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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
2025-07-14 02:38:35
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A382115 | a(n) is the smallest positive number not already used and whose binary expansion occurs, ending at position n, in the binary Champernowne word. | [
"1",
"3",
"2",
"5",
"11",
"7",
"6",
"4",
"9",
"18",
"37",
"75",
"23",
"14",
"13",
"27",
"55",
"15",
"30",
"12",
"8",
"17",
"34",
"68",
"137",
"19",
"38",
"77",
"10",
"21",
"42",
"85",
"43",
"87",
"47",
"94",
"28",
"25",
"51",
"102",
"205",
"155",
"311",
"111",
"222",
"29",
"59",
"119",
"239",
"31",
"62",
"60",
"24",
"16",
"33",
"66",
"132",
"264",
"529",
"35",
"70",
"140",
"281",
"50"
]
| [
"nonn",
"base"
]
| 34 | 1 | 2 | [
"A030190",
"A083652",
"A382115"
]
| null | Ruud H.G. van Tol, Mar 16 2025 | 2025-03-27T20:28:32 | oeisdata/seq/A382/A382115.seq | 688e696ce5907527a9a301492f2394a5 |
A382116 | a(n) = floor(n*g+(g-1)/2), where g is the golden ratio. | [
"0",
"1",
"3",
"5",
"6",
"8",
"10",
"11",
"13",
"14",
"16",
"18",
"19",
"21",
"22",
"24",
"26",
"27",
"29",
"31",
"32",
"34",
"35",
"37",
"39",
"40",
"42",
"43",
"45",
"47",
"48",
"50",
"52",
"53",
"55",
"56",
"58",
"60",
"61",
"63",
"65",
"66",
"68",
"69",
"71",
"73",
"74",
"76",
"77",
"79",
"81",
"82",
"84",
"86",
"87",
"89",
"90",
"92",
"94",
"95",
"97",
"99",
"100",
"102",
"103",
"105"
]
| [
"nonn",
"easy"
]
| 13 | 0 | 3 | [
"A001622",
"A382113",
"A382116"
]
| null | Jeffrey Shallit, Mar 16 2025 | 2025-03-23T20:52:28 | oeisdata/seq/A382/A382116.seq | c29e57dc07a339f58997cf9a307d8bd5 |
A382117 | a(n) = sum (-1)^(((x - 1)*(y - 1))/4), where x and y are coprime positive integers, equidistant from n, such that x <= y. | [
"1",
"1",
"1",
"2",
"0",
"2",
"1",
"4",
"1",
"4",
"1",
"4",
"0",
"6",
"0",
"8",
"0",
"6",
"1",
"8",
"2",
"10",
"1",
"8",
"0",
"12",
"1",
"12",
"0",
"8",
"1",
"16",
"2",
"16",
"0",
"12",
"0",
"18",
"0",
"16",
"0",
"12",
"1",
"20",
"0",
"22",
"1",
"16",
"1",
"20",
"0",
"24",
"0",
"18",
"0",
"24",
"2",
"28",
"1",
"16",
"0",
"30",
"2",
"32",
"0",
"20",
"1",
"32",
"2",
"24",
"1",
"24",
"0",
"36",
"0",
"36",
"2",
"24"
]
| [
"nonn"
]
| 51 | 1 | 4 | [
"A309812",
"A382117"
]
| null | Mike Jones, Apr 26 2025 | 2025-05-03T18:55:36 | oeisdata/seq/A382/A382117.seq | 7b09f4a4c3d188928dddad70c3561d96 |
A382118 | Prime indices k such that prime(k) and prime(k) + 9 are anagrams. | [
"19",
"73",
"79",
"163",
"197",
"241",
"269",
"281",
"431",
"439",
"619",
"647",
"691",
"739",
"751",
"761",
"823",
"877",
"953",
"1019",
"1051",
"1109",
"1223",
"1259",
"1291",
"1307",
"1423",
"1471",
"1723",
"1741",
"1747",
"1847",
"1949",
"1979",
"2213",
"2371",
"2473",
"2503",
"2647",
"2789",
"2803",
"2819",
"2879",
"2903",
"2909",
"3019",
"3163",
"3361"
]
| [
"nonn",
"base"
]
| 14 | 1 | 1 | [
"A140353",
"A228157",
"A379208",
"A382118"
]
| null | Vincenzo Librandi, Apr 15 2025 | 2025-04-22T08:01:50 | oeisdata/seq/A382/A382118.seq | b3b23a86168fe6cb6f3cae863bcba091 |
A382119 | Numbers k = x*y such that (x*2^k - 1)*(y*2^k - 1) is semiprime. | [
"2",
"3",
"4",
"6",
"16",
"126"
]
| [
"nonn",
"more"
]
| 27 | 1 | 1 | [
"A000668",
"A001358",
"A161904",
"A382119"
]
| null | Juri-Stepan Gerasimov, Mar 25 2025 | 2025-04-07T17:46:15 | oeisdata/seq/A382/A382119.seq | 43cfbafc8c76f1fd37c772f7dd0e6ec4 |
A382120 | Numbers k in A024619 such that there exists a prime p | k for which p^(m+1) == r (mod k), where r is also in A024619, and a prime q | k for which q^(m+1) == r (mod k), where r is a prime power. | [
"10",
"18",
"20",
"21",
"22",
"26",
"28",
"30",
"34",
"36",
"38",
"40",
"42",
"46",
"48",
"50",
"52",
"54",
"55",
"57",
"58",
"60",
"68",
"72",
"74",
"78",
"82",
"84",
"86",
"93",
"94",
"96",
"98",
"100",
"106",
"108",
"110",
"111",
"114",
"116",
"117",
"118",
"122",
"124",
"126",
"129",
"132",
"134",
"136",
"142",
"146",
"147",
"148",
"150",
"156",
"158",
"162",
"164",
"165"
]
| [
"nonn"
]
| 23 | 1 | 1 | [
"A000961",
"A024619",
"A381750",
"A381864",
"A382120"
]
| null | Michael De Vlieger, Apr 06 2025 | 2025-05-30T23:15:22 | oeisdata/seq/A382/A382120.seq | c0c317353293a1a0fdce48127988d60c |
A382121 | Minimal polynomials of nimbers *(2^(2^n)-1), evaluated at 2. | [
"7",
"25",
"425",
"101021",
"7158330089",
"27971386341277386797",
"557019405516812760530014815489825522433",
"200070165806576462487855236097886014378133571492030310620129377307348366314169"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A051775",
"A382121"
]
| null | Simon Tatham, Mar 16 2025 | 2025-03-24T11:54:05 | oeisdata/seq/A382/A382121.seq | d49bdc33216fc8e0f11122a9b4281b7f |
A382122 | G.f. satisfies Sum_{n>=0} x^n * abs(1/A(x)^n) = C(x), where C(x) = 1 + x*C(x)^2 and abs(F(x)) equals the series expansion formed by the unsigned coefficients in F(x). | [
"1",
"1",
"3",
"12",
"49",
"202",
"838",
"3486",
"14575",
"60820",
"254406",
"1061438",
"4444802",
"18602018",
"78066384",
"326985608",
"1365996909",
"5697914836",
"23752394338",
"99027785702",
"413203462516",
"1726164299990",
"7219911692522",
"30228722494504",
"126658682953328",
"530772842793396",
"2224199143900798",
"9319843329508200",
"39051457052597480"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A000108",
"A382122",
"A382123"
]
| null | Paul D. Hanna, Mar 16 2025 | 2025-03-28T04:38:23 | oeisdata/seq/A382/A382122.seq | d7f16ba4758b9cf431a7ed18f7470656 |
A382123 | a(n) = sigma(n)*sigma(2*n)/3 for n >= 1. | [
"1",
"7",
"16",
"35",
"36",
"112",
"64",
"155",
"169",
"252",
"144",
"560",
"196",
"448",
"576",
"651",
"324",
"1183",
"400",
"1260",
"1024",
"1008",
"576",
"2480",
"961",
"1372",
"1600",
"2240",
"900",
"4032",
"1024",
"2667",
"2304",
"2268",
"2304",
"5915",
"1444",
"2800",
"3136",
"5580",
"1764",
"7168",
"1936",
"5040",
"6084",
"4032",
"2304",
"10416",
"3249",
"6727",
"5184",
"6860"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A000203",
"A062731",
"A087943",
"A329963",
"A347108",
"A382123",
"A382124",
"A382125"
]
| null | Paul D. Hanna, Apr 06 2025 | 2025-04-06T16:51:29 | oeisdata/seq/A382/A382123.seq | 58ba6426ca2eb2ec4a1f76852c817835 |
A382124 | G.f. A(x) = exp( Sum_{n>=1} sigma(n)*sigma(2*n)/3 * x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n. | [
"1",
"1",
"4",
"9",
"22",
"44",
"105",
"200",
"425",
"825",
"1634",
"3072",
"5917",
"10846",
"20153",
"36436",
"65882",
"116831",
"207293",
"361502",
"629539",
"1083068",
"1856251",
"3150554",
"5328137",
"8933266",
"14920357",
"24745481",
"40869317",
"67089425",
"109697089",
"178379353",
"288953043",
"465805681",
"748079686",
"1196148976",
"1905801579",
"3024212984"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A000041",
"A000203",
"A087943",
"A156302",
"A329963",
"A347108",
"A382123",
"A382124",
"A382125"
]
| null | Paul D. Hanna, Apr 06 2025 | 2025-04-06T14:55:22 | oeisdata/seq/A382/A382124.seq | f6a4415ba1f547d13106584b564d0314 |
A382125 | G.f. A(x) = exp( Sum_{n>=1} sigma(n)*sigma(2*n) * x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n. | [
"1",
"3",
"15",
"52",
"180",
"555",
"1696",
"4809",
"13410",
"35844",
"93771",
"238305",
"594403",
"1449441",
"3476607",
"8190824",
"19015548",
"43492230",
"98197506",
"218885763",
"482337864",
"1051051262",
"2266904481",
"4840955055",
"10242621395",
"21479302368",
"44666897613",
"92139573135",
"188617118541",
"383280793962",
"773395096907"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000041",
"A000203",
"A087943",
"A156302",
"A329963",
"A347108",
"A382123",
"A382124",
"A382125"
]
| null | Paul D. Hanna, Apr 06 2025 | 2025-04-06T14:55:34 | oeisdata/seq/A382/A382125.seq | b0ed6ed8c3d492650f403b280ea676bb |
A382126 | G.f. satisfies A(x) = A(x^2)*A(x^3) / (1-x). | [
"1",
"1",
"2",
"3",
"5",
"6",
"11",
"13",
"20",
"26",
"36",
"44",
"66",
"78",
"106",
"132",
"174",
"208",
"282",
"332",
"430",
"520",
"656",
"774",
"1000",
"1166",
"1456",
"1731",
"2131",
"2486",
"3097",
"3585",
"4374",
"5125",
"6177",
"7144",
"8700",
"9994",
"11966",
"13874",
"16482",
"18908",
"22598",
"25800",
"30472",
"35014",
"41062",
"46802",
"55178",
"62624",
"73094",
"83384",
"96834"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A003586",
"A007814",
"A007949",
"A382126"
]
| null | Paul D. Hanna, Apr 14 2025 | 2025-04-15T08:56:26 | oeisdata/seq/A382/A382126.seq | eba158c7fdcf5dce883a81d1566be076 |
A382127 | Smallest prime p with n distinct digits, such that for each digit of p, 2*p*(digit) + 1 is prime. | [
"3",
"131",
"173",
"4391",
"4746616799"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 40 | 1 | 1 | [
"A000040",
"A005384",
"A382127",
"A382179",
"A382198",
"A382199"
]
| null | Jakub Buczak, Mar 16 2025 | 2025-03-19T23:20:59 | oeisdata/seq/A382/A382127.seq | c11762aa3d5e4754dd33ed25b5b19d02 |
A382128 | Fractalization of the Recamán sequence. | [
"0",
"0",
"1",
"0",
"3",
"1",
"6",
"0",
"2",
"3",
"7",
"1",
"13",
"6",
"20",
"0",
"12",
"2",
"21",
"3",
"11",
"7",
"22",
"1",
"10",
"13",
"23",
"6",
"9",
"20",
"24",
"0",
"8",
"12",
"25",
"2",
"43",
"21",
"62",
"3",
"42",
"11",
"63",
"7",
"41",
"22",
"18",
"1",
"42",
"10",
"17",
"13",
"43",
"23",
"16",
"6",
"44",
"9",
"15",
"20",
"45",
"24",
"14",
"0",
"46",
"8",
"79",
"12",
"113",
"25",
"78",
"2",
"114",
"43",
"77",
"21",
"39",
"62",
"78"
]
| [
"nonn",
"easy"
]
| 25 | 1 | 5 | [
"A003602",
"A005132",
"A110766",
"A110779",
"A110812",
"A382128",
"A382129",
"A382130"
]
| null | David Cleaver, Mar 16 2025 | 2025-03-22T22:50:37 | oeisdata/seq/A382/A382128.seq | cdd63f2b6c0cd99599156813680c702e |
A382129 | Fractalization of the prime numbers. | [
"2",
"2",
"3",
"2",
"5",
"3",
"7",
"2",
"11",
"5",
"13",
"3",
"17",
"7",
"19",
"2",
"23",
"11",
"29",
"5",
"31",
"13",
"37",
"3",
"41",
"17",
"43",
"7",
"47",
"19",
"53",
"2",
"59",
"23",
"61",
"11",
"67",
"29",
"71",
"5",
"73",
"31",
"79",
"13",
"83",
"37",
"89",
"3",
"97",
"41",
"101",
"17",
"103",
"43",
"107",
"7",
"109",
"47",
"113",
"19",
"127",
"53",
"131",
"2",
"137",
"59",
"139",
"23",
"149",
"61",
"151",
"11",
"157"
]
| [
"nonn",
"easy"
]
| 29 | 1 | 1 | [
"A000040",
"A003602",
"A110766",
"A110779",
"A110812",
"A382128",
"A382129",
"A382130"
]
| null | David Cleaver, Mar 16 2025 | 2025-03-22T22:50:51 | oeisdata/seq/A382/A382129.seq | f910ff7a886205a6aec5ca5f39d468c2 |
A382130 | Fractalization of the golden ratio. | [
"1",
"1",
"6",
"1",
"1",
"6",
"8",
"1",
"0",
"1",
"3",
"6",
"3",
"8",
"9",
"1",
"8",
"0",
"8",
"1",
"7",
"3",
"4",
"6",
"9",
"3",
"8",
"8",
"9",
"9",
"4",
"1",
"8",
"8",
"4",
"0",
"8",
"8",
"2",
"1",
"0",
"7",
"4",
"3",
"5",
"4",
"8",
"6",
"6",
"9",
"8",
"3",
"3",
"8",
"4",
"8",
"3",
"9",
"6",
"9",
"5",
"4",
"6",
"1",
"3",
"8",
"8",
"8",
"1",
"4",
"1",
"0",
"7",
"8",
"7",
"8",
"2",
"2",
"0",
"1",
"3",
"0",
"0",
"7",
"9",
"4",
"1",
"3",
"7",
"5",
"9",
"4",
"8",
"8",
"0"
]
| [
"nonn",
"easy",
"base"
]
| 28 | 1 | 3 | [
"A001622",
"A003602",
"A110766",
"A110779",
"A110812",
"A382128",
"A382129",
"A382130"
]
| null | David Cleaver, Mar 16 2025 | 2025-03-22T22:51:21 | oeisdata/seq/A382/A382130.seq | 9c2fc6000e8d84db8e1690fe2b91f41a |
A382131 | Complement of A381767. | [
"2",
"3",
"5",
"15",
"46",
"136",
"385",
"1072",
"2949",
"8063",
"21977",
"59814",
"162683",
"442329",
"1202507",
"3268905",
"8885983",
"24154809",
"65659808",
"178482121",
"485164996",
"1318815514",
"3584912605",
"9744803182",
"26489121842",
"72004899025",
"195729609091",
"532048240238",
"1446257063900",
"3931334296724",
"10686474581075"
]
| [
"nonn"
]
| 28 | 1 | 1 | [
"A381767",
"A382131"
]
| null | Mike Sheppard, Mar 16 2025 | 2025-06-14T00:16:25 | oeisdata/seq/A382/A382131.seq | 519d4de7de7bc98f25dd7d21dc24006b |
A382132 | Centered pentagonal numbers which are semiprimes. | [
"6",
"51",
"106",
"141",
"226",
"391",
"526",
"681",
"766",
"951",
"1501",
"1891",
"2031",
"2326",
"2481",
"2641",
"3151",
"3901",
"4101",
"4306",
"6631",
"6891",
"7981",
"8266",
"8851",
"10081",
"10401",
"11391",
"13141",
"14631",
"15406",
"16201",
"20931",
"22801",
"23281",
"24751",
"27301",
"27826",
"28891",
"29431",
"30526",
"32206",
"33351",
"35701",
"36301",
"38131",
"38751"
]
| [
"nonn"
]
| 19 | 1 | 1 | [
"A001358",
"A005891",
"A364610",
"A382132"
]
| null | Massimo Kofler, Mar 17 2025 | 2025-03-25T18:01:53 | oeisdata/seq/A382/A382132.seq | 27d1390ab409898c4dce96010e5e4403 |
A382133 | Products of 4 distinct primes that are the average of two consecutive primes. | [
"462",
"570",
"714",
"858",
"870",
"1190",
"1230",
"1254",
"1290",
"1302",
"1482",
"1590",
"1722",
"1785",
"1806",
"1995",
"2046",
"2130",
"2170",
"2210",
"2470",
"2490",
"2870",
"3030",
"3045",
"3255",
"3390",
"3410",
"3705",
"3774",
"3795",
"3885",
"3930",
"4002",
"4218",
"4242",
"4278",
"4422",
"4510",
"4515",
"4641",
"4785",
"4935",
"5010",
"5110"
]
| [
"nonn"
]
| 21 | 1 | 1 | [
"A024675",
"A046386",
"A078443",
"A130178",
"A382133"
]
| null | Massimo Kofler, Mar 17 2025 | 2025-03-31T21:25:27 | oeisdata/seq/A382/A382133.seq | 3831b013c27094104ff5be3232f736e9 |
A382134 | Number of completely asymmetric matchings (not containing centered or coupled arcs) of [2n]. | [
"1",
"0",
"0",
"8",
"48",
"384",
"4480",
"59520",
"897792",
"15368192",
"293769216",
"6198589440",
"143130972160",
"3590253477888",
"97214510235648",
"2826205634330624",
"87801981951344640",
"2902989352269250560",
"101776549707306237952",
"3771425415371470405632",
"147285455218020210180096"
]
| [
"nonn"
]
| 18 | 0 | 4 | [
"A000079",
"A001205",
"A047974",
"A053871",
"A382134"
]
| null | R. J. Mathar, Mar 17 2025 | 2025-03-17T16:01:46 | oeisdata/seq/A382/A382134.seq | 20130d6e1858ae3d922c943062dbabc8 |
A382135 | Square array read by antidiagonals: T(n,k) = S(n+k) - S(n) - S(k) - min(n,k), where S(k) = A000788(k-1). | [
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"2",
"2",
"2",
"0",
"2",
"2",
"2",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"2",
"2",
"2",
"0",
"1",
"0",
"1",
"0",
"2",
"2",
"2",
"1",
"2",
"2",
"1",
"0",
"0",
"0",
"0",
"1",
"2",
"2",
"1",
"2",
"2",
"3",
"2",
"2",
"0",
"0",
"0",
"2"
]
| [
"nonn",
"easy",
"base",
"tabl"
]
| 25 | 1 | 22 | [
"A000120",
"A000788",
"A382135"
]
| null | Yifan Xie, Mar 17 2025 | 2025-04-02T15:04:25 | oeisdata/seq/A382/A382135.seq | 86b45624565919dc216af1a2099bc908 |
A382136 | Number of triples of non-crossing lattice paths from (0,0) to (n,n) using (1,0) and (0,1) as steps. | [
"1",
"4",
"50",
"980",
"24696",
"731808",
"24293412",
"877262100",
"33803832920",
"1371597504992",
"58043512597616",
"2543610972177184",
"114801908084920000",
"5313688317073440000",
"251370667949555421000",
"12120154230252872020500",
"594283640753967620247000",
"29576997448419995135100000"
]
| [
"nonn",
"easy",
"changed"
]
| 35 | 0 | 2 | [
"A000108",
"A000891",
"A382136"
]
| null | Yifan Xie, Mar 27 2025 | 2025-07-03T02:35:40 | oeisdata/seq/A382/A382136.seq | cecc22baeca9462428c1cc7ecb0f4344 |
A382137 | Smallest integer that cannot be be converted to a multiple of n by changing at most one of its decimal digit. | [
"545",
"51",
"44",
"31",
"21",
"21",
"22",
"21",
"21",
"11",
"15",
"11",
"11",
"11",
"11",
"11",
"12",
"11",
"11",
"11",
"14",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"13",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"12",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"12",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"12",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"12"
]
| [
"nonn",
"base"
]
| 36 | 11 | 1 | [
"A192545",
"A353023",
"A382137"
]
| null | Mickaël Launay, Mar 27 2025 | 2025-04-03T02:51:56 | oeisdata/seq/A382/A382137.seq | ec97c8319a87155f03fe2c50000ae272 |
A382138 | a(n) = A381800(n) - A381798(n). | [
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"2",
"0",
"1",
"1",
"0",
"0",
"3",
"0",
"2",
"1",
"1",
"0",
"4",
"0",
"1",
"0",
"2",
"0",
"8",
"0",
"0",
"1",
"1",
"1",
"5",
"0",
"1",
"1",
"3",
"0",
"10",
"0",
"2",
"3",
"1",
"0",
"6",
"0",
"5",
"1",
"2",
"0",
"9",
"1",
"4",
"1",
"1",
"0",
"16",
"0",
"1",
"2",
"0",
"1",
"14",
"0",
"2",
"1",
"12",
"0",
"8",
"0",
"1",
"5",
"2",
"1",
"16",
"0",
"5",
"0",
"1",
"0",
"19",
"1"
]
| [
"nonn"
]
| 24 | 1 | 12 | [
"A000961",
"A024619",
"A381798",
"A381799",
"A381800",
"A381801",
"A382138"
]
| null | Michael De Vlieger, Apr 12 2025 | 2025-04-19T18:06:30 | oeisdata/seq/A382/A382138.seq | 62b1ad18c27ee071a5a8751ce8b8ebf0 |
A382139 | Number of matchings of [2n] with no coupled arcs. | [
"1",
"1",
"1",
"9",
"81",
"705",
"7665",
"100905",
"1524705",
"26022465",
"496042785",
"10445342985",
"240779831985",
"6030718158465",
"163087008669585",
"4735950860666025",
"146987669673669825",
"4855606200012593025",
"170101350767940617025",
"6298861062893921346825",
"245834199405298416337425"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A001147",
"A047974",
"A053871",
"A067994",
"A382134",
"A382139"
]
| null | R. J. Mathar, Mar 17 2025 | 2025-03-17T14:23:42 | oeisdata/seq/A382/A382139.seq | 9b24818dba754478c357ab0d997c42af |
A382140 | Number of facets of the semigroup S_1 arising in studying the "saturation question" for the Lie group A_n. | [
"6",
"18",
"50",
"154",
"536"
]
| [
"nonn",
"more"
]
| 12 | 1 | 1 | [
"A382140",
"A382141",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:17:14 | oeisdata/seq/A382/A382140.seq | 5560db2c80ec7d97a587d413ae6685d1 |
A382141 | Number of extremal rays of the semigroup S_1 arising in studying the "saturation question" for the Lie group A_n. | [
"3",
"8",
"18",
"42",
"112"
]
| [
"nonn",
"more"
]
| 11 | 1 | 1 | [
"A382140",
"A382141",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:17:20 | oeisdata/seq/A382/A382141.seq | 3fdcf9102351c5e32ade165ff78a14ff |
A382142 | Number of facets of the semigroup S_1 arising in studying the "saturation question" for the Lie group C_n. | [
"24",
"102",
"486",
"2436"
]
| [
"nonn",
"more"
]
| 9 | 2 | 1 | [
"A382140",
"A382142",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:17:26 | oeisdata/seq/A382/A382142.seq | f52e77b635cc104d6d2f26a895d6f0e6 |
A382143 | Number of extremal rays of the semigroup S_1 arising in studying the "saturation question" for the Lie group C_n. | [
"12",
"51",
"237",
"1122"
]
| [
"nonn",
"more"
]
| 9 | 2 | 1 | [
"A382140",
"A382143",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:17:31 | oeisdata/seq/A382/A382143.seq | 4760434196831d0682321e874270e7b3 |
A382144 | Number of Hilbert basis elements for the semigroup S_1 arising in studying the "saturation question" for the Lie group C_n. | [
"13",
"58",
"302",
"1598"
]
| [
"nonn",
"more"
]
| 9 | 2 | 1 | [
"A382140",
"A382144",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:17:43 | oeisdata/seq/A382/A382144.seq | b015c5fab2b61cf97bd2c780611f2bcc |
A382145 | Number of facets of the semigroup S_1 arising in studying the "saturation question" for the Lie group D_n. | [
"50",
"306",
"1982",
"12162"
]
| [
"nonn",
"more"
]
| 9 | 3 | 1 | [
"A382140",
"A382145",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:17:52 | oeisdata/seq/A382/A382145.seq | dd55f604347fd17225713eedbce67031 |
A382146 | Number of extremal rays of the semigroup S_1 arising in studying the "saturation question" for the Lie group D_n. | [
"18",
"81",
"492",
"3258"
]
| [
"nonn",
"more"
]
| 14 | 3 | 1 | [
"A382140",
"A382146",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:18:08 | oeisdata/seq/A382/A382146.seq | 428b9287fc747bdaaca263d01e2709a5 |
A382147 | Number of Hilbert basis elements for the semigroup S_1 arising in studying the "saturation question" for the Lie group D_n. | [
"18",
"82",
"505",
"3470"
]
| [
"nonn",
"more"
]
| 10 | 3 | 1 | [
"A382140",
"A382146",
"A382147"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-17T22:18:14 | oeisdata/seq/A382/A382147.seq | 0205a705b9b2f9b65d393161a74e5b3f |
A382148 | Index of first occurrence of n in A381238, or -1 if n does not appear there. | [
"0",
"14",
"1",
"3",
"79",
"11",
"30",
"8",
"108",
"17",
"6",
"111",
"169",
"18",
"76",
"78",
"74",
"388",
"239",
"86",
"383",
"345",
"191",
"1017",
"178",
"486",
"163",
"1828",
"209",
"364",
"484",
"582",
"160",
"289",
"436",
"878",
"174",
"320",
"37",
"1029",
"698",
"1386",
"768",
"618",
"558",
"212",
"1318",
"2213",
"826",
"350",
"877",
"1780",
"1033",
"407",
"188",
"229",
"1478",
"467",
"305"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A381238",
"A382148"
]
| null | N. J. A. Sloane, Mar 17 2025 | 2025-03-18T15:46:37 | oeisdata/seq/A382/A382148.seq | e8cf66c1bdeed420b5895b518dabf674 |
A382149 | Primes p such that the elliptic curve X_0^{+}(p) has genus 2. | [
"67",
"73",
"103",
"107",
"167",
"191"
]
| [
"nonn",
"fini",
"full"
]
| 5 | 1 | 1 | [
"A382149",
"A382150"
]
| null | N. J. A. Sloane, Mar 22 2025 | 2025-03-22T13:32:46 | oeisdata/seq/A382/A382149.seq | f4a7f323661b5ef2a668cbe8e8c365f0 |
A382150 | Primes p such that the elliptic curve X_0^{+}(p) has genus 3. | [
"97",
"109",
"113",
"127",
"139",
"149",
"151",
"179",
"239"
]
| [
"nonn",
"fini",
"full"
]
| 7 | 1 | 1 | [
"A382149",
"A382150"
]
| null | N. J. A. Sloane, Mar 22 2025 | 2025-03-22T13:33:54 | oeisdata/seq/A382/A382150.seq | 17f8eb384b27f9265fd39b19f6e44b5c |
A382151 | Primes p such that some elliptic curve over Q admits a Q-rational p-isogeny. | [
"2",
"3",
"5",
"7",
"11",
"13",
"17",
"19",
"37",
"43",
"67",
"163"
]
| [
"nonn",
"fini",
"full"
]
| 6 | 1 | 1 | [
"A382151",
"A382152"
]
| null | N. J. A. Sloane, Mar 22 2025 | 2025-03-22T13:45:45 | oeisdata/seq/A382/A382151.seq | e6ce7b08c98c110e912a07a3a3064076 |
A382152 | Numbers k such that there is an elliptic curve defined over Q with a Q-rational cyclic isogeny of degree k. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"21",
"25",
"27",
"37",
"43",
"67",
"163"
]
| [
"nonn",
"fini",
"full"
]
| 7 | 1 | 2 | [
"A382151",
"A382152"
]
| null | N. J. A. Sloane, Mar 22 2025 | 2025-03-22T13:55:53 | oeisdata/seq/A382/A382152.seq | 76021c83863deaac4079b1dc0e5293f4 |
A382153 | Numbers k such that there is an exceptional k-isogeny arising from the rational points on an elliptic curve X_0^{+}(k) of genus at most 6. | [
"73",
"91",
"103",
"125",
"137",
"191",
"311"
]
| [
"nonn",
"fini",
"full"
]
| 7 | 1 | 1 | null | null | N. J. A. Sloane, Mar 22 2025 | 2025-03-22T14:17:24 | oeisdata/seq/A382/A382153.seq | aaf778167f5b3485c48577e98482e73f |
A382154 | a(0) = 1; thereafter a(n) = 2*n if n even or 4*n if n odd. | [
"1",
"4",
"4",
"12",
"8",
"20",
"12",
"28",
"16",
"36",
"20",
"44",
"24",
"52",
"28",
"60",
"32",
"68",
"36",
"76",
"40",
"84",
"44",
"92",
"48",
"100",
"52",
"108",
"56",
"116",
"60",
"124",
"64",
"132",
"68",
"140",
"72",
"148",
"76",
"156",
"80",
"164",
"84",
"172",
"88",
"180",
"92",
"188",
"96",
"196",
"100",
"204",
"104",
"212",
"108",
"220",
"112",
"228",
"116",
"236",
"120",
"244",
"124",
"252",
"128",
"260",
"132",
"268",
"136",
"276",
"140",
"284",
"144",
"292"
]
| [
"nonn"
]
| 40 | 0 | 2 | [
"A319384",
"A382154",
"A382155",
"A382156"
]
| null | N. J. A. Sloane, Mar 23 2025 | 2025-03-24T13:51:53 | oeisdata/seq/A382/A382154.seq | 87ff024c3e8ac096f6b6fd2f7a6b3ede |
A382155 | a(n) = (n+1)! if n <= 2; thereafter a(n) = 4*n if n even or 2*n if n odd. | [
"1",
"2",
"6",
"6",
"16",
"10",
"24",
"14",
"32",
"18",
"40",
"22",
"48",
"26",
"56",
"30",
"64",
"34",
"72",
"38",
"80",
"42",
"88",
"46",
"96",
"50",
"104",
"54",
"112",
"58",
"120",
"62",
"128",
"66",
"136",
"70",
"144",
"74",
"152",
"78",
"160",
"82",
"168",
"86",
"176",
"90",
"184",
"94",
"192",
"98",
"200",
"102",
"208",
"106",
"216",
"110",
"224",
"114",
"232",
"118",
"240",
"122",
"248",
"126",
"256",
"130",
"264",
"134",
"272",
"138",
"280",
"142",
"288",
"146",
"296"
]
| [
"nonn"
]
| 35 | 0 | 2 | [
"A319384",
"A382154",
"A382155",
"A382156"
]
| null | N. J. A. Sloane, Mar 23 2025 | 2025-03-24T11:53:50 | oeisdata/seq/A382/A382155.seq | 27eee300a4c9a684c66bc0d3a0001d13 |
A382156 | Partial sums of A382155. | [
"1",
"3",
"9",
"15",
"31",
"41",
"65",
"79",
"111",
"129",
"169",
"191",
"239",
"265",
"321",
"351",
"415",
"449",
"521",
"559",
"639",
"681",
"769",
"815",
"911",
"961",
"1065",
"1119",
"1231",
"1289",
"1409",
"1471",
"1599",
"1665",
"1801",
"1871",
"2015",
"2089",
"2241",
"2319",
"2479",
"2561",
"2729",
"2815",
"2991",
"3081",
"3265",
"3359",
"3551",
"3649",
"3849",
"3951",
"4159",
"4265",
"4481",
"4591",
"4815",
"4929",
"5161",
"5279",
"5519"
]
| [
"nonn",
"changed"
]
| 13 | 0 | 2 | [
"A319384",
"A382154",
"A382155",
"A382156"
]
| null | N. J. A. Sloane, Mar 23 2025 | 2025-07-09T05:08:14 | oeisdata/seq/A382/A382156.seq | bd7d03d90ae38c8bba996dd72d64c8eb |
A382157 | Number of n-node digraphs without loops, not necessarily connected, which are squares. | [
"1",
"1",
"3",
"9",
"46",
"473",
"13763",
"1121383"
]
| [
"nonn",
"more",
"changed"
]
| 12 | 0 | 3 | [
"A382157",
"A382158",
"A382159",
"A382180"
]
| null | N. J. A. Sloane, Mar 24 2025, based on an email from Brendan McKay, Mar 18 2025 | 2025-07-09T05:08:21 | oeisdata/seq/A382/A382157.seq | 62e0e2fa3844a6d038505c81d54c244d |
A382158 | Number of n-node oriented graphs (no loops or cycles of length 2), not necessarily connected, which are squares. | [
"1",
"1",
"2",
"6",
"26",
"209",
"4115",
"206205",
"24982238"
]
| [
"nonn",
"more",
"changed"
]
| 11 | 0 | 3 | [
"A382157",
"A382158",
"A382159",
"A382180"
]
| null | N. J. A. Sloane, Mar 24 2025, based on an email from Brendan McKay, Mar 18 2025 | 2025-07-09T05:08:28 | oeisdata/seq/A382/A382158.seq | 8c0a031983711065b78f3e92ecf344e1 |
A382159 | Number of n-node acyclic digraphs, not necessarily connected, which are squares. | [
"1",
"1",
"2",
"5",
"17",
"81",
"600",
"7182",
"142425",
"4664203",
"4071974770"
]
| [
"nonn",
"more",
"changed"
]
| 17 | 0 | 3 | [
"A382157",
"A382158",
"A382159",
"A382180"
]
| null | N. J. A. Sloane, Mar 24 2025, based on an email from Brendan McKay, Mar 18 2025 | 2025-07-09T05:08:34 | oeisdata/seq/A382/A382159.seq | 57d8f310cbe7fe5ce0a24c6bafd7df02 |
A382160 | Kaprekar numbers according to the definition in A006886 that are not in A053816. | [
"4879",
"5292",
"38962",
"627615",
"5479453",
"8161912",
"243902440",
"665188470",
"867208672",
"909090909",
"2646002646",
"7359343993",
"8975672343",
"19481019481",
"65098401732",
"71428071429",
"74074074075",
"74761738129",
"81433418067",
"81933418567",
"90909090910",
"93555093555",
"98268434902",
"218400870420"
]
| [
"nonn",
"base"
]
| 15 | 1 | 1 | [
"A006886",
"A053816",
"A382160"
]
| null | N. J. A. Sloane, Mar 25 2025 | 2025-03-26T16:17:47 | oeisdata/seq/A382/A382160.seq | e305c7970459de79560545ff7d41ed1a |
A382161 | "Repunit" Kaprekar numbers. | [
"1",
"1111111111",
"1111111111111111111",
"1111111111111111111111111111",
"1111111111111111111111111111111111111",
"1111111111111111111111111111111111111111111111"
]
| [
"nonn",
"base",
"more"
]
| 10 | 1 | 2 | [
"A006886",
"A145875",
"A382161"
]
| null | N. J. A. Sloane, Mar 25 2025 | 2025-03-26T08:27:13 | oeisdata/seq/A382/A382161.seq | db0b223b4958b41be980d704598effaf |
A382162 | Number of pairs (i,j), 1 <= i < j <= n such that A019444(i) < A019444(j). | [
"0",
"1",
"2",
"5",
"9",
"12",
"18",
"22",
"30",
"39",
"45",
"56",
"68",
"76",
"90",
"99",
"115",
"132",
"143",
"162",
"174",
"195",
"217",
"231",
"255",
"280",
"296",
"323",
"340",
"369",
"399",
"418",
"450",
"483",
"504",
"539",
"561",
"598",
"636",
"660",
"700",
"725",
"767",
"810",
"837",
"882",
"928",
"957",
"1005",
"1035",
"1085",
"1136",
"1168",
"1221",
"1254",
"1309",
"1365",
"1400",
"1458",
"1517",
"1554",
"1615",
"1653",
"1716",
"1780",
"1820"
]
| [
"nonn"
]
| 8 | 1 | 3 | [
"A019444",
"A382162"
]
| null | N. J. A. Sloane, Mar 31 2025 | 2025-04-01T03:29:01 | oeisdata/seq/A382/A382162.seq | 7cf0d59d482b3a967ff565c53d68aad2 |
A382163 | Palindromic Kaprekar numbers. | [
"1",
"9",
"55",
"99",
"999",
"7777",
"9999",
"22222",
"99999",
"999999",
"4444444",
"9999999",
"88888888",
"99999999",
"909090909",
"999999999",
"1111111111",
"9999999999",
"55555555555",
"99999999999",
"999999999999",
"7777777777777",
"9999999999999",
"22222222222222",
"99999999999999",
"999999999999999",
"4444444444444444",
"9999999999999999",
"88888888888888888"
]
| [
"nonn",
"base",
"changed"
]
| 21 | 1 | 2 | [
"A002113",
"A006886",
"A382163",
"A382164"
]
| null | N. J. A. Sloane, Mar 26 2025 | 2025-07-09T05:08:40 | oeisdata/seq/A382/A382163.seq | 08b7bae1e708edacc51f0a3f65aa738c |
A382164 | Palindromic Kaprekar numbers that are not repdigit Kaprekar numbers. | [
"909090909",
"9090909090909090909090909090909",
"81188118811881188118811881188118",
"545545545545545545545545545545545",
"277227722772277227722772277227722772",
"505050505050505050505050505050505050505",
"4040404040404040404040404040404040404040404040404"
]
| [
"nonn",
"base"
]
| 9 | 1 | 1 | [
"A006886",
"A145875",
"A382163",
"A382164"
]
| null | N. J. A. Sloane, Mar 26 2025 | 2025-03-26T08:28:40 | oeisdata/seq/A382/A382164.seq | 45056ec7cc9a39b3f74717018920d30d |
A382165 | Kaprekar numbers (A006886) that are divisible by the sum of their digits. | [
"1",
"9",
"45",
"999",
"2223",
"4950",
"5050",
"5292",
"7272",
"142857",
"148149",
"187110",
"356643",
"466830",
"499500",
"500500",
"538461",
"627615",
"648648",
"681318",
"791505",
"818181",
"961038",
"994708",
"5555556",
"11111112",
"16590564",
"30884184",
"36363636",
"49995000",
"50005000",
"55474452",
"74747475",
"234567901",
"432432432",
"665188470",
"999999999",
"2020202020",
"3846956652",
"4132841328",
"4999950000",
"5000050000"
]
| [
"nonn",
"base"
]
| 10 | 1 | 2 | [
"A005349",
"A006886",
"A382165"
]
| null | N. J. A. Sloane, Mar 26 2025 | 2025-03-26T16:17:33 | oeisdata/seq/A382/A382165.seq | e0c8f16ba6f7a30e1db4b8345e813ab5 |
A382166 | Self-numbers (A003052) that are cubes. | [
"1",
"64",
"512",
"1728",
"35937",
"50653",
"195112",
"287496",
"300763",
"314432",
"681472",
"804357",
"884736",
"1000000",
"2248091",
"2744000",
"3241792",
"4173281",
"4913000",
"5929741",
"6434856",
"6859000",
"10077696",
"10360232",
"12167000",
"13481272",
"15813251",
"18399744",
"19902511",
"22188041",
"27270901",
"29791000",
"36264691",
"37933056",
"47045881"
]
| [
"nonn",
"base"
]
| 9 | 1 | 2 | [
"A000578",
"A003052",
"A171671",
"A382166"
]
| null | N. J. A. Sloane, Mar 26 2025 | 2025-03-26T17:49:17 | oeisdata/seq/A382/A382166.seq | f77a8eedead3cfc0e82d10c92b32cc60 |
A382167 | Repdigit self-numbers that are not in A337208. | [
"3",
"5",
"7",
"9",
"222",
"88888",
"666666",
"7777777",
"44444444",
"555555555",
"3333333333",
"777777777777",
"999999999999",
"44444444444444",
"222222222222222",
"5555555555555555",
"333333333333333333",
"8888888888888888888",
"666666666666666666666",
"9999999999999999999999",
"77777777777777777777777",
"4444444444444444444444444"
]
| [
"nonn",
"base"
]
| 5 | 1 | 1 | [
"A003052",
"A337208",
"A382167"
]
| null | N. J. A. Sloane, Mar 26 2025 | 2025-03-26T09:12:41 | oeisdata/seq/A382/A382167.seq | 57e0528134905db17a920a5dd247f98a |
A382168 | Number of triples (i,j,k), 1 <= i < j < k <= n such that A019444(i) < A019444(k) < A019444(j). | [
"0",
"0",
"1",
"1",
"1",
"7",
"7",
"17",
"17",
"17",
"38",
"38",
"38",
"74",
"74",
"119",
"119",
"119",
"185",
"185",
"263",
"263",
"263",
"368",
"368",
"368",
"504",
"504",
"657",
"657",
"657",
"847",
"847",
"847",
"1078",
"1078",
"1331",
"1331",
"1331",
"1631",
"1631",
"1956",
"1956",
"1956",
"2334",
"2334",
"2334",
"2769",
"2769",
"3234",
"3234",
"3234",
"3762",
"3762",
"4323",
"4323",
"4323",
"4953",
"4953",
"4953",
"5656",
"5656",
"6397",
"6397",
"6397"
]
| [
"nonn"
]
| 9 | 1 | 6 | [
"A000108",
"A019444",
"A382162",
"A382168",
"A382169"
]
| null | N. J. A. Sloane, Mar 31 2025 | 2025-03-31T22:30:30 | oeisdata/seq/A382/A382168.seq | 593cddc8a1caa170f664b84b88cc74ee |
A382169 | A382168 with duplicates removed. | [
"0",
"1",
"7",
"17",
"38",
"74",
"119",
"185",
"263",
"368",
"504",
"657",
"847",
"1078",
"1331",
"1631",
"1956",
"2334",
"2769",
"3234",
"3762",
"4323",
"4953",
"5656",
"6397",
"7217",
"8120",
"9066",
"10101",
"11182",
"12358",
"13633",
"14959",
"16390",
"17930",
"19526",
"21237",
"23007",
"24898",
"26914",
"28994",
"31205",
"33483",
"35898"
]
| [
"nonn"
]
| 12 | 1 | 3 | [
"A000217",
"A019444",
"A382168",
"A382169"
]
| null | N. J. A. Sloane, Mar 31 2025 | 2025-04-01T19:33:07 | oeisdata/seq/A382/A382169.seq | 1c2d54dff58b81ed26f7cb28aef6f152 |
A382170 | a(0) = 0; for n >= 1, one-eighth of the number of points on the elliptic curve y^2 = x^3 - x defined over GF(5^n). | [
"0",
"1",
"4",
"13",
"80",
"401",
"1924",
"9773",
"48960",
"243841",
"1220644",
"6105133",
"30514640",
"152585681",
"762958564",
"3814670093",
"19073445120",
"95367649921",
"476836927684",
"2384185160653",
"11920931368400",
"59604643100561",
"298023215160004",
"1490116145192813",
"7450580588892480",
"37252902871641601",
"186264515189207524"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 3 | [
"A382170",
"A382171"
]
| null | Jianing Song, Mar 17 2025 | 2025-03-18T03:08:20 | oeisdata/seq/A382/A382170.seq | 4e0049bc2ed62fe8ffd01b0c0b3c0439 |
A382171 | a(0) = 0; for n >= 1, one quarter of the number of points on the elliptic curve y^2 = x^3 - x defined over GF(3^n). | [
"0",
"1",
"4",
"7",
"16",
"61",
"196",
"547",
"1600",
"4921",
"14884",
"44287",
"132496",
"398581",
"1196836",
"3587227",
"10758400",
"32285041",
"96864964",
"290565367",
"871666576",
"2615088301",
"7845353476",
"23535794707",
"70607118400",
"211822152361",
"635467254244",
"1906399371247",
"5719195722256",
"17157594341221",
"51472790198116"
]
| [
"nonn",
"easy"
]
| 16 | 0 | 3 | [
"A382170",
"A382171"
]
| null | Jianing Song, Mar 17 2025 | 2025-03-18T03:08:04 | oeisdata/seq/A382/A382171.seq | a36e8ab039afad6e0110c83eed36f5da |
A382172 | Irregular triangle read by rows in which row n contains the digits of the period of 1/n when expanded in golden ratio base. | [
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0"
]
| [
"nonn",
"tabf",
"easy",
"base"
]
| 9 | 1 | null | [
"A001175",
"A001622",
"A055778",
"A173856",
"A173857",
"A173858",
"A173859",
"A173860",
"A173861",
"A173864",
"A294168",
"A354948",
"A382172",
"A382173",
"A382174",
"A382175",
"A382176"
]
| null | Amiram Eldar, Mar 17 2025 | 2025-03-19T09:04:04 | oeisdata/seq/A382/A382172.seq | 147babb374a1bb3c9a592991250b700e |
A382173 | a(n) is the sum of row n of A382172. | [
"0",
"1",
"2",
"1",
"6",
"7",
"4",
"2",
"6",
"16",
"1",
"5",
"8",
"14",
"10",
"5",
"10",
"6",
"3",
"15",
"2",
"7",
"13",
"4",
"26",
"24",
"19",
"9",
"1",
"31",
"6",
"10",
"8",
"10",
"20",
"4",
"22",
"2",
"13",
"14",
"11",
"11",
"24",
"5",
"31",
"13",
"8",
"4",
"30",
"80",
"17",
"20",
"30",
"18",
"2",
"11",
"17",
"9",
"14",
"30",
"16",
"5",
"10",
"25",
"36",
"29",
"38",
"6",
"9",
"63",
"16",
"2",
"40",
"64"
]
| [
"nonn",
"easy",
"base"
]
| 7 | 1 | 3 | [
"A000032",
"A002878",
"A007733",
"A055778",
"A093960",
"A276350",
"A382172",
"A382173",
"A382174",
"A382175",
"A382176"
]
| null | Amiram Eldar, Mar 17 2025 | 2025-03-19T09:03:57 | oeisdata/seq/A382/A382173.seq | 7b91c5f38f6bde981ed55b832486bafb |
A382174 | Numbers k such that A382173(k) >= k. | [
"5",
"6",
"10",
"14",
"25",
"30",
"50",
"125",
"150",
"250",
"625",
"750",
"1250",
"3125",
"3750",
"6250",
"15625",
"18750",
"31250",
"78125"
]
| [
"nonn",
"base",
"more"
]
| 5 | 1 | 1 | [
"A382172",
"A382173",
"A382174",
"A382175",
"A382176"
]
| null | Amiram Eldar, Mar 17 2025 | 2025-03-19T09:03:51 | oeisdata/seq/A382/A382174.seq | 5dd7643a78e0c6cfeb64f29a2370a747 |
A382175 | Indices of records in A382173. | [
"1",
"2",
"3",
"5",
"6",
"10",
"25",
"30",
"50",
"98",
"125",
"150",
"194",
"206",
"243",
"250",
"490",
"554",
"566",
"625",
"750",
"1030",
"1046",
"1094",
"1154",
"1214",
"1226",
"1250",
"2450",
"2738",
"2846",
"2894",
"2906",
"3086",
"3125",
"3750",
"4802",
"5534",
"5594",
"5606",
"5666",
"5714",
"5770",
"5774",
"5834",
"5906",
"5990",
"6070",
"6074",
"6130"
]
| [
"nonn",
"base"
]
| 8 | 1 | 2 | [
"A001175",
"A326612",
"A382172",
"A382173",
"A382174",
"A382175",
"A382176"
]
| null | Amiram Eldar, Mar 17 2025 | 2025-03-19T09:03:45 | oeisdata/seq/A382/A382175.seq | d5f50416a988d2bf7e81d98b3d32dafe |
A382176 | Numbers k such that the period of 1/k when expanded in golden ratio base is palindromic. | [
"1",
"2",
"36",
"38",
"644",
"646",
"682",
"11556",
"11558",
"11592",
"12198",
"12238"
]
| [
"nonn",
"base",
"more"
]
| 5 | 1 | 2 | [
"A330722",
"A362781",
"A373085",
"A382172",
"A382173",
"A382174",
"A382175",
"A382176"
]
| null | Amiram Eldar, Mar 17 2025 | 2025-03-19T09:03:40 | oeisdata/seq/A382/A382176.seq | f635009e3762b9133365fa517ab0f515 |
A382177 | a(n) is the least k > 1 such that the factorial base expansion of k*n starts with that of n while the remaining digits are zeros. | [
"2",
"2",
"3",
"10",
"3",
"312",
"4",
"18",
"18",
"96",
"96",
"600",
"4",
"6168960",
"6120",
"18",
"18",
"11017036800",
"4",
"56229997824000",
"114",
"760",
"68947200",
"18",
"5",
"14544",
"141120",
"192",
"13320",
"9092075324665919034015350784000000",
"28",
"520412336961032355840000",
"27",
"1400",
"199584000",
"116496",
"180"
]
| [
"nonn",
"base"
]
| 8 | 0 | 1 | [
"A153880",
"A382177",
"A382178"
]
| null | Rémy Sigrist, Mar 17 2025 | 2025-03-20T09:29:36 | oeisdata/seq/A382/A382177.seq | 6eeecbb636fac53c03ed015bdccd28ea |
A382178 | a(n) is the least k > 1 such that the factorial base expansion of k*n starts with that of n. | [
"2",
"2",
"3",
"3",
"3",
"3",
"4",
"18",
"18",
"17",
"17",
"16",
"4",
"19",
"19",
"18",
"18",
"101",
"4",
"115",
"114",
"110",
"110",
"18",
"5",
"203",
"199",
"192",
"189",
"183",
"28",
"187",
"27",
"179",
"177",
"1341",
"180",
"176",
"26",
"170",
"168",
"165",
"1320",
"168",
"1277",
"1251",
"162",
"159",
"5",
"1649",
"204",
"1598",
"1579",
"1551",
"200",
"197",
"195"
]
| [
"nonn",
"base"
]
| 8 | 0 | 1 | [
"A153880",
"A382177",
"A382178"
]
| null | Rémy Sigrist, Mar 17 2025 | 2025-03-20T09:29:28 | oeisdata/seq/A382/A382178.seq | 9f98cbbcfe7dcafc7ac5f2c90903e22e |
A382179 | Numbers k such that for each digit of k, 2*k*(digit) + 1 is prime. | [
"1",
"3",
"6",
"9",
"11",
"14",
"15",
"22",
"24",
"25",
"27",
"28",
"33",
"44",
"54",
"63",
"75",
"78",
"81",
"88",
"99",
"111",
"119",
"131",
"141",
"153",
"168",
"173",
"219",
"249",
"252",
"255",
"279",
"282",
"322",
"325",
"333",
"357",
"363",
"414",
"441",
"459",
"474",
"491",
"538",
"553",
"558",
"565",
"611",
"666",
"674",
"699",
"794",
"797",
"828",
"831",
"832",
"858",
"895",
"924",
"947",
"955"
]
| [
"nonn",
"base"
]
| 43 | 1 | 2 | [
"A000040",
"A382127",
"A382179",
"A382198",
"A382199"
]
| null | Jakub Buczak, Mar 17 2025 | 2025-03-30T08:17:02 | oeisdata/seq/A382/A382179.seq | bd03067077b2912d5b500b8de8e72d6a |
A382180 | Number of unlabeled connected graphs with n vertices which are squares. | [
"1",
"1",
"1",
"1",
"2",
"4",
"13",
"42",
"206",
"1310",
"12622",
"180700",
"3925282"
]
| [
"nonn",
"more"
]
| 23 | 0 | 5 | [
"A000055",
"A001349",
"A382180",
"A382181",
"A382194"
]
| null | Brendan McKay and Sean A. Irvine, Mar 17 2025 | 2025-03-24T14:00:32 | oeisdata/seq/A382/A382180.seq | e8317bd9731e2ab6e208a6123cbe039e |
A382181 | Number of unlabeled graphs with n vertices (including disconnected graphs) which are squares. | [
"1",
"1",
"2",
"3",
"6",
"11",
"28",
"77",
"307",
"1688",
"14620",
"197050",
"4137271"
]
| [
"nonn",
"more"
]
| 13 | 0 | 3 | [
"A382180",
"A382181"
]
| null | Brendan McKay and Sean A. Irvine, Mar 17 2025 | 2025-03-18T21:40:11 | oeisdata/seq/A382/A382181.seq | 80e139cbac52eef46725f06a19ce8a17 |
A382182 | Lexicographically earliest increasing sequence starting with a(0) = 1 such that the polynomial which interpolates the first k values has degree k-1 and only integer coefficients. | [
"1",
"2",
"5",
"16",
"17",
"86",
"1237",
"1940",
"25601",
"617482",
"1386821",
"25329272",
"815052625",
"2379750686",
"55319082197",
"2225093600956",
"7995962217857",
"225701855249810",
"10894058270134021",
"46488524334434912",
"1543800689908468241",
"86934584995669200742",
"429553964850178236245",
"16404426130967383104356"
]
| [
"nonn"
]
| 20 | 0 | 2 | [
"A000522",
"A182386",
"A382182"
]
| null | Thomas Scheuerle, Mar 17 2025 | 2025-03-19T10:18:17 | oeisdata/seq/A382/A382182.seq | 2df4a0865d33ac81495893fa54e385bd |
A382183 | Binary sequence linking A105774 and A382113. | [
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1"
]
| [
"nonn"
]
| 10 | 1 | null | [
"A105774",
"A382113",
"A382183"
]
| null | Jeffrey Shallit, Mar 17 2025 | 2025-03-19T10:20:57 | oeisdata/seq/A382/A382183.seq | 1a66e5b1c5f4207b02c39ed958d422c7 |
A382184 | a(n) is the least k >= 0 such that the factorial base expansion of n starts with that of k while the remaining digits are zeros. | [
"0",
"1",
"1",
"3",
"4",
"5",
"1",
"7",
"3",
"9",
"10",
"11",
"4",
"13",
"5",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"1",
"25",
"7",
"27",
"28",
"29",
"3",
"31",
"9",
"33",
"34",
"35",
"10",
"37",
"11",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"4",
"49",
"13",
"51",
"52",
"53",
"5",
"55",
"15",
"57",
"58",
"59",
"16",
"61",
"17",
"63",
"64",
"65",
"66",
"67",
"68",
"69"
]
| [
"nonn",
"base"
]
| 9 | 0 | 4 | [
"A000265",
"A004151",
"A153880",
"A273670",
"A382177",
"A382184",
"A382217"
]
| null | Rémy Sigrist, Mar 17 2025 | 2025-03-20T09:29:22 | oeisdata/seq/A382/A382184.seq | 7a7d0c32be1c3a88f6eb3963ac79c827 |
A382185 | a(n) is the n-th tribonacci number modulo the n-th prime. | [
"0",
"1",
"1",
"2",
"4",
"7",
"13",
"5",
"21",
"23",
"25",
"15",
"12",
"24",
"13",
"9",
"45",
"56",
"16",
"35",
"20",
"71",
"47",
"9",
"40",
"80",
"18",
"46",
"75",
"101",
"55",
"48",
"65",
"36",
"142",
"34",
"91",
"0",
"43",
"147",
"118",
"41",
"175",
"24",
"131",
"152",
"189",
"213",
"116",
"201",
"116",
"66",
"73",
"9",
"0",
"53",
"210",
"239",
"167",
"171",
"87",
"262",
"251",
"111",
"115",
"69",
"284",
"186",
"211",
"321",
"331",
"135"
]
| [
"nonn",
"look",
"easy"
]
| 23 | 1 | 4 | [
"A000040",
"A000073",
"A072123",
"A382185"
]
| null | Michael Figelius, Mar 17 2025 | 2025-04-15T16:37:50 | oeisdata/seq/A382/A382185.seq | 288171807b8c56511fa44ec615473426 |
A382186 | Prime numbers that are the sum of the m-th prime and the m-th semiprime for some m. | [
"17",
"41",
"71",
"131",
"281",
"331",
"353",
"397",
"449",
"487",
"563",
"953",
"1279",
"1289",
"1409",
"1627",
"2621",
"2999",
"3533",
"3631",
"3697",
"3989",
"4057",
"4133",
"4523",
"4603",
"4733",
"4919",
"5273",
"5591",
"5641",
"6211",
"6247",
"6269",
"6299",
"6469",
"6803",
"7753",
"7879",
"7937",
"8353",
"8543",
"8971",
"8999",
"9041",
"9181",
"9413",
"9479",
"9787",
"9887",
"9941",
"10487"
]
| [
"nonn"
]
| 12 | 1 | 1 | [
"A000040",
"A001358",
"A092108",
"A133796",
"A382186"
]
| null | Zak Seidov and Robert Israel, Mar 18 2025 | 2025-03-20T13:59:08 | oeisdata/seq/A382/A382186.seq | bd21ba2f73a59ffbbe33fe18caf2b99e |
A382187 | Expansion of 1/(1 - 4 * Sum_{k>=0} x^(2^k))^(1/2). | [
"1",
"2",
"8",
"32",
"138",
"604",
"2696",
"12176",
"55512",
"254888",
"1177064",
"5461040",
"25435296",
"118856272",
"556962928",
"2616287392",
"12315914698",
"58084552572",
"274395134600",
"1298187523792",
"6150051540460",
"29170558879736",
"138512004786624",
"658362443599296",
"3132140164624680"
]
| [
"nonn",
"easy"
]
| 8 | 0 | 2 | [
"A023359",
"A223142",
"A382187",
"A382188"
]
| null | Seiichi Manyama, Mar 18 2025 | 2025-03-18T16:24:02 | oeisdata/seq/A382/A382187.seq | 2d746cfb8511e3caebbb0487afa0577e |
A382188 | Expansion of 1/(1 - 9 * Sum_{k>=0} x^(2^k))^(1/3). | [
"1",
"3",
"21",
"162",
"1344",
"11565",
"102033",
"916002",
"8330331",
"76515363",
"708379137",
"6600436794",
"61829064882",
"581783753232",
"5495344743924",
"52079440119336",
"494985533135250",
"4716537209764020",
"45043670723519952",
"431041661857081656",
"4132290587464466820",
"39680088682182010749"
]
| [
"nonn",
"easy"
]
| 8 | 0 | 2 | [
"A023359",
"A382187",
"A382188"
]
| null | Seiichi Manyama, Mar 18 2025 | 2025-03-18T21:44:16 | oeisdata/seq/A382/A382188.seq | 4bc90bb24ac8fbcd99a1bdd1b2b356d2 |
A382189 | Expansion of 1/(1 - 4 * Sum_{k>=0} x^(3^k))^(1/2). | [
"1",
"2",
"6",
"22",
"82",
"312",
"1210",
"4752",
"18834",
"75186",
"301868",
"1217664",
"4930918",
"20033432",
"81621456",
"333357656",
"1364395770",
"5594799576",
"22980090870",
"94529049296",
"389367825444",
"1605758772136",
"6629456308464",
"27397510466856",
"113329594803078",
"469183242566016",
"1943927996932656"
]
| [
"nonn",
"easy"
]
| 7 | 0 | 2 | [
"A078932",
"A382189",
"A382190"
]
| null | Seiichi Manyama, Mar 18 2025 | 2025-03-18T21:44:10 | oeisdata/seq/A382/A382189.seq | 608b83e1f1c260b28b4208f035837fa3 |
A382190 | Expansion of 1/(1 - 9 * Sum_{k>=0} x^(3^k))^(1/3). | [
"1",
"3",
"18",
"129",
"981",
"7749",
"62766",
"517401",
"4320864",
"36446565",
"309876444",
"2651681826",
"22812645339",
"197144727876",
"1710267824304",
"14886242261595",
"129946357148661",
"1137235357935279",
"9975129925544568",
"87672540348112779",
"771962724133452441",
"6808329943495097076"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 2 | [
"A078932",
"A382189",
"A382190",
"A382196"
]
| null | Seiichi Manyama, Mar 18 2025 | 2025-03-18T16:23:45 | oeisdata/seq/A382/A382190.seq | b4da2589a4be1898cdd601add2ae256e |
A382191 | Number of edges of the graph with code A076184(n). | [
"0",
"1",
"2",
"3",
"3",
"2",
"3",
"4",
"4",
"5",
"6",
"4",
"3",
"4",
"5",
"4",
"5",
"5",
"6",
"4",
"5",
"6",
"7",
"6",
"7",
"6",
"5",
"6",
"7",
"7",
"8",
"8",
"9",
"10",
"5",
"4",
"5",
"6",
"4",
"5",
"5",
"6",
"6",
"7",
"5",
"6",
"7",
"8",
"6",
"7",
"3",
"4",
"5",
"6",
"5",
"6",
"5",
"6",
"6",
"7",
"7",
"8",
"7",
"8",
"7",
"6",
"7",
"8",
"6",
"7",
"7",
"8",
"8",
"9",
"5",
"6",
"7",
"6",
"7",
"8",
"7",
"8",
"7",
"8",
"9",
"9",
"8"
]
| [
"nonn",
"tabf"
]
| 6 | 1 | 3 | [
"A000120",
"A002494",
"A076184",
"A382191"
]
| null | Pontus von Brömssen, Mar 18 2025 | 2025-03-21T09:46:30 | oeisdata/seq/A382/A382191.seq | 48cb6f468d665ec1e860b2fa746e0e6b |
A382192 | Number of components of the graph with code A076184(n). | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1"
]
| [
"nonn",
"tabf"
]
| 5 | 1 | 6 | [
"A002494",
"A076184",
"A382192",
"A382193"
]
| null | Pontus von Brömssen, Mar 18 2025 | 2025-03-21T09:46:59 | oeisdata/seq/A382/A382192.seq | 0468e36d5da7ecf0fe4a7ac9368d0421 |
A382193 | List of connected graphs, encoded as in A076184. | [
"0",
"1",
"3",
"7",
"11",
"13",
"15",
"30",
"31",
"63",
"75",
"77",
"79",
"86",
"87",
"94",
"95",
"117",
"119",
"127",
"222",
"223",
"235",
"236",
"237",
"239",
"254",
"255",
"507",
"511",
"1023",
"1099",
"1101",
"1103",
"1109",
"1110",
"1111",
"1118",
"1119",
"1141",
"1143",
"1151",
"1182",
"1183",
"1187",
"1191",
"1195",
"1196",
"1197",
"1198",
"1199",
"1214"
]
| [
"nonn",
"tabf"
]
| 7 | 1 | 3 | [
"A001349",
"A076184",
"A382192",
"A382193"
]
| null | Pontus von Brömssen, Mar 18 2025 | 2025-03-21T11:14:36 | oeisdata/seq/A382/A382193.seq | c1ea7c73aabdcd3c1313ec3b2ee9e6e7 |
A382194 | List of connected graphs that are squares, encoded as in A076184. | [
"0",
"1",
"7",
"31",
"63",
"239",
"255",
"511",
"1023",
"3455",
"3887",
"3951",
"3967",
"4095",
"7679",
"7903",
"7935",
"8191",
"16350",
"16351",
"16383",
"32767",
"104063",
"104447",
"106287",
"106351",
"111587",
"111599",
"112511",
"112623",
"112639",
"127791",
"127855",
"127871",
"128879",
"128895",
"129023",
"131071",
"237567"
]
| [
"nonn",
"tabf"
]
| 15 | 1 | 3 | [
"A076184",
"A382180",
"A382193",
"A382194",
"A382195",
"A382283"
]
| null | Pontus von Brömssen, Mar 18 2025 | 2025-03-22T12:00:48 | oeisdata/seq/A382/A382194.seq | 41de2ea2891cf3c63967e5d1e087d79a |
A382195 | a(n) is the code (in the encoding given by A076184) of the square of the graph with code A076184(n). | [
"0",
"1",
"7",
"7",
"63",
"12",
"31",
"63",
"63",
"63",
"63",
"1023",
"116",
"255",
"1023",
"239",
"511",
"511",
"1023",
"116",
"255",
"511",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"1023",
"32767",
"1972",
"4095",
"32767",
"3873",
"7903",
"3951",
"8191",
"8191",
"32767",
"3873",
"7903",
"8191",
"32767"
]
| [
"nonn",
"tabf",
"base"
]
| 12 | 1 | 3 | [
"A002494",
"A076184",
"A382194",
"A382195"
]
| null | Pontus von Brömssen, Mar 18 2025 | 2025-03-21T11:14:02 | oeisdata/seq/A382/A382195.seq | 4e8f90a9a7a37049965c4552e0713afc |
A382196 | Expansion of (1 + 9 * Sum_{k>=0} x^(3^k))^(1/3). | [
"1",
"3",
"-9",
"48",
"-288",
"1917",
"-13563",
"99927",
"-758079",
"5879757",
"-46401705",
"371337021",
"-3005974710",
"24568145019",
"-202442064183",
"1679864383800",
"-14024716370064",
"117715927282470",
"-992725129013121",
"8407191323492226",
"-71467963130581758",
"609605555349330009"
]
| [
"sign",
"easy"
]
| 9 | 0 | 2 | [
"A223142",
"A223143",
"A298308",
"A382190",
"A382196"
]
| null | Seiichi Manyama, Mar 18 2025 | 2025-03-18T21:45:30 | oeisdata/seq/A382/A382196.seq | fe4622ffaf3038a48559b4370ca23215 |
A382197 | Decimal expansion of 24^(1/6). | [
"1",
"6",
"9",
"8",
"3",
"8",
"1",
"3",
"2",
"9",
"5",
"6",
"4",
"9",
"5",
"2",
"7",
"8",
"4",
"9",
"1",
"2",
"5",
"6",
"4",
"5",
"2",
"4",
"6",
"5",
"9",
"7",
"4",
"9",
"3",
"6",
"0",
"2",
"0",
"3",
"5",
"0",
"0",
"0",
"9",
"0",
"3",
"3",
"5",
"9",
"7",
"1",
"4",
"4",
"8",
"9",
"0",
"4",
"1",
"0",
"6",
"1",
"6",
"1",
"9",
"6",
"9",
"5",
"4",
"9",
"3",
"2",
"0",
"1",
"3",
"8",
"0",
"8",
"9",
"0",
"0",
"9",
"2",
"7",
"8",
"1",
"3",
"6",
"7",
"0",
"0",
"3",
"4",
"1",
"9",
"8",
"8",
"0",
"2",
"1"
]
| [
"nonn",
"cons",
"easy"
]
| 7 | 1 | 2 | [
"A002193",
"A010480",
"A010596",
"A011020",
"A011109",
"A246708",
"A382197"
]
| null | Stefano Spezia, Mar 18 2025 | 2025-03-19T10:03:30 | oeisdata/seq/A382/A382197.seq | 5ed60622f792823288a303897da58eaf |
A382198 | Smallest integer k with n distinct digits, such that for each digit of k, 2*k*(digit) + 1 is prime. | [
"3",
"14",
"153",
"2169",
"48165",
"125769",
"327174495"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 11 | 1 | 1 | [
"A382127",
"A382179",
"A382198",
"A382199"
]
| null | Michel Marcus, Mar 18 2025 | 2025-03-18T16:23:14 | oeisdata/seq/A382/A382198.seq | 60187c9f9dc569ca8f25d1ebf815e5fc |
A382199 | Primes p such that for each digit of p, 2*p*(digit) + 1 is prime. | [
"3",
"11",
"131",
"173",
"491",
"797",
"947",
"1931",
"3583",
"4391",
"6173",
"7937",
"32323",
"49919",
"64499",
"79997",
"83383",
"149111",
"232333",
"296269",
"366161",
"477947",
"611333",
"616169",
"616961",
"635563",
"667673",
"969179",
"1111991",
"1779779",
"2232523",
"2662669",
"2922229",
"3444341",
"5333353",
"5599999",
"6853663",
"6919691",
"6929929"
]
| [
"nonn",
"base"
]
| 7 | 1 | 1 | [
"A382127",
"A382179",
"A382198",
"A382199"
]
| null | Michel Marcus, Mar 18 2025 | 2025-03-18T13:47:16 | oeisdata/seq/A382/A382199.seq | af2c200ed3c4a7e28c7e5f2873fdafcb |
A382200 | Numbers that can be written as a product of distinct squarefree numbers. | [
"1",
"2",
"3",
"5",
"6",
"7",
"10",
"11",
"12",
"13",
"14",
"15",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"26",
"28",
"29",
"30",
"31",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"50",
"51",
"52",
"53",
"55",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"82",
"83",
"84"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A000720",
"A001055",
"A001222",
"A005117",
"A045778",
"A050320",
"A050326",
"A050342",
"A050345",
"A089259",
"A116539",
"A270995",
"A279785",
"A292432",
"A292444",
"A293243",
"A293511",
"A300383",
"A302494",
"A317141",
"A358914",
"A381441",
"A381992",
"A381996",
"A382075",
"A382077",
"A382078",
"A382200",
"A382201",
"A382214",
"A382216"
]
| null | Gus Wiseman, Mar 21 2025 | 2025-04-21T17:00:45 | oeisdata/seq/A382/A382200.seq | 7070ad0f35a46f4649364ec41e5bf0ca |
A382201 | MM-numbers of sets of sets with distinct sums. | [
"1",
"2",
"3",
"5",
"6",
"10",
"11",
"13",
"15",
"17",
"22",
"26",
"29",
"30",
"31",
"33",
"34",
"39",
"41",
"43",
"47",
"51",
"55",
"58",
"59",
"62",
"65",
"66",
"67",
"73",
"78",
"79",
"82",
"83",
"85",
"86",
"87",
"93",
"94",
"101",
"102",
"109",
"110",
"113",
"118",
"123",
"127",
"129",
"130",
"134",
"137",
"139",
"141",
"145",
"146",
"149",
"155",
"157",
"158",
"163",
"165"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A000720",
"A001055",
"A003963",
"A005117",
"A007716",
"A045778",
"A050320",
"A050326",
"A055396",
"A056239",
"A061395",
"A112798",
"A275780",
"A279785",
"A293511",
"A302242",
"A302478",
"A302494",
"A302497",
"A319899",
"A321455",
"A321469",
"A326519",
"A326533",
"A326534",
"A326535",
"A326537",
"A368100",
"A368101",
"A381633",
"A381635",
"A381718",
"A382080",
"A382201",
"A382215"
]
| null | Gus Wiseman, Mar 21 2025 | 2025-03-23T08:40:28 | oeisdata/seq/A382/A382201.seq | e23c4777c31e1280405651b7a3e346ff |
A382202 | Number of normal multisets of size n that cannot be partitioned into a set of sets with distinct sums. | [
"0",
"0",
"1",
"1",
"3",
"5",
"9",
"16",
"27",
"48",
"78",
"133"
]
| [
"nonn",
"more"
]
| 8 | 0 | 5 | [
"A000110",
"A000670",
"A001055",
"A007716",
"A019536",
"A034691",
"A035310",
"A045778",
"A050320",
"A050326",
"A050342",
"A055932",
"A089259",
"A116539",
"A116540",
"A255903",
"A255906",
"A270995",
"A275780",
"A279785",
"A292432",
"A292444",
"A293243",
"A296119",
"A296120",
"A318360",
"A318361",
"A321469",
"A326517",
"A326518",
"A326519",
"A333217",
"A358914",
"A381633",
"A381718",
"A381806",
"A381990",
"A381992",
"A381996",
"A382075",
"A382077",
"A382078",
"A382200",
"A382202",
"A382214",
"A382216",
"A382428",
"A382429",
"A382430",
"A382458",
"A382459",
"A382460"
]
| null | Gus Wiseman, Mar 29 2025 | 2025-03-30T20:24:25 | oeisdata/seq/A382/A382202.seq | 3dc887bb8415b9de7ecd866f68157e92 |
A382203 | Number of normal multiset partitions of weight n into constant multisets with distinct sums. | [
"1",
"1",
"2",
"4",
"9",
"19",
"37",
"76",
"159",
"326",
"671",
"1376",
"2815",
"5759",
"11774",
"24083",
"49249",
"100632",
"205490",
"419420",
"855799",
"1745889",
"3561867",
"7268240",
"14836127",
"30295633",
"61888616"
]
| [
"nonn",
"more"
]
| 13 | 0 | 3 | [
"A000670",
"A001055",
"A007716",
"A019536",
"A035310",
"A045778",
"A055887",
"A055932",
"A089259",
"A116539",
"A116540",
"A255903",
"A255906",
"A275780",
"A279785",
"A279786",
"A304969",
"A317532",
"A317583",
"A321469",
"A326517",
"A326518",
"A326519",
"A326535",
"A333217",
"A381633",
"A381635",
"A381636",
"A381718",
"A381806",
"A381870",
"A382203",
"A382204",
"A382216",
"A382428",
"A382429"
]
| null | Gus Wiseman, Mar 26 2025 | 2025-04-04T23:42:07 | oeisdata/seq/A382/A382203.seq | 2847e1d4592ab325641cde5cdb15778f |
A382204 | Number of normal multiset partitions of weight n into constant blocks with a common sum. | [
"1",
"1",
"2",
"3",
"4",
"4",
"7",
"5",
"8",
"8",
"10",
"8",
"15",
"9",
"14",
"15",
"17",
"13",
"22",
"14",
"25",
"21",
"23",
"19",
"34",
"24",
"29",
"28",
"37",
"27",
"45",
"29",
"44",
"38",
"43",
"43",
"59",
"40",
"51",
"48",
"69",
"48",
"71",
"52",
"73",
"69",
"72",
"61",
"93",
"72",
"91",
"77",
"99",
"78",
"105",
"95",
"119",
"95",
"113",
"96",
"146",
"107",
"126",
"123",
"151",
"130"
]
| [
"nonn"
]
| 28 | 0 | 3 | [
"A000670",
"A001055",
"A007716",
"A019536",
"A034691",
"A034729",
"A035310",
"A045778",
"A055887",
"A055932",
"A089259",
"A116539",
"A116540",
"A255903",
"A255906",
"A270995",
"A279785",
"A279789",
"A296119",
"A304969",
"A317532",
"A317583",
"A318360",
"A321469",
"A326518",
"A326520",
"A326535",
"A333217",
"A356945",
"A381635",
"A381636",
"A381716",
"A381718",
"A381806",
"A381870",
"A381995",
"A382203",
"A382204",
"A382216",
"A382429"
]
| null | Gus Wiseman, Mar 26 2025 | 2025-04-05T12:01:55 | oeisdata/seq/A382/A382204.seq | 4887a7bdff44390ff04775779161d6b3 |
A382205 | Number of minimum connected dominating sets in the n-halved cube graph. | [
"1",
"2",
"4",
"24",
"240",
"1440",
"80640"
]
| [
"nonn",
"more"
]
| 4 | 1 | 2 | null | null | Eric W. Weisstein, Mar 18 2025 | 2025-03-18T21:44:25 | oeisdata/seq/A382/A382205.seq | d6ae27413d40cb900798dd74b291017b |
A382206 | Number of minimum connected dominating sets in the n X n king graph. | [
"1",
"4",
"1",
"21",
"1",
"21",
"843",
"720",
"556841",
"99357",
"458",
"32",
"3600",
"30580044",
"826720",
"4"
]
| [
"nonn",
"more"
]
| 25 | 1 | 2 | [
"A289180",
"A347554",
"A370428",
"A381730",
"A382206"
]
| null | Eric W. Weisstein, Mar 18 2025 | 2025-03-31T15:20:41 | oeisdata/seq/A382/A382206.seq | d2009128af68d6269bbfeb02a758f9c7 |
A382207 | Number of minimum connected dominating sets in the n X n knight graph. | [
"1",
"0",
"0",
"64",
"4",
"18",
"78",
"184",
"648",
"344"
]
| [
"nonn",
"more"
]
| 16 | 1 | 4 | [
"A382047",
"A382207"
]
| null | Eric W. Weisstein, Mar 18 2025 | 2025-03-21T07:00:27 | oeisdata/seq/A382/A382207.seq | 02c2b248ecf9f989c3ac2e9d95482e13 |
A382208 | Numbers k for which pi(bigomega(k)) = omega(k). | [
"1",
"4",
"9",
"12",
"18",
"20",
"24",
"25",
"28",
"36",
"40",
"44",
"45",
"49",
"50",
"52",
"54",
"56",
"63",
"68",
"75",
"76",
"88",
"92",
"98",
"99",
"100",
"104",
"116",
"117",
"120",
"121",
"124",
"135",
"136",
"147",
"148",
"152",
"153",
"164",
"168",
"169",
"171",
"172",
"175",
"180",
"184",
"188",
"189",
"196",
"207",
"212",
"225",
"232",
"236",
"240",
"242",
"244",
"245"
]
| [
"nonn"
]
| 22 | 1 | 2 | [
"A000720",
"A001221",
"A001222",
"A001248",
"A046386",
"A054753",
"A065036",
"A085986",
"A162143",
"A179644",
"A179693",
"A179700",
"A179704",
"A382208"
]
| null | Felix Huber, Mar 30 2025 | 2025-04-05T15:27:00 | oeisdata/seq/A382/A382208.seq | 7e179f09919867a163e8ec89551392f1 |
A382209 | Numbers k such that 10+k and 10*k are perfect squares. | [
"90",
"136890",
"197402490",
"284654260890",
"410471246808090",
"591899253243012090",
"853518312705176632890",
"1230772815021611461622490",
"1774773545742851022483004890",
"2559222222188376152809031436090",
"3690396669622092669499600847844090",
"5321549438372835441042271613559748890"
]
| [
"nonn",
"easy"
]
| 102 | 1 | 1 | [
"A005667",
"A008843",
"A075796",
"A081071",
"A097315",
"A158490",
"A173127",
"A245226",
"A382209",
"A383734"
]
| null | Emilio Martín, Mar 18 2025 | 2025-05-22T05:18:59 | oeisdata/seq/A382/A382209.seq | 7f328292a98ee8b3f1299c0e14a945fd |
A382210 | Irregular triangle read by rows: T(n,k) = k^2 - k + (A003173(n) + 1)/4 with 1 <= k < (A003173(n) + 1)/4. | [
"2",
"3",
"5",
"5",
"7",
"11",
"17",
"11",
"13",
"17",
"23",
"31",
"41",
"53",
"67",
"83",
"101",
"17",
"19",
"23",
"29",
"37",
"47",
"59",
"73",
"89",
"107",
"127",
"149",
"173",
"199",
"227",
"257",
"41",
"43",
"47",
"53",
"61",
"71",
"83",
"97",
"113",
"131",
"151",
"173",
"197",
"223",
"251",
"281",
"313",
"347",
"383",
"421",
"461",
"503",
"547",
"593",
"641",
"691",
"743",
"797",
"853",
"911",
"971",
"1033",
"1097",
"1163",
"1231",
"1301",
"1373",
"1447",
"1523",
"1601"
]
| [
"nonn",
"easy",
"fini",
"full",
"tabf"
]
| 7 | 4 | 1 | [
"A003173",
"A048058",
"A302445",
"A382210"
]
| null | Stefano Spezia, Mar 18 2025 | 2025-03-18T21:41:15 | oeisdata/seq/A382/A382210.seq | bc20c258b3e67f7310123e6034e9c41b |
A382211 | Prime of the form p^q + q^r + r^p, for primes p, q and r. | [
"61",
"181",
"2557",
"98057",
"338323",
"8389141",
"48829699",
"536871757",
"1162268353",
"2147484613",
"2199023257237",
"27368747340087430811",
"196525143636054676607",
"4656612873077421210401",
"239072435917782732706099",
"1978419655679387077928203",
"9671406556917033397656301"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A123207",
"A382211"
]
| null | Karst Koymans, Mar 18 2025 | 2025-03-25T23:17:55 | oeisdata/seq/A382/A382211.seq | e5a4a2160298774af2f06f07bf9b0968 |
A382212 | Number of labeled Eulerian oriented graphs with n nodes without isolated vertices. | [
"0",
"0",
"2",
"6",
"168",
"6700",
"726360",
"202827786"
]
| [
"nonn",
"more"
]
| 8 | 1 | 3 | [
"A007081",
"A382212"
]
| null | Bert Dobbelaere, Mar 18 2025 | 2025-03-19T09:04:17 | oeisdata/seq/A382/A382212.seq | 279f8ee5b3962c58244d097b45a49cbe |
A382213 | Largest squarefree number dividing the numerator of harmonic number H(n). | [
"1",
"3",
"11",
"5",
"137",
"7",
"33",
"761",
"7129",
"671",
"83711",
"6617",
"1145993",
"1171733",
"1195757",
"143327",
"42142223",
"751279",
"275295799",
"55835135",
"18858053",
"830139",
"444316699",
"1347822955",
"34052522467",
"34395742267",
"312536252003",
"10876020307",
"214582477009",
"300151059037",
"290774257297357"
]
| [
"nonn"
]
| 46 | 1 | 2 | [
"A001008",
"A002805",
"A007913",
"A333196",
"A382213",
"A382329"
]
| null | Ali Sada, Mar 22 2025 | 2025-04-24T13:20:47 | oeisdata/seq/A382/A382213.seq | 27a56c36059262f4c934bbaa1a2e887d |
A382214 | Number of normal multisets of size n that can be partitioned into a set of sets. | [
"1",
"1",
"1",
"3",
"5",
"11",
"23",
"48",
"101",
"210",
"436",
"894"
]
| [
"nonn",
"more"
]
| 15 | 0 | 4 | [
"A000110",
"A000670",
"A001055",
"A007716",
"A019536",
"A034691",
"A035310",
"A045778",
"A050320",
"A050326",
"A050342",
"A055932",
"A089259",
"A116539",
"A116540",
"A255903",
"A255906",
"A270995",
"A279785",
"A292432",
"A292444",
"A293243",
"A296119",
"A296120",
"A317532",
"A318360",
"A318361",
"A326517",
"A326519",
"A333217",
"A358914",
"A381633",
"A381718",
"A381990",
"A381992",
"A381996",
"A382077",
"A382078",
"A382200",
"A382202",
"A382214",
"A382216",
"A382428",
"A382458",
"A382459",
"A382460"
]
| null | Gus Wiseman, Mar 29 2025 | 2025-03-30T20:24:20 | oeisdata/seq/A382/A382214.seq | ffcfe6cf9dea1397905a5ea83c8a00c4 |
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