328928",
"A328929",
"A357046"
]
| null | M. F. Hasler, Oct 19 2022 | 2022-12-25T22:48:19 | oeisdata/seq/A357/A357046.seq | 45804da38131e5b856629804f8733b7e |
A357047 | Lexicographically earliest sequence of distinct nonnegative integers such that a(2n)*a(2n+1) has n as substring, for all n >= 0. | [
"0",
"1",
"2",
"5",
"3",
"4",
"6",
"22",
"7",
"12",
"8",
"19",
"9",
"14",
"10",
"17",
"11",
"18",
"13",
"15",
"16",
"63",
"20",
"55",
"21",
"58",
"23",
"31",
"24",
"59",
"25",
"46",
"26",
"62",
"27",
"64",
"28",
"65",
"29",
"66",
"30",
"34",
"32",
"38",
"33",
"37",
"35",
"67",
"36",
"68",
"39",
"75",
"40",
"315",
"41",
"47",
"42",
"69",
"43",
"103",
"44",
"70",
"45",
"71",
"48",
"84",
"49",
"117",
"50",
"268",
"51",
"85",
"52",
"93",
"53"
]
| [
"nonn",
"base",
"tabf"
]
| 16 | 0 | 3 | null | null | Eric Angelini and M. F. Hasler, Dec 07 2022 | 2025-05-06T11:25:16 | oeisdata/seq/A357/A357047.seq | 9e483409b0aca84efb02a4ba0fe78146 |
A357048 | Terms in the Fibostracci sequence A359128 that arise as the sum of the two previous terms. | [
"1",
"3",
"5",
"8",
"13",
"16",
"21",
"25",
"29",
"35",
"39",
"41",
"58",
"59",
"66",
"76",
"78",
"81",
"88",
"99",
"103",
"107",
"117",
"118",
"119",
"139",
"149",
"151",
"159",
"160",
"173",
"177",
"183",
"198",
"202",
"209",
"239",
"245",
"280",
"351",
"399",
"599",
"631",
"703",
"798",
"800",
"899",
"999",
"1198",
"1200",
"1399",
"1499",
"1600",
"1798",
"1998",
"2099",
"3999",
"5999",
"7998",
"8000",
"8999",
"9999",
"11998",
"12000",
"13999",
"14999",
"16000",
"17998"
]
| [
"nonn",
"base"
]
| 34 | 1 | 2 | [
"A000045",
"A357048",
"A359128"
]
| null | M. F. Hasler and Eric Angelini, Dec 08 2022 | 2024-12-21T18:15:43 | oeisdata/seq/A357/A357048.seq | 5609c28a2d111b4fb2c7b47b1345eb17 |
A357049 | Lexicographically earliest sequence of distinct nonnegative integers such that, when the digits fill a square array read by falling antidiagonals, the "bitmap" of even digits reproduces the same square array. | [
"0",
"2",
"4",
"6",
"1",
"8",
"3",
"21",
"20",
"5",
"23",
"22",
"7",
"9",
"24",
"10",
"12",
"14",
"16",
"18",
"26",
"11",
"30",
"25",
"27",
"29",
"41",
"28",
"43",
"32",
"13",
"40",
"34",
"36",
"38",
"15",
"50",
"17",
"19",
"42",
"31",
"45",
"52",
"33",
"47",
"49",
"61",
"54",
"35",
"63",
"44",
"37",
"46",
"39",
"56",
"51",
"58",
"48",
"70",
"72",
"74",
"53",
"65",
"76",
"78",
"90",
"67",
"55",
"69",
"57"
]
| [
"nonn",
"base"
]
| 18 | 0 | 2 | null | null | Eric Angelini and M. F. Hasler, Oct 20 2022 | 2022-10-23T01:45:58 | oeisdata/seq/A357/A357049.seq | 170092be2e73511ffcad10d66aa2083d |
A357050 | Number of ways A005101(n)+1 can be written as sum of a subset of the proper divisors of A005101(n), the n-th abundant number. | [
"2",
"1",
"1",
"4",
"4",
"7",
"2",
"2",
"10",
"2",
"2",
"32",
"2",
"1",
"26",
"1",
"6",
"24",
"1",
"19",
"20",
"2",
"1",
"1",
"20",
"4",
"1",
"270",
"11",
"14",
"1",
"14",
"116",
"12",
"9",
"12",
"3",
"195",
"1",
"2",
"719",
"1",
"42",
"1",
"8",
"9",
"8",
"2",
"148",
"142",
"6",
"1",
"8",
"6",
"6",
"2154",
"1",
"534",
"1",
"6",
"125",
"108",
"1",
"6",
"117",
"1",
"447",
"4"
]
| [
"nonn"
]
| 4 | 1 | 1 | [
"A002975",
"A005101",
"A005835",
"A006037",
"A033880",
"A100696",
"A357050"
]
| null | M. F. Hasler, Dec 13 2022 | 2022-12-15T13:52:57 | oeisdata/seq/A357/A357050.seq | aa18d4aee81877083bc2ea3858414f21 |
A357051 | a(n) = Sum_{d|n} 3^(n-d). | [
"1",
"4",
"10",
"37",
"82",
"352",
"730",
"2998",
"7291",
"26488",
"59050",
"263170",
"531442",
"2127952",
"5373460",
"19669879",
"43046722",
"187086916",
"387420490",
"1607136634",
"3878987860",
"13947314752",
"31381059610",
"139902374692",
"285916320883",
"1129719740248",
"2824682785300",
"10460357985970"
]
| [
"nonn",
"easy"
]
| 39 | 1 | 2 | [
"A074854",
"A112329",
"A342628",
"A342629",
"A357051",
"A359203",
"A359206"
]
| null | Seiichi Manyama, Dec 20 2022 | 2023-08-23T08:42:22 | oeisdata/seq/A357/A357051.seq | cc5f08e5635fcabbee9340dd80b02b5a |
A357052 | Distance from 10^n to the next prime triplet. | [
"4",
"1",
"1",
"87",
"267",
"357",
"33",
"451",
"2011",
"2821",
"10687",
"2497",
"5073",
"5557",
"15243",
"7147",
"7357",
"7197",
"6627",
"9157",
"26317",
"25833",
"39207",
"56067",
"6667",
"32937",
"70561",
"106533",
"597",
"28503",
"19167",
"74551",
"301711",
"6747",
"246871",
"223353",
"63057",
"75183",
"48513",
"61323",
"16107",
"554287",
"160141",
"29821",
"220711",
"49441"
]
| [
"nonn",
"base"
]
| 25 | 0 | 1 | [
"A007529",
"A022004",
"A022005",
"A343635",
"A357052"
]
| null | M. F. Hasler, Sep 14 2022 | 2022-10-26T18:16:45 | oeisdata/seq/A357/A357052.seq | 721ab75c88929fb5ac497643ea61f5d1 |
A357053 | Decimal expansion of Sum_{k>=1} k/Fibonacci(2*k). | [
"2",
"3",
"9",
"7",
"4",
"1",
"4",
"1",
"8",
"7",
"9",
"1",
"6",
"5",
"2",
"1",
"2",
"0",
"0",
"4",
"0",
"9",
"2",
"2",
"4",
"4",
"9",
"5",
"6",
"8",
"1",
"7",
"7",
"8",
"7",
"0",
"8",
"5",
"2",
"0",
"7",
"2",
"2",
"2",
"9",
"6",
"3",
"7",
"5",
"5",
"4",
"4",
"4",
"8",
"5",
"8",
"3",
"1",
"9",
"7",
"3",
"7",
"0",
"8",
"7",
"2",
"8",
"2",
"3",
"7",
"7",
"7",
"8",
"9",
"3",
"2",
"2",
"1",
"5",
"9",
"9",
"2",
"3",
"2",
"8",
"7",
"6",
"1",
"8",
"6",
"8",
"5",
"6",
"7",
"0",
"3",
"3",
"6",
"6",
"5",
"1",
"0",
"8",
"4",
"9"
]
| [
"nonn",
"cons"
]
| 12 | 1 | 1 | [
"A000045",
"A001622",
"A001906",
"A002448",
"A002878",
"A079586",
"A081071",
"A153386",
"A153387",
"A357053",
"A357054"
]
| null | Amiram Eldar, Sep 10 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357053.seq | 9e3cc5ee1f81d401abbbb590c527b243 |
A357054 | Decimal expansion of Sum_{k>=1} (-1)^(k+1)*k/Fibonacci(2*k). | [
"5",
"8",
"0",
"0",
"0",
"4",
"7",
"3",
"9",
"5",
"0",
"7",
"7",
"7",
"0",
"6",
"8",
"0",
"0",
"6",
"7",
"4",
"7",
"0",
"9",
"8",
"1",
"8",
"9",
"5",
"5",
"2",
"2",
"8",
"0",
"2",
"6",
"9",
"8",
"5",
"0",
"1",
"2",
"6",
"0",
"9",
"6",
"4",
"6",
"1",
"6",
"3",
"9",
"0",
"1",
"5",
"7",
"7",
"5",
"6",
"1",
"0",
"0",
"1",
"7",
"7",
"6",
"7",
"3",
"7",
"5",
"7",
"5",
"2",
"1",
"9",
"9",
"7",
"8",
"4",
"8",
"9",
"4",
"9",
"2",
"1",
"0",
"4",
"4",
"7",
"8",
"6",
"6",
"9",
"4",
"0",
"2",
"2",
"3",
"7",
"1",
"4",
"1",
"1",
"5"
]
| [
"nonn",
"cons"
]
| 12 | 0 | 1 | [
"A000045",
"A001519",
"A001906",
"A079586",
"A081068",
"A153386",
"A153387",
"A158933",
"A265288",
"A357053",
"A357054"
]
| null | Amiram Eldar, Sep 10 2022 | 2025-01-05T19:51:42 | oeisdata/seq/A357/A357054.seq | b498d6526f0ce393c69f52ebef69e858 |
A357055 | Integers k such that k^k + k^2 + 3*k + 2 is prime. | [
"0",
"1",
"3",
"5",
"11",
"209",
"1281"
]
| [
"nonn",
"more"
]
| 39 | 1 | 3 | [
"A058912",
"A187605",
"A231712",
"A357055"
]
| null | Marco Ripà, Sep 10 2022 | 2024-09-17T12:44:40 | oeisdata/seq/A357/A357055.seq | bd45b4efcb4bdf506014153711fa5231 |
A357056 | Integers k such that k^k + k^2 + 2*k + 1 is prime. | [
"0",
"1",
"2",
"3",
"4",
"9",
"10",
"13",
"15",
"24"
]
| [
"nonn",
"more",
"hard"
]
| 27 | 1 | 3 | [
"A058912",
"A187605",
"A231712",
"A357056"
]
| null | Marco Ripà, Sep 10 2022 | 2024-09-17T14:17:04 | oeisdata/seq/A357/A357056.seq | 9fb935b5adea0dfe2749e53b775c260a |
A357057 | a(n) = A356886(2^n+1)/A356886(2^n-1). | [
"3",
"3",
"3",
"5",
"5",
"7",
"11",
"11",
"13",
"17",
"19",
"19",
"23",
"29",
"31",
"37",
"37",
"41",
"43",
"47",
"53",
"59",
"59",
"61",
"67",
"71",
"73",
"79",
"83",
"83",
"89"
]
| [
"nonn",
"more"
]
| 64 | 1 | 1 | [
"A000051",
"A000225",
"A065091",
"A356886",
"A357057"
]
| null | Paul Curtz, Sep 09 2022 | 2022-10-02T00:10:41 | oeisdata/seq/A357/A357057.seq | 19c573ac8a72ed492b22a9d1e88836b3 |
A357058 | Number of regions in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts. | [
"1",
"5",
"17",
"37",
"65",
"93",
"145",
"181",
"257",
"309",
"401",
"457",
"577",
"653",
"785",
"869",
"1025",
"1109",
"1297",
"1413",
"1601",
"1725",
"1937",
"2041",
"2305",
"2453",
"2705",
"2861",
"3137",
"3289",
"3601",
"3765",
"4089",
"4293",
"4625",
"4801",
"5185",
"5405",
"5769",
"5993",
"6401",
"6605",
"7057",
"7309",
"7737",
"8013",
"8465",
"8673",
"9217",
"9477",
"9993",
"10309"
]
| [
"nonn"
]
| 22 | 0 | 2 | [
"A108914",
"A355798",
"A355838",
"A356984",
"A357058",
"A357060",
"A357061"
]
| null | Scott R. Shannon, Sep 10 2022 | 2022-09-17T14:14:24 | oeisdata/seq/A357/A357058.seq | 4d04b75aa179c4ef67e1d4d09b232c63 |
A357059 | Decimal expansion of sum of squares of reciprocals of primes whose distance to the next prime is equal to 4, Sum_{j>=1} 1/A029710(j)^2. | [
"0",
"3",
"1",
"3",
"2",
"1",
"6",
"2",
"0",
"6",
"4",
"6"
]
| [
"nonn",
"cons",
"hard",
"more"
]
| 48 | 0 | 2 | [
"A006512",
"A023200",
"A029710",
"A046132",
"A065421",
"A077800",
"A078437",
"A085548",
"A096247",
"A160910",
"A194098",
"A209328",
"A209329",
"A242301",
"A242302",
"A242303",
"A242304",
"A306539",
"A342714",
"A356793",
"A357059"
]
| null | Artur Jasinski, Sep 10 2022 | 2022-09-29T08:51:57 | oeisdata/seq/A357/A357059.seq | 5bcfd06a82d9e83ae4bea4c009af5e45 |
A357060 | Number of vertices in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts. | [
"4",
"8",
"20",
"40",
"68",
"88",
"148",
"168",
"260",
"296",
"404",
"436",
"580",
"632",
"788",
"840",
"1028",
"1072",
"1300",
"1384",
"1604",
"1688",
"1940",
"1972",
"2308",
"2408",
"2708",
"2808",
"3140",
"3220",
"3604",
"3696",
"4084",
"4232",
"4628",
"4716",
"5188",
"5336",
"5764",
"5908",
"6404",
"6496",
"7060",
"7224",
"7732",
"7928",
"8468",
"8524",
"9220",
"9368",
"9988",
"10216"
]
| [
"nonn"
]
| 23 | 0 | 1 | [
"A355799",
"A355839",
"A355949",
"A357007",
"A357058",
"A357060",
"A357061"
]
| null | Scott R. Shannon, Sep 10 2022 | 2022-09-17T13:06:58 | oeisdata/seq/A357/A357060.seq | 33d921eadf72bbcfab262235b45913fb |
A357061 | Number of edges in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts. | [
"4",
"12",
"36",
"76",
"132",
"180",
"292",
"348",
"516",
"604",
"804",
"892",
"1156",
"1284",
"1572",
"1708",
"2052",
"2180",
"2596",
"2796",
"3204",
"3412",
"3876",
"4012",
"4612",
"4860",
"5412",
"5668",
"6276",
"6508",
"7204",
"7460",
"8172",
"8524",
"9252",
"9516",
"10372",
"10740",
"11532",
"11900",
"12804",
"13100",
"14116",
"14532",
"15468",
"15940",
"16932",
"17196",
"18436"
]
| [
"nonn"
]
| 14 | 0 | 1 | [
"A355800",
"A355840",
"A355948",
"A357008",
"A357058",
"A357060",
"A357061"
]
| null | Scott R. Shannon, Sep 10 2022 | 2022-09-17T11:41:20 | oeisdata/seq/A357/A357061.seq | 592946e4fa872c6f459002b04ce6ad99 |
A357062 | Number of ordered solutions to n = x*y*z + x + y + z in positive integers. | [
"0",
"0",
"0",
"0",
"1",
"0",
"3",
"0",
"3",
"3",
"3",
"0",
"9",
"0",
"4",
"6",
"6",
"0",
"9",
"3",
"9",
"6",
"3",
"0",
"18",
"3",
"6",
"6",
"9",
"3",
"15",
"0",
"9",
"12",
"6",
"6",
"19",
"0",
"3",
"9",
"21",
"0",
"18",
"0",
"12",
"12",
"6",
"6",
"21",
"6",
"9",
"12",
"9",
"0",
"24",
"6",
"18",
"6",
"3",
"6",
"33",
"6",
"6",
"12",
"15",
"6",
"18",
"0",
"15",
"15",
"15",
"0",
"33",
"6",
"6",
"18",
"13",
"6",
"21",
"3",
"21",
"9",
"9",
"0",
"36",
"12",
"9",
"12",
"18",
"9",
"27",
"6",
"9",
"9",
"6"
]
| [
"nonn"
]
| 36 | 0 | 7 | [
"A350535",
"A357062",
"A357809"
]
| null | Charles R Greathouse IV, Oct 13 2022 | 2022-10-23T01:09:47 | oeisdata/seq/A357/A357062.seq | 050bc4821ff41efc2b35ad593e45b82a |
A357063 | Lengths of the B blocks associated with A091787. | [
"1",
"4",
"13",
"42",
"127",
"382",
"1149",
"3448",
"10345",
"31044",
"93133",
"279400",
"838203",
"2514610",
"7543831",
"22631496",
"67894489",
"203683468",
"611050413",
"1833151240",
"5499453721",
"16498361166",
"49495083499",
"148485250498",
"445455751497",
"1336367254492",
"4009101763477",
"12027305290463",
"36081915871390",
"108245747614173",
"324737242842520",
"974211728527561",
"2922635185582686",
"8767905556748059",
"26303716670244178",
"78911150010732543",
"236733450032197630",
"710200350096592891"
]
| [
"nonn"
]
| 31 | 1 | 2 | [
"A091787",
"A357063",
"A357068"
]
| null | Levi van de Pol, Sep 10 2022 | 2022-11-22T22:36:40 | oeisdata/seq/A357/A357063.seq | 50a4c547f2ad3a5e76586f9d20b6f51a |
A357064 | a(n) = k such that A091411(k) = A091409(n). | [
"1",
"2",
"3",
"7",
"418090195952691922788354"
]
| [
"nonn"
]
| 23 | 1 | 2 | [
"A091409",
"A091411",
"A357064"
]
| null | Levi van de Pol, Sep 10 2022 | 2022-10-25T05:13:25 | oeisdata/seq/A357/A357064.seq | bd951a26efe4d7939ad064fbc7b323f1 |
A357065 | Numbers k with the following property: the value A091839(k+1) is not a 1 that is obtained from smoothing A091579. | [
"0",
"1",
"2",
"3",
"5",
"7",
"8",
"9",
"10",
"11",
"13",
"15",
"16",
"17",
"18",
"19",
"21",
"23",
"24",
"25",
"26",
"27",
"29",
"31",
"33",
"34",
"35",
"37",
"39",
"40",
"41",
"42",
"43",
"45",
"47",
"49",
"50",
"51",
"53",
"55",
"56",
"57",
"58",
"59",
"61",
"63",
"65",
"66",
"67",
"69",
"71",
"73",
"74",
"75",
"77",
"79",
"80",
"81",
"82",
"83",
"85",
"87",
"88",
"89",
"90",
"91",
"93",
"95",
"97",
"98",
"99",
"101",
"103"
]
| [
"nonn",
"base"
]
| 31 | 1 | 3 | [
"A090822",
"A091787",
"A357065",
"A357066",
"A357067"
]
| null | Levi van de Pol, Sep 10 2022 | 2022-10-23T02:29:03 | oeisdata/seq/A357/A357065.seq | 7a6f06c39e093153197ec8fa32651fcb |
A357066 | Decimal expansion of the limit of k/A357065(k) as k goes to infinity. | [
"6",
"9",
"1",
"6",
"7",
"2",
"2",
"0",
"8",
"7",
"8",
"1",
"1",
"2",
"6",
"1",
"5",
"3",
"3",
"8"
]
| [
"nonn",
"cons",
"more"
]
| 24 | 0 | 1 | [
"A090822",
"A091409",
"A357065",
"A357066"
]
| null | Levi van de Pol, Oct 21 2022 | 2022-11-03T10:08:13 | oeisdata/seq/A357/A357066.seq | 5e1374637cf37a86f74162cfdae76af3 |
A357067 | Decimal expansion of the limit of A091411(k)/2^(k-1) as k goes to infinity. | [
"3",
"4",
"8",
"6",
"6",
"9",
"8",
"8",
"6",
"4",
"3",
"8",
"3",
"6",
"5",
"5",
"9",
"7",
"0",
"2",
"3",
"5",
"8",
"7",
"2",
"7",
"0",
"0",
"7",
"0",
"2",
"2",
"2",
"0",
"6",
"6",
"7",
"3",
"3",
"5",
"4",
"1",
"3",
"6",
"6",
"2"
]
| [
"nonn",
"cons",
"more"
]
| 23 | 1 | 1 | [
"A090822",
"A091409",
"A091411",
"A091579",
"A357066",
"A357067",
"A357068"
]
| null | Levi van de Pol, Oct 22 2022 | 2023-02-28T09:23:57 | oeisdata/seq/A357/A357067.seq | d1319d6cf8272535cd6dd37fa52c9dd5 |
A357068 | Decimal expansion of the limit of A357063(k)/3^(k-1) as k goes to infinity. | [
"1",
"5",
"7",
"7",
"2",
"2",
"7",
"9",
"2",
"3",
"9",
"9",
"4",
"5",
"0",
"0",
"6",
"9",
"4",
"1",
"0"
]
| [
"nonn",
"cons",
"more"
]
| 11 | 1 | 2 | [
"A091787",
"A091840",
"A357063",
"A357066",
"A357067",
"A357068"
]
| null | Levi van de Pol, Oct 24 2022 | 2022-10-25T11:38:34 | oeisdata/seq/A357/A357068.seq | 77ea474bece7f9f77319a33082263b66 |
A357069 | Number of partitions of n into at most 4 distinct positive squares. | [
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"2",
"2",
"0",
"0",
"2",
"2",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"0",
"0",
"2",
"2",
"0",
"0",
"2",
"3",
"1",
"1",
"2",
"2",
"0",
"1",
"1",
"1",
"1",
"0",
"2",
"3",
"1",
"1",
"4",
"2",
"0",
"1",
"2",
"2",
"1",
"0",
"1",
"4",
"2",
"0",
"2",
"4",
"1",
"1",
"3",
"1",
"1",
"2",
"3",
"3",
"1",
"0",
"3",
"5",
"2",
"0",
"2",
"4",
"2",
"0",
"1",
"3",
"2",
"2",
"4"
]
| [
"nonn"
]
| 10 | 0 | 26 | [
"A000290",
"A002635",
"A025435",
"A025443",
"A033461",
"A341040",
"A347534",
"A347586",
"A347711",
"A357069"
]
| null | Ilya Gutkovskiy, Oct 25 2022 | 2022-10-25T20:39:19 | oeisdata/seq/A357/A357069.seq | b5682e5f72a1cdb9460fb0cc298d254c |
A357070 | Number of partitions of n into at most 2 distinct positive triangular numbers. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"0",
"0",
"2",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"2",
"0",
"0",
"1",
"0",
"2",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"2",
"0",
"1",
"1",
"0",
"2",
"0",
"0",
"0",
"2",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"2",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"2",
"0",
"1",
"1",
"0",
"3",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"2",
"1",
"1",
"2",
"0",
"0",
"1",
"0",
"1",
"1",
"1"
]
| [
"nonn"
]
| 7 | 0 | 17 | [
"A000217",
"A024940",
"A052343",
"A307597",
"A347730",
"A357070",
"A357071",
"A357072"
]
| null | Ilya Gutkovskiy, Oct 25 2022 | 2022-11-19T21:15:20 | oeisdata/seq/A357/A357070.seq | e40a67863173c193d3d277fe511a6967 |
A357071 | Number of partitions of n into at most 3 distinct positive triangular numbers. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"1",
"0",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"0",
"2",
"2",
"0",
"2",
"2",
"1",
"1",
"3",
"1",
"1",
"3",
"2",
"0",
"2",
"1",
"2",
"4",
"1",
"3",
"1",
"1",
"2",
"2",
"2",
"2",
"4",
"1",
"1",
"4",
"1",
"2",
"4",
"1",
"2",
"3",
"2",
"2",
"3",
"2",
"2",
"4",
"1",
"2",
"3",
"2",
"4",
"4",
"1",
"2",
"4",
"2",
"3",
"3",
"2",
"1",
"5",
"2",
"1",
"5",
"1",
"4",
"5",
"2",
"4",
"2",
"2",
"4",
"3",
"2",
"1",
"6",
"2",
"3",
"6",
"2",
"2",
"4",
"2",
"2",
"4",
"3"
]
| [
"nonn"
]
| 7 | 0 | 11 | [
"A000217",
"A002636",
"A024940",
"A307598",
"A347731",
"A357070",
"A357071",
"A357072"
]
| null | Ilya Gutkovskiy, Oct 25 2022 | 2022-11-19T21:15:28 | oeisdata/seq/A357/A357071.seq | 07b0dc0b0546bd023cd66c2a22d9b0b5 |
A357072 | Number of partitions of n into at most 4 distinct positive triangular numbers. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"1",
"0",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"0",
"2",
"3",
"1",
"1",
"3",
"2",
"1",
"4",
"3",
"0",
"3",
"2",
"2",
"4",
"3",
"3",
"3",
"1",
"3",
"3",
"2",
"4",
"5",
"4",
"1",
"5",
"3",
"2",
"6",
"3",
"3",
"6",
"4",
"2",
"5",
"4",
"4",
"5",
"4",
"2",
"7",
"5",
"5",
"7",
"3",
"4",
"7",
"4",
"4",
"8",
"5",
"4",
"7",
"6",
"2",
"7",
"6",
"5",
"10",
"5",
"6",
"7",
"5",
"7",
"7",
"6",
"4",
"10",
"8",
"3",
"12",
"6",
"4",
"11",
"6",
"5",
"9",
"7"
]
| [
"nonn"
]
| 7 | 0 | 11 | [
"A000217",
"A024940",
"A341021",
"A347586",
"A347627",
"A347732",
"A357070",
"A357071",
"A357072"
]
| null | Ilya Gutkovskiy, Oct 25 2022 | 2022-11-19T21:15:36 | oeisdata/seq/A357/A357072.seq | 8f0bc82db209ef8c46ee9c7626a94070 |
A357073 | For n >= 1, a(n) = A003714(n) mod n. | [
"0",
"0",
"1",
"1",
"3",
"3",
"3",
"0",
"8",
"8",
"9",
"9",
"6",
"5",
"4",
"4",
"3",
"4",
"3",
"2",
"1",
"21",
"20",
"20",
"19",
"20",
"19",
"18",
"22",
"21",
"20",
"20",
"19",
"26",
"24",
"22",
"21",
"19",
"19",
"17",
"15",
"18",
"16",
"14",
"13",
"11",
"19",
"17",
"15",
"14",
"12",
"12",
"10",
"8",
"36",
"33",
"30",
"28",
"25",
"24",
"21",
"18",
"20",
"17",
"14",
"12",
"9",
"16",
"13",
"10",
"8",
"5"
]
| [
"nonn"
]
| 13 | 1 | 5 | [
"A003714",
"A276488",
"A357073"
]
| null | Ctibor O. Zizka, Sep 10 2022 | 2022-09-11T16:20:09 | oeisdata/seq/A357/A357073.seq | a5e874b0eb6494d3b4f891374b098829 |
A357074 | Numbers sandwiched between a pair of numbers each with exactly two prime factors (counted without multiplicity). | [
"11",
"13",
"19",
"21",
"23",
"25",
"27",
"34",
"35",
"37",
"39",
"45",
"47",
"49",
"51",
"53",
"55",
"56",
"57",
"64",
"73",
"75",
"76",
"81",
"86",
"87",
"92",
"93",
"94",
"95",
"97",
"99",
"105",
"107",
"116",
"117",
"118",
"123",
"134",
"135",
"142",
"143",
"144",
"145",
"146",
"147",
"154",
"159",
"160",
"161",
"163",
"165",
"176",
"177",
"184",
"186",
"188",
"193",
"195"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A007774",
"A357074"
]
| null | Tanya Khovanova, Sep 10 2022 | 2022-09-11T19:13:28 | oeisdata/seq/A357/A357074.seq | 3e0c1415e3f4b85b4f90de5185f432ec |
A357075 | Numbers sandwiched between numbers with exactly three distinct prime factors. | [
"131",
"139",
"155",
"169",
"181",
"221",
"229",
"239",
"259",
"265",
"281",
"307",
"309",
"311",
"341",
"349",
"365",
"371",
"373",
"379",
"407",
"409",
"439",
"441",
"443",
"469",
"475",
"491",
"493",
"505",
"517",
"519",
"521",
"529",
"531",
"533",
"551",
"559",
"573",
"581",
"589",
"599",
"601",
"611",
"617",
"619",
"637",
"643",
"645",
"664",
"671",
"679",
"681",
"683"
]
| [
"nonn",
"easy",
"changed"
]
| 18 | 1 | 1 | [
"A033992",
"A080569",
"A357074",
"A357075"
]
| null | Tanya Khovanova, Sep 10 2022 | 2025-07-06T15:15:09 | oeisdata/seq/A357/A357075.seq | 99d72a852da46f8945dfd89231098c53 |
A357076 | Numbers k sandwiched between twin primes, such that k times the reverse of k is also sandwiched between twin primes. | [
"198",
"642",
"1050",
"2730",
"3000",
"4050",
"4230",
"4272",
"4548",
"4638",
"4968",
"5010",
"6270",
"7950",
"8970",
"9630",
"9858",
"10092",
"11700",
"12240",
"17490",
"18918",
"22740",
"25470",
"33750",
"37200",
"39240",
"45180",
"48648",
"48732",
"48822",
"49548",
"52182",
"53172",
"55620",
"56532",
"57330",
"58602",
"60918",
"65100",
"65730",
"70140"
]
| [
"nonn",
"base"
]
| 10 | 1 | 1 | [
"A014574",
"A357076"
]
| null | Tanya Khovanova, Sep 10 2022 | 2022-09-26T20:34:37 | oeisdata/seq/A357/A357076.seq | 548de6b3eba7e22b2e56fb9b5b425e38 |
A357077 | The lesser of two consecutive numbers with at least 3 prime factors (counted with multiplicity). | [
"27",
"44",
"63",
"75",
"80",
"98",
"99",
"104",
"116",
"124",
"125",
"135",
"147",
"152",
"153",
"164",
"170",
"171",
"174",
"175",
"188",
"189",
"195",
"207",
"224",
"230",
"231",
"242",
"243",
"244",
"245",
"255",
"260",
"272",
"275",
"279",
"284",
"285",
"296",
"315",
"324",
"332",
"342",
"343",
"344",
"350",
"351",
"356",
"363",
"368",
"369",
"374",
"375",
"384",
"387",
"399"
]
| [
"nonn"
]
| 12 | 1 | 1 | [
"A033942",
"A344843",
"A357077"
]
| null | Tanya Khovanova, Sep 10 2022 | 2022-09-16T13:39:25 | oeisdata/seq/A357/A357077.seq | f215838b1ff2a33fe5ebc65211c1245d |
A357078 | Triangle read by rows. The partition transform of A355488, which are the alternating row sums of the number of permutations of [n] with k components (A059438). | [
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"0",
"8",
"4",
"0",
"1",
"0",
"48",
"16",
"6",
"0",
"1",
"0",
"328",
"100",
"24",
"8",
"0",
"1",
"0",
"2560",
"688",
"156",
"32",
"10",
"0",
"1",
"0",
"22368",
"5376",
"1080",
"216",
"40",
"12",
"0",
"1",
"0",
"216224",
"46816",
"8456",
"1504",
"280",
"48",
"14",
"0",
"1",
"0",
"2291456",
"450240",
"73440",
"11808",
"1960",
"348",
"56",
"16",
"0",
"1"
]
| [
"nonn",
"tabl"
]
| 17 | 0 | 8 | [
"A003319",
"A059438",
"A269941",
"A355488",
"A356265",
"A357078",
"A357079"
]
| null | Peter Luschny, Sep 10 2022 | 2022-09-15T14:44:00 | oeisdata/seq/A357/A357078.seq | 6326520d5bd4ccacca0e8c2b428400cc |
A357079 | Triangle read by rows. T(n, k) = A356265(n, k) + A357078(n, k) for 0 <= k <= n. | [
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"3",
"2",
"1",
"0",
"9",
"12",
"2",
"1",
"0",
"49",
"37",
"31",
"2",
"1",
"0",
"329",
"149",
"176",
"63",
"2",
"1",
"0",
"2561",
"794",
"853",
"702",
"127",
"2",
"1",
"0",
"22369",
"5599",
"3836",
"5709",
"2549",
"255",
"2",
"1",
"0",
"216225",
"47275",
"18422",
"37609",
"33949",
"8886",
"511",
"2",
"1",
"2291457",
"451176",
"107535",
"218506",
"344670",
"184653",
"29777",
"1023",
"2",
"1"
]
| [
"nonn",
"tabl"
]
| 10 | 0 | 8 | [
"A003319",
"A059438",
"A356265",
"A357078",
"A357079"
]
| null | Peter Luschny, Sep 11 2022 | 2022-09-15T14:44:27 | oeisdata/seq/A357/A357079.seq | b037e04195a600527cfe5ce329a924d7 |
A357080 | Numbers k such that the sum of the digits of k multiplied by the sum of the digits of k^2 equals k. | [
"0",
"1",
"80",
"162",
"243",
"476",
"486"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 14 | 1 | 3 | [
"A004159",
"A007953",
"A130181",
"A357080"
]
| null | Tanya Khovanova, Sep 10 2022 | 2022-09-26T20:35:20 | oeisdata/seq/A357/A357080.seq | eb3647f756205bd189255d23db68612e |
A357081 | Leader at step n of the THROWBACK procedure (see definition in comments). | [
"3",
"4",
"5",
"6",
"3",
"7",
"4",
"8",
"3",
"5",
"9",
"4",
"3",
"6",
"10",
"5",
"3",
"4",
"7",
"11",
"3",
"6",
"4",
"5",
"3",
"8",
"12",
"4",
"3",
"7",
"5",
"6",
"3",
"4",
"9",
"13",
"3",
"5",
"4",
"8",
"3",
"6",
"7",
"4",
"3",
"5",
"10",
"14",
"3",
"4",
"6",
"5",
"3",
"9",
"4",
"7",
"3",
"8",
"5",
"4",
"3",
"6",
"11",
"15",
"3",
"4",
"5",
"7",
"3",
"6",
"4",
"10",
"3",
"5",
"8",
"4",
"3",
"9",
"6",
"5",
"3",
"4",
"7",
"12",
"3",
"16",
"4",
"5",
"3",
"6",
"8",
"4",
"3",
"7",
"5",
"11",
"3",
"4",
"6",
"9"
]
| [
"nonn",
"easy"
]
| 26 | 0 | 1 | [
"A087165",
"A155167",
"A354223",
"A355080",
"A357081"
]
| null | Anthony M. Kozar Jr., Sep 08 2022 | 2024-03-24T11:03:05 | oeisdata/seq/A357/A357081.seq | 5b979ce07dd65da042fd8c6b96ef37fe |
A357082 | a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n-1) + a(n) does not appear in the binary string concatenation of a(0)..a(n-1). | [
"0",
"1",
"2",
"3",
"4",
"5",
"10",
"6",
"9",
"7",
"17",
"12",
"20",
"13",
"16",
"18",
"11",
"21",
"15",
"19",
"23",
"38",
"26",
"8",
"24",
"37",
"27",
"34",
"30",
"31",
"33",
"32",
"40",
"36",
"28",
"44",
"41",
"35",
"29",
"43",
"39",
"25",
"47",
"53",
"51",
"49",
"42",
"22",
"50",
"14",
"58",
"46",
"54",
"62",
"65",
"63",
"66",
"67",
"61",
"68",
"60",
"69",
"59",
"70",
"74",
"55",
"73",
"56",
"72",
"57",
"71",
"75",
"78",
"76",
"52",
"77",
"92"
]
| [
"nonn",
"base",
"look"
]
| 35 | 0 | 3 | [
"A007088",
"A030302",
"A118248",
"A341766",
"A357082"
]
| null | Scott R. Shannon, Sep 11 2022 | 2023-02-15T07:49:10 | oeisdata/seq/A357/A357082.seq | a2f7032ca88388a4a8375c7fb2fecc1b |
A357083 | a(n) is the number of free polycubes of size n with holes. | [
"11",
"215",
"3173",
"38564"
]
| [
"nonn",
"more",
"hard"
]
| 11 | 11 | 1 | [
"A038119",
"A355966",
"A357083"
]
| null | John Mason, Sep 11 2022 | 2022-09-13T09:33:57 | oeisdata/seq/A357/A357083.seq | 9379e5744a5f599e66a3abb49bf1c857 |
A357084 | E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^2 * A(x). | [
"1",
"0",
"2",
"6",
"98",
"990",
"19082",
"347046",
"8512226",
"220737390",
"6776521082",
"225532370646",
"8413133799314",
"339965749171230",
"14995100013227882",
"711308930246853126",
"36278600375671552322",
"1974411768891211652430",
"114394542828023045764442"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A349557",
"A357024",
"A357084",
"A357085"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:06:30 | oeisdata/seq/A357/A357084.seq | ee963a16e22bd15f842354de46fe4d3a |
A357085 | E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^3 * A(x). | [
"1",
"0",
"0",
"6",
"36",
"150",
"3780",
"77406",
"1059156",
"21669990",
"640319940",
"16622025486",
"450085011156",
"15416323450710",
"561938117029380",
"20587443165165246",
"835816881563118036",
"37282225483118856390",
"1722621978491064495300",
"83817942806509377794286"
]
| [
"nonn"
]
| 9 | 0 | 4 | [
"A349557",
"A357025",
"A357084",
"A357085"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:06:42 | oeisdata/seq/A357/A357085.seq | e4a7da333b65f6e37f700f9b1436529c |
A357086 | E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2. | [
"1",
"0",
"2",
"6",
"50",
"510",
"5882",
"88326",
"1502258",
"29368590",
"650366762",
"15974149686",
"433095937826",
"12829712583870",
"412295632858202",
"14292175302568806",
"531485147656990994",
"21107739762958541550",
"891673745283286886282",
"39923664347178352362006"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A349588",
"A357084",
"A357086",
"A357087",
"A357088"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:06:51 | oeisdata/seq/A357/A357086.seq | 6263472731ac39b56711af8fea1729e8 |
A357087 | E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3. | [
"1",
"0",
"0",
"6",
"36",
"150",
"2340",
"47166",
"676116",
"10602150",
"248197860",
"6304530606",
"154511054676",
"4227889233750",
"134462460901860",
"4519745455581726",
"157756124072317716",
"5960350758700381830",
"243292987180534250340",
"10433760831781705395726",
"469420864688765414084436"
]
| [
"nonn"
]
| 9 | 0 | 4 | [
"A349588",
"A357085",
"A357086",
"A357087",
"A357089"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:06:59 | oeisdata/seq/A357/A357087.seq | c4a9d14759eb320ad067c0e27b8eb491 |
A357088 | E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2 / 2. | [
"1",
"0",
"1",
"3",
"16",
"135",
"1246",
"14238",
"192613",
"2948025",
"51071236",
"985911003",
"20952667660",
"486857940660",
"12275673296251",
"333786662478363",
"9737819506544272",
"303399477464036175",
"10054949172135522106",
"353197317869395005258",
"13108298181041284002769"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A349588",
"A357088",
"A357089"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:07:10 | oeisdata/seq/A357/A357088.seq | fa0f1786c6ce49383158604ae43f51de |
A357089 | E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^3 / 6. | [
"1",
"0",
"0",
"1",
"6",
"25",
"140",
"1561",
"19586",
"228425",
"2870160",
"44172601",
"780614846",
"14499946825",
"284310704860",
"6089231941521",
"142225796401786",
"3537029819020905",
"92766573133851240",
"2577870903366020521",
"75999605064376599606",
"2362944241092314079145"
]
| [
"nonn"
]
| 8 | 0 | 5 | [
"A349588",
"A357088",
"A357089"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:07:18 | oeisdata/seq/A357/A357089.seq | a170788bb05c89517a5d496bca4a0d22 |
A357090 | E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) * A(x)). | [
"1",
"0",
"2",
"6",
"106",
"1060",
"21728",
"396648",
"10174764",
"267855264",
"8517836832",
"289596897480",
"11137252365600",
"461124747706896",
"20922578332613904",
"1018268757357253920",
"53372000211252229392",
"2981808910524462942720",
"177468245487057424475136"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A349556",
"A357028",
"A357090",
"A357091"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:07:33 | oeisdata/seq/A357/A357090.seq | ffe3dba99f627d8f3bc71af9522ca336 |
A357091 | E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 * A(x)). | [
"1",
"0",
"0",
"6",
"36",
"210",
"4590",
"85344",
"1353912",
"30525384",
"836587440",
"22585438656",
"676820305656",
"23377203675072",
"857981143380816",
"33416782099297344",
"1417453025671696320",
"64371985604089220160",
"3086958605328618687360",
"157142856384519974847360"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A349556",
"A357029",
"A357090",
"A357091"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:07:46 | oeisdata/seq/A357/A357091.seq | aef8e0cc8afc6d61dc45c14d8e38f6d6 |
A357092 | E.g.f. satisfies A(x)^A(x) = (1 - x * A(x))^log(1 - x * A(x)). | [
"1",
"0",
"2",
"6",
"58",
"580",
"7568",
"119448",
"2195772",
"46413792",
"1106667072",
"29403619080",
"861570383232",
"27600893313552",
"959793100481616",
"36006430081497120",
"1449539553826089360",
"62334045415459189248",
"2851721291051846833152",
"138299011223141244621024"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A141209",
"A357028",
"A357092",
"A357093"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:07:54 | oeisdata/seq/A357/A357092.seq | c3f61d10418a25131869e542bf633fe3 |
A357093 | E.g.f. satisfies A(x)^A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2). | [
"1",
"0",
"0",
"6",
"36",
"210",
"3150",
"55104",
"890232",
"16735944",
"386223120",
"9790441056",
"265867900056",
"7943197796352",
"260063260578576",
"9156071916788544",
"344740627648393920",
"13880862578534022720",
"595178180505073088640",
"27035591386823290224000"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A141209",
"A357029",
"A357092",
"A357093"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:08:04 | oeisdata/seq/A357/A357093.seq | c8942e7be7f762453373ae849a94e68b |
A357094 | E.g.f. satisfies A(x)^A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2). | [
"1",
"0",
"1",
"3",
"20",
"170",
"1789",
"22869",
"342222",
"5874840",
"113865786",
"2459446440",
"58588151148",
"1526055579828",
"43149414029604",
"1316279791377810",
"43090904609439900",
"1506889769163738432",
"56062825134853664328",
"2211097753021838716116",
"92149286987928381312972"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A141209",
"A357036",
"A357094",
"A357095"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:08:15 | oeisdata/seq/A357/A357094.seq | 8103d8a50bf87407acd50d218062bd2a |
A357095 | E.g.f. satisfies A(x)^A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6). | [
"1",
"0",
"0",
"1",
"6",
"35",
"275",
"2884",
"35672",
"494724",
"7673670",
"132896676",
"2544253426",
"53252983992",
"1208888367596",
"29592833903424",
"777311220788320",
"21808542026480120",
"650880782773059840",
"20590135175285212800",
"688212821908314587880",
"24235789570607605377680"
]
| [
"nonn"
]
| 10 | 0 | 5 | [
"A141209",
"A357037",
"A357094",
"A357095"
]
| null | Seiichi Manyama, Sep 11 2022 | 2022-09-11T10:08:43 | oeisdata/seq/A357/A357095.seq | ea57cda4a2c8a6047834b2cfa81590ba |
A357096 | Least number whose set of decimal digits coincides with the set of decimal digits of prime(n). | [
"2",
"3",
"5",
"7",
"1",
"13",
"17",
"19",
"23",
"29",
"13",
"37",
"14",
"34",
"47",
"35",
"59",
"16",
"67",
"17",
"37",
"79",
"38",
"89",
"79",
"10",
"103",
"107",
"109",
"13",
"127",
"13",
"137",
"139",
"149",
"15",
"157",
"136",
"167",
"137",
"179",
"18",
"19",
"139",
"179",
"19",
"12",
"23",
"27",
"29",
"23",
"239",
"124",
"125",
"257",
"236",
"269",
"127",
"27",
"128",
"238",
"239"
]
| [
"nonn",
"base"
]
| 93 | 1 | 1 | [
"A179239",
"A179308",
"A357096"
]
| null | Jean-Marc Rebert, Sep 12 2022 | 2022-09-13T09:33:26 | oeisdata/seq/A357/A357096.seq | 355e83ccf34caefb84d370f4b2d1c826 |
A357097 | A multiplication table for the rows of the extended Wythoff array. See comments for definition. | [
"0",
"1",
"1",
"2",
"15",
"2",
"3",
"8",
"8",
"3",
"4",
"12",
"4",
"12",
"4",
"5",
"44",
"18",
"18",
"44",
"5",
"6",
"19",
"24",
"27",
"24",
"19",
"6",
"7",
"62",
"28",
"96",
"96",
"28",
"62",
"7",
"8",
"26",
"34",
"42",
"128",
"42",
"34",
"26",
"8",
"9",
"30",
"14",
"51",
"56",
"56",
"51",
"14",
"30",
"9",
"10",
"91",
"44",
"57",
"180",
"65",
"180",
"57",
"44",
"91",
"10",
"11",
"37",
"50",
"66",
"76",
"79",
"79",
"76",
"66",
"50",
"37",
"11"
]
| [
"nonn",
"tabl"
]
| 28 | 0 | 4 | [
"A000201",
"A003622",
"A019586",
"A022344",
"A035336",
"A035513",
"A101330",
"A120873",
"A287870",
"A348853",
"A357097"
]
| null | Peter Munn, Sep 11 2022 | 2025-01-05T19:51:42 | oeisdata/seq/A357/A357097.seq | 3e074a375b84826055b81c252590c4d7 |
A357098 | Emirps p such that the average of p and its digit reversal is an emirp. | [
"1001941",
"1008701",
"1012481",
"1012861",
"1034861",
"1035641",
"1037081",
"1040981",
"1052041",
"1060781",
"1078001",
"1092061",
"1101571",
"1101931",
"1102571",
"1124951",
"1141391",
"1142131",
"1142171",
"1146791",
"1149131",
"1152071",
"1157491",
"1161331",
"1165991",
"1171231",
"1185791",
"1256681",
"1267381",
"1312411",
"1319411",
"1321571",
"1321711"
]
| [
"nonn",
"base"
]
| 13 | 1 | 1 | [
"A006567",
"A357098"
]
| null | Robert Israel, Sep 11 2022 | 2022-10-02T13:29:07 | oeisdata/seq/A357/A357098.seq | 245fcaea8c3640846c6eef5b514e7656 |
A357099 | Second nontrivial square root of unity mod A033949(n), i.e., second smallest x > 1 such that x^2 == 1 mod the n-th positive integer that does not have a primitive root. | [
"5",
"7",
"11",
"9",
"11",
"13",
"7",
"15",
"19",
"17",
"23",
"29",
"19",
"25",
"11",
"29",
"23",
"26",
"17",
"35",
"27",
"34",
"15",
"37",
"19",
"55",
"33",
"51",
"43",
"35",
"47",
"41",
"19",
"49",
"39",
"43",
"53",
"31",
"29",
"69",
"59",
"23",
"71",
"64",
"47",
"61",
"56",
"31",
"89",
"51",
"67",
"27",
"34",
"55",
"89",
"73",
"41",
"77",
"91",
"59",
"64",
"69",
"19",
"83",
"63",
"71"
]
| [
"nonn"
]
| 38 | 1 | 1 | [
"A033949",
"A082568",
"A277776",
"A357099"
]
| null | Alois P. Heinz, Oct 25 2022 | 2022-10-26T16:11:38 | oeisdata/seq/A357/A357099.seq | c2ef22282d83e7082a9dbb1dce715f42 |
A357100 | Decimal expansion of the real root of x^3 + x^2 - 3. | [
"1",
"1",
"7",
"4",
"5",
"5",
"9",
"4",
"1",
"0",
"2",
"9",
"2",
"9",
"8",
"0",
"0",
"7",
"4",
"2",
"0",
"2",
"3",
"1",
"8",
"9",
"8",
"8",
"6",
"9",
"5",
"6",
"5",
"3",
"9",
"2",
"5",
"6",
"7",
"5",
"9",
"4",
"8",
"7",
"2",
"5",
"3",
"3",
"7",
"0",
"8",
"2",
"4",
"9",
"8",
"3",
"3",
"6",
"7",
"3",
"3",
"9",
"2",
"0",
"3",
"0",
"2",
"3",
"6",
"4",
"7",
"6",
"4",
"7",
"9",
"2"
]
| [
"nonn",
"cons",
"easy"
]
| 18 | 1 | 3 | [
"A356034",
"A357100"
]
| null | Wolfdieter Lang, Sep 13 2022 | 2022-11-09T04:40:24 | oeisdata/seq/A357/A357100.seq | 44293b1d8575bc7c06e6ede8d850de1a |
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