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2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
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stringlengths 29
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A359601 | Dirichlet inverse of A244042, where A244042(n) replaces 2's with 0's in the ternary representation of n. | [
"1",
"0",
"-3",
"-4",
"-3",
"0",
"-1",
"0",
"0",
"-10",
"-9",
"12",
"-13",
"-12",
"9",
"6",
"-9",
"0",
"-1",
"24",
"3",
"-4",
"-3",
"0",
"8",
"0",
"0",
"-20",
"-27",
"30",
"-31",
"-30",
"27",
"-28",
"-21",
"0",
"-37",
"-36",
"39",
"40",
"-39",
"36",
"-37",
"36",
"0",
"-28",
"-27",
"-18",
"-30",
"30",
"27",
"76",
"-27",
"0",
"53",
"96",
"3",
"-4",
"-3",
"-72",
"-1",
"0",
"0",
"6",
"69",
"12",
"-13",
"60",
"9",
"82",
"-9",
"0",
"-1",
"0",
"-24",
"4",
"15"
]
| [
"sign",
"base",
"easy",
"look"
]
| 12 | 1 | 3 | [
"A056911",
"A244042",
"A300821",
"A323239",
"A337945",
"A359601",
"A359602"
]
| null | Antti Karttunen, Jan 11 2023 | 2023-01-11T20:59:45 | oeisdata/seq/A359/A359601.seq | 2f0bd9963edcf7556c41c64b6f0a7268 |
A359602 | Sum of A244042 and its Dirichlet inverse, where A244042(n) replaces 2's with 0's in the ternary representation of n. | [
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"9",
"0",
"0",
"24",
"0",
"0",
"18",
"16",
"0",
"0",
"0",
"24",
"6",
"0",
"0",
"0",
"9",
"0",
"27",
"8",
"0",
"60",
"0",
"0",
"54",
"0",
"6",
"36",
"0",
"0",
"78",
"80",
"0",
"72",
"0",
"72",
"27",
"0",
"0",
"12",
"1",
"60",
"54",
"104",
"0",
"0",
"54",
"96",
"6",
"0",
"0",
"-72",
"0",
"0",
"9",
"16",
"78",
"24",
"0",
"72",
"18",
"92",
"0",
"0",
"0",
"0",
"-21",
"8",
"18",
"0",
"0",
"-84",
"81",
"0",
"0",
"144",
"54",
"0",
"162",
"32"
]
| [
"sign",
"base",
"easy"
]
| 10 | 1 | 1 | [
"A053850",
"A244042",
"A353569",
"A359601",
"A359602"
]
| null | Antti Karttunen, Jan 11 2023 | 2023-01-11T20:59:51 | oeisdata/seq/A359/A359602.seq | e7ed78f0059badd289beeefbe8d4155f |
A359603 | Dirichlet inverse of function f(n) = 1+(A003415(n)*A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | [
"1",
"-4",
"-7",
"-21",
"-19",
"30",
"-11",
"51",
"-132",
"-164",
"-91",
"-11",
"-51",
"-588",
"-935",
"-5904",
"-451",
"-1402",
"-251",
"-5979",
"-7347",
"-13898",
"-2251",
"-25507",
"-12140",
"-27718",
"-99060",
"-174307",
"-11251",
"11610",
"-15",
"52653",
"685",
"2410",
"-1095",
"24800",
"-71",
"-198",
"-2647",
"53673",
"-631",
"61020",
"-351",
"94173",
"-20052",
"-21368",
"-3151",
"207838"
]
| [
"sign",
"easy"
]
| 11 | 1 | 2 | [
"A003415",
"A276086",
"A358669",
"A359427",
"A359589",
"A359590",
"A359603",
"A359604"
]
| null | Antti Karttunen, Jan 11 2023 | 2023-01-11T20:59:58 | oeisdata/seq/A359/A359603.seq | 9028e96d1a568f7dc32b55b212041d68 |
A359604 | a(n) = A359603(n) mod 60. | [
"1",
"56",
"53",
"39",
"41",
"30",
"49",
"51",
"48",
"16",
"29",
"49",
"9",
"12",
"25",
"36",
"29",
"38",
"49",
"21",
"33",
"22",
"29",
"53",
"40",
"2",
"0",
"53",
"29",
"30",
"45",
"33",
"25",
"10",
"45",
"20",
"49",
"42",
"53",
"33",
"29",
"0",
"9",
"33",
"48",
"52",
"29",
"58",
"40",
"58",
"13",
"13",
"29",
"26",
"17",
"33",
"33",
"22",
"29",
"31",
"21",
"8",
"44",
"57",
"41",
"14",
"49",
"9",
"13",
"52",
"29",
"16",
"9",
"42",
"40",
"53",
"21",
"20"
]
| [
"nonn",
"easy"
]
| 8 | 1 | 2 | [
"A358669",
"A358765",
"A359590",
"A359603",
"A359604"
]
| null | Antti Karttunen, Jan 11 2023 | 2023-01-11T21:00:04 | oeisdata/seq/A359/A359604.seq | 4f7d3d8ba8e56f312742e26a57d5a82b |
A359605 | a(n) = 1 if A355690(n) is positive (+1), otherwise 0. | [
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0"
]
| [
"nonn",
"easy"
]
| 9 | 1 | null | [
"A355690",
"A359590",
"A359605",
"A359606"
]
| null | Antti Karttunen, Jan 12 2023 | 2023-02-18T22:48:42 | oeisdata/seq/A359/A359605.seq | be0a6af987e83e43ee0178642bb74cc7 |
A359606 | a(n) = 1 if A355690(n) is negative (-1), otherwise 0. | [
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1"
]
| [
"nonn",
"easy"
]
| 8 | 1 | null | [
"A355690",
"A359590",
"A359605",
"A359606"
]
| null | Antti Karttunen, Jan 12 2023 | 2023-02-18T22:48:38 | oeisdata/seq/A359/A359606.seq | 5554cbe2a39d5f6ac80ac0dafc7448e8 |
A359607 | Terms of A046337 for which A358777 is zero, where the latter is the Dirichlet inverse of former's characteristic function. | [
"81",
"625",
"729",
"1215",
"1701",
"2401",
"2673",
"3159",
"4131",
"4617",
"5589",
"6561",
"7047",
"7533",
"8991",
"9375",
"9963",
"10449",
"10935",
"11421",
"12879",
"14337",
"14641",
"14823",
"15309",
"15625",
"16281",
"17253",
"17739",
"18225",
"19197",
"20169",
"21627",
"21875",
"23571",
"24057",
"24543",
"25029",
"25515",
"26001",
"26487",
"27459",
"28431",
"28561",
"30861",
"31833"
]
| [
"nonn"
]
| 5 | 1 | 1 | [
"A046337",
"A353557",
"A358777",
"A359607"
]
| null | Antti Karttunen, Jan 12 2023 | 2023-01-12T13:56:12 | oeisdata/seq/A359/A359607.seq | ca6b5ed5e870b4701b9ed3b299c14622 |
A359608 | Indices at which A358777 attains a new value. | [
"1",
"2",
"9",
"225",
"315",
"1155",
"2835",
"4725",
"10395",
"11025",
"17325",
"45045",
"70875",
"93555",
"99225",
"155925",
"165375",
"255255",
"259875",
"363825",
"405405",
"637875",
"675675",
"1063125",
"1334025",
"1488375",
"1576575",
"2297295",
"2338875",
"2480625",
"3274425",
"3472875",
"3648645",
"3828825",
"5457375",
"6081075",
"10135125",
"12006225",
"12733875",
"13395375"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A046337",
"A353557",
"A358777",
"A359598",
"A359600",
"A359608",
"A359609"
]
| null | Antti Karttunen, Jan 12 2023 | 2024-01-03T17:19:20 | oeisdata/seq/A359/A359608.seq | 65a3a71c302871d64b32c5cfe640838f |
A359609 | Distinct values of A358777 in the order of their appearance. | [
"1",
"0",
"-1",
"2",
"3",
"5",
"-2",
"-6",
"-11",
"-10",
"-18",
"-33",
"9",
"6",
"14",
"27",
"22",
"-61",
"42",
"66",
"52",
"-4",
"126",
"-12",
"104",
"-26",
"198",
"241",
"-51",
"-40",
"-78",
"-58",
"-24",
"378",
"-174",
"-153",
"-339",
"-268",
"-254",
"10",
"-522",
"723",
"15",
"-392",
"-300",
"20",
"-762",
"30",
"58",
"-1017",
"83",
"64",
"174",
"-1176",
"124"
]
| [
"sign"
]
| 5 | 1 | 4 | [
"A358777",
"A359599",
"A359608",
"A359609"
]
| null | Antti Karttunen, Jan 12 2023 | 2023-01-12T13:56:20 | oeisdata/seq/A359/A359609.seq | 7ef9f492ce0770010393695062fd105d |
A359610 | Numbers k such that the sum of the 5th powers of the digits of k is prime. | [
"11",
"101",
"110",
"111",
"119",
"128",
"133",
"182",
"188",
"191",
"218",
"223",
"227",
"229",
"232",
"247",
"272",
"274",
"281",
"292",
"313",
"322",
"331",
"337",
"346",
"359",
"364",
"368",
"373",
"377",
"379",
"386",
"395",
"397",
"427",
"436",
"463",
"472",
"478",
"487",
"539",
"557",
"568",
"575",
"577",
"586",
"593",
"634",
"638",
"643",
"658",
"667"
]
| [
"nonn",
"base",
"easy"
]
| 28 | 1 | 1 | [
"A028834",
"A031974",
"A055014",
"A108662",
"A210767",
"A225534",
"A245358",
"A359610"
]
| null | José Hernández, Jan 06 2023 | 2023-01-28T03:55:31 | oeisdata/seq/A359/A359610.seq | 515877884074fea1f55edb2d6f402579 |
A359611 | The lexicographically earliest "Increasing Term Fractal Jump Sequence". | [
"1",
"2",
"20",
"22",
"100",
"200",
"201",
"1000",
"20000",
"20001",
"110000",
"2000000",
"2000001",
"110100000",
"200000000",
"200000001",
"1101001000000",
"2000000000020",
"2000000010101",
"10100010000000",
"20000000000002",
"20020000000001",
"101001010010000",
"100000000200000000000000"
]
| [
"nonn",
"base"
]
| 15 | 1 | 2 | [
"A105395",
"A105396",
"A105397",
"A105398",
"A105647",
"A359385",
"A359611"
]
| null | Tyler Busby, Jan 06 2023 | 2023-01-30T07:42:52 | oeisdata/seq/A359/A359611.seq | 288941bf7564106320c7e3b7f5cf198c |
A359612 | Largest prime factor with minimal exponent in canonical prime factorization of n. | [
"2",
"3",
"2",
"5",
"3",
"7",
"2",
"3",
"5",
"11",
"3",
"13",
"7",
"5",
"2",
"17",
"2",
"19",
"5",
"7",
"11",
"23",
"3",
"5",
"13",
"3",
"7",
"29",
"5",
"31",
"2",
"11",
"17",
"7",
"3",
"37",
"19",
"13",
"5",
"41",
"7",
"43",
"11",
"5",
"23",
"47",
"3",
"7",
"2",
"17",
"13",
"53",
"2",
"11",
"7",
"19",
"29",
"59",
"5",
"61",
"31",
"7",
"2",
"13",
"11",
"67",
"17",
"23",
"7",
"71",
"3",
"73",
"37",
"3"
]
| [
"nonn"
]
| 30 | 2 | 1 | [
"A006530",
"A067695",
"A356838",
"A356840",
"A359612"
]
| null | Jens Ahlström, Jan 06 2023 | 2023-02-08T10:10:23 | oeisdata/seq/A359/A359612.seq | cee307df736abd369778bf5a02e2a099 |
A359613 | Greatest k such that a polynomial f(x) with nonnegative integral coefficients with degree at most k is irreducible if f(n) is a prime. | [
"6",
"9",
"12",
"15",
"19",
"22",
"25",
"28",
"31",
"34",
"37",
"40",
"44",
"47",
"50",
"53",
"56",
"59",
"62"
]
| [
"nonn",
"hard",
"more",
"nice"
]
| 13 | 2 | 1 | [
"A253280",
"A359613"
]
| null | Ondrej Kutal, Jan 07 2023 | 2023-01-08T10:13:16 | oeisdata/seq/A359/A359613.seq | 299afc9c37ed7bf6b7c84b920c654dfc |
A359614 | a(n) is the minimal determinant of an n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary. | [
"1",
"1",
"-3",
"-30",
"-256",
"-7595",
"-358301",
"-7665804",
"-227965955",
"-13089461984",
"-2467071630448"
]
| [
"sign",
"hard",
"more"
]
| 23 | 0 | 3 | [
"A350953",
"A359559",
"A359561",
"A359614",
"A359615",
"A359616",
"A359617"
]
| null | Stefano Spezia, Jan 07 2023 | 2023-01-25T20:50:05 | oeisdata/seq/A359/A359614.seq | 26cfaa91ba30c9bca06bacaa99971700 |
A359615 | a(n) is the maximal determinant of an n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary. | [
"1",
"1",
"3",
"9",
"512",
"9195",
"242931",
"7459494",
"524426191",
"17012915860",
"773407040859"
]
| [
"nonn",
"hard",
"more"
]
| 23 | 0 | 3 | [
"A350954",
"A359559",
"A359561",
"A359614",
"A359615",
"A359616",
"A359617"
]
| null | Stefano Spezia, Jan 07 2023 | 2023-01-25T20:50:17 | oeisdata/seq/A359/A359615.seq | 233913f709cfea3a037273888e8a3be5 |
A359616 | a(n) is the minimal permanent of an n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary. | [
"1",
"1",
"5",
"18",
"245",
"2249",
"57213",
"947177",
"50431724",
"1282453618"
]
| [
"nonn",
"hard",
"more"
]
| 23 | 0 | 3 | [
"A351019",
"A359560",
"A359562",
"A359614",
"A359615",
"A359616",
"A359617"
]
| null | Stefano Spezia, Jan 07 2023 | 2023-01-25T21:10:57 | oeisdata/seq/A359/A359616.seq | 982871f85d394089642a683db1558a26 |
A359617 | a(n) is the maximal permanent of an n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with all off-diagonal elements purely imaginary. | [
"1",
"1",
"5",
"54",
"980",
"26775",
"1061841",
"56647472",
"4103545288",
"367479636012"
]
| [
"nonn",
"hard",
"more"
]
| 21 | 0 | 3 | [
"A351020",
"A359560",
"A359562",
"A359614",
"A359615",
"A359616",
"A359617"
]
| null | Stefano Spezia, Jan 07 2023 | 2023-01-25T22:07:22 | oeisdata/seq/A359/A359617.seq | b0c419ed7199a051284a5e1682882334 |
A359618 | a(n) is the minimal absolute value of the determinant of a nonsingular n X n Hermitian Toeplitz matrix using all the integers 1, 2, ..., n and with off-diagonal elements purely imaginary. | [
"1",
"1",
"3",
"9",
"16",
"21",
"20",
"17",
"131",
"62",
"1"
]
| [
"nonn",
"hard",
"more"
]
| 11 | 0 | 3 | [
"A348891",
"A358325",
"A359559",
"A359561",
"A359614",
"A359615",
"A359616",
"A359617",
"A359618"
]
| null | Stefano Spezia, Jan 21 2023 | 2023-01-25T02:54:30 | oeisdata/seq/A359/A359618.seq | eee159d8088b44d36e9fcc6da6a4d304 |
A359619 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=1, after n iterations of constructing circles from all current vertices using only a compass, starting with one vertex. See the Comments. | [
"0",
"1",
"0",
"0",
"2",
"1",
"0",
"1",
"16",
"4",
"0",
"16",
"2470",
"3599",
"902",
"168",
"14"
]
| [
"nonn",
"more",
"hard",
"tabf"
]
| 5 | 1 | 5 | [
"A359009",
"A359061",
"A359258",
"A359569",
"A359570",
"A359571",
"A359619"
]
| null | Scott R. Shannon, Jan 07 2023 | 2023-01-09T09:32:10 | oeisdata/seq/A359/A359619.seq | 834f5796235f769f6c3c775c108c108a |
A359620 | Number of edge cuts in the n-antiprism graph. | [
"1",
"4",
"62",
"1440",
"30346",
"589556",
"10858046",
"192811016",
"3336192082",
"56642890908",
"948242161382",
"15706527467824",
"258068117928826",
"4214126476848580",
"68489478048350222",
"1109069751830483544",
"17909240724783047842",
"288575383662532867820",
"4642173797092097149238"
]
| [
"nonn"
]
| 23 | 0 | 2 | [
"A359620",
"A359621"
]
| null | Eric W. Weisstein, Jan 07 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359620.seq | adf1443fb10ff3850692679915567fae |
A359621 | Number of edge cuts in the n-prism graph. | [
"1",
"4",
"31",
"314",
"3013",
"27060",
"232671",
"1947118",
"16021801",
"130447976",
"1055068595",
"8498016994",
"68269451069",
"547562782044",
"4387403278023",
"35132904838614",
"281226897433681",
"2250607478637648",
"18008682685966299",
"144087851840540874",
"1152791046751807845"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A359620",
"A359621"
]
| null | Eric W. Weisstein, Jan 07 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359621.seq | d172c33ef38e21f602c5329c1399b3f9 |
A359622 | Number of edge cuts in the n-Moebius ladder. | [
"1",
"26",
"307",
"3004",
"27049",
"232658",
"1947103",
"16021784",
"130447957",
"1055068574",
"8498016971",
"68269451044",
"547562782017",
"4387403277994",
"35132904838583",
"281226897433648",
"2250607478637613",
"18008682685966262",
"144087851840540835",
"1152791046751807804",
"9222750661998396185",
"73784021962658308290"
]
| [
"nonn",
"easy"
]
| 14 | 1 | 2 | null | null | Eric W. Weisstein, Jan 07 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359622.seq | e8ccc675a4271b1cff38a86c984ea785 |
A359623 | a(n) is the least integer of the form sum(X)/sum(Y) where {X, Y} runs through the partitions of the divisors of n into two nonempty sets (and sum(Z) is the sum of the elements of Z). | [
"2",
"3",
"6",
"5",
"1",
"7",
"2",
"12",
"2",
"11",
"1",
"13",
"2",
"2",
"30",
"17",
"2",
"19",
"1",
"3",
"2",
"23",
"1",
"30",
"2",
"3",
"1",
"29",
"1",
"31",
"2",
"3",
"2",
"3",
"6",
"37",
"2",
"3",
"1",
"41",
"1",
"43",
"2",
"5",
"2",
"47",
"1",
"56",
"2",
"3",
"6",
"53",
"1",
"5",
"1",
"3",
"2",
"59",
"1",
"61",
"2",
"7",
"126",
"5",
"1",
"67",
"5",
"3",
"1",
"71",
"2",
"73",
"2",
"3",
"6",
"7",
"1",
"79",
"1"
]
| [
"nonn"
]
| 74 | 2 | 1 | [
"A039653",
"A083207",
"A359623"
]
| null | Rémy Sigrist, Feb 17 2023 | 2023-02-19T09:18:06 | oeisdata/seq/A359/A359623.seq | dabe6e999fd5e7f57c14eebdda994bbc |
A359624 | Centered triangular numbers which are products of three distinct primes. | [
"1054",
"1786",
"2110",
"2710",
"4294",
"5134",
"6634",
"7885",
"8326",
"10210",
"12835",
"13114",
"14554",
"17014",
"22510",
"24769",
"25546",
"26335",
"30889",
"32635",
"36271",
"42085",
"44635",
"45154",
"47794",
"49414",
"52174",
"52735",
"53866",
"56746",
"58510",
"61510",
"63346",
"66466",
"68374",
"71614",
"73594",
"75601",
"76954",
"84610",
"88210"
]
| [
"nonn"
]
| 19 | 1 | 1 | [
"A005448",
"A007304",
"A359624"
]
| null | Massimo Kofler, Jan 08 2023 | 2023-01-27T13:34:13 | oeisdata/seq/A359/A359624.seq | 4f8003a07403408d5b941f032d73962e |
A359625 | Least number m such that denominator(sigma(m)/(m+1)) = n, or zero if no such m exists. | [
"2",
"1",
"8",
"95",
"4",
"143",
"6",
"63",
"26",
"9",
"10",
"16415",
"12",
"111",
"44",
"255",
"16",
"273023",
"18",
"159",
"62",
"175",
"22",
"575",
"74",
"25",
"80",
"671",
"28",
"3599",
"30",
"511",
"395",
"441",
"34",
"5183",
"36",
"303",
"116",
"8639",
"40",
"163295",
"42",
"1055",
"134",
"101567",
"46",
"19191876318719",
"48",
"49",
"152",
"415",
"52",
"3887"
]
| [
"nonn"
]
| 31 | 1 | 1 | [
"A063906",
"A162657",
"A339966",
"A359625"
]
| null | Michel Marcus, Jan 07 2023 | 2023-08-28T08:21:15 | oeisdata/seq/A359/A359625.seq | c10e329e57680040212186fee3dc1aa2 |
A359626 | a(n) is equal to the number of filled unit triangles in a regular triangle whose coloring scheme is given in the comments. | [
"1",
"4",
"9",
"15",
"21",
"27",
"34",
"43",
"54",
"66",
"78",
"90",
"103",
"118",
"135",
"153",
"171",
"189",
"208",
"229",
"252",
"276",
"300",
"324",
"349",
"376",
"405",
"435",
"465",
"495",
"526",
"559",
"594",
"630",
"666",
"702",
"739",
"778",
"819",
"861",
"903",
"945",
"988",
"1033",
"1080",
"1128",
"1176",
"1224",
"1273",
"1324",
"1377",
"1431",
"1485",
"1539",
"1594",
"1651",
"1710",
"1770",
"1830",
"1890",
"1951",
"2014",
"2079"
]
| [
"nonn",
"easy"
]
| 21 | 1 | 2 | [
"A000096",
"A077859",
"A359626"
]
| null | Nicolay Avilov, Apr 20 2023 | 2023-08-05T21:21:50 | oeisdata/seq/A359/A359626.seq | 52fcfb7c9234376aecd56b6b65b969ec |
A359627 | Irregular table read by rows; the n-th row lists the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit. | [
"1",
"1",
"2",
"1",
"1",
"2",
"4",
"1",
"5",
"1",
"2",
"3",
"1",
"1",
"2",
"4",
"8",
"1",
"9",
"1",
"2",
"10",
"1",
"1",
"2",
"3",
"4",
"6",
"1",
"1",
"2",
"1",
"1",
"2",
"4",
"8",
"16",
"1",
"17",
"1",
"2",
"3",
"9",
"18",
"1",
"1",
"2",
"4",
"5",
"20",
"1",
"21",
"1",
"2",
"1",
"1",
"2",
"3",
"4",
"6",
"8",
"12",
"1",
"5",
"1",
"2",
"1",
"9",
"1",
"2",
"4",
"7",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"4",
"8",
"16",
"32"
]
| [
"nonn",
"base",
"tabf"
]
| 24 | 1 | 3 | [
"A307314",
"A359079",
"A359627",
"A359708"
]
| null | Rémy Sigrist, Jan 12 2023 | 2024-01-25T12:35:02 | oeisdata/seq/A359/A359627.seq | 18fc406b4da9ffa6778e47bcda901af0 |
A359628 | Triangle read by rows: T(n,k) is the maximum number of connected endofunctions that are spanning subgraphs of a semi-regular loopless digraph on n vertices each with out-degree k. | [
"1",
"1",
"8",
"1",
"16",
"78",
"1",
"32",
"234",
"944",
"1",
"64",
"710",
"3776",
"13800",
"1",
"128"
]
| [
"nonn",
"tabl",
"more"
]
| 30 | 2 | 3 | [
"A000435",
"A359628"
]
| null | Yali Harrary, Jan 08 2023 | 2023-02-16T05:27:35 | oeisdata/seq/A359/A359628.seq | 0eeb7d84679df0be31e5f9e722cf3c8e |
A359629 | Indices of the primes of |A007442|. | [
"1",
"5",
"7",
"8",
"11",
"13",
"40",
"106",
"132",
"154",
"478",
"647",
"1576",
"2067",
"2656",
"3837",
"5158",
"6985",
"7844",
"9777",
"11607",
"21027",
"22638",
"31979",
"33592",
"34279"
]
| [
"nonn",
"more"
]
| 30 | 1 | 2 | [
"A007442",
"A359629"
]
| null | Robert G. Wilson v, Jan 08 2023 | 2025-06-20T20:22:53 | oeisdata/seq/A359/A359629.seq | 14a293655c5a6ed283b86a6e43979628 |
A359630 | Primes p such that 10^p+3 or 10^p+9 is also prime. | [
"2",
"3",
"5",
"11",
"17",
"101",
"107",
"26927",
"48109"
]
| [
"nonn",
"base",
"hard",
"more"
]
| 43 | 1 | 1 | [
"A049054",
"A088275",
"A359630"
]
| null | Mikk Heidemaa, Jan 08 2023 | 2025-02-09T19:03:09 | oeisdata/seq/A359/A359630.seq | f6a5c140bd4a95fc60e85419f7dc9fe8 |
A359631 | a(n) is the smallest positive integer which can be represented as the sum of distinct positive Fibonacci n-step numbers (with a single type of 1) in exactly n ways, or -1 if no such integer exists. | [
"1",
"3",
"44",
"416",
"26815",
"464031"
]
| [
"nonn",
"more"
]
| 20 | 1 | 2 | [
"A000119",
"A013583",
"A117546",
"A287656",
"A288120",
"A359631"
]
| null | Ilya Gutkovskiy, Jan 08 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359631.seq | 1618030e0af7f56a489e482cd1bf7286 |
A359632 | Sequence of gaps between deletions of multiples of 7 in step 4 of the sieve of Eratosthenes. | [
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3",
"12",
"7",
"4",
"7",
"4",
"7",
"12",
"3"
]
| [
"nonn",
"easy"
]
| 58 | 1 | 1 | [
"A002110",
"A005867",
"A007395",
"A010701",
"A010705",
"A054272",
"A236175",
"A359632"
]
| null | Alexandre Herrera, Jan 08 2023 | 2024-07-02T02:16:38 | oeisdata/seq/A359/A359632.seq | 490cc42969a2f3ead9b5f50e34826c9e |
A359633 | a(n) is the least prime > a(n-1) such that a(n-1) and a(n) are quadratic residues mod each other. | [
"2",
"7",
"29",
"53",
"59",
"137",
"139",
"173",
"179",
"193",
"197",
"223",
"241",
"251",
"317",
"353",
"383",
"389",
"409",
"419",
"457",
"461",
"467",
"541",
"557",
"563",
"593",
"601",
"607",
"701",
"743",
"761",
"769",
"773",
"787",
"797",
"811",
"853",
"857",
"859",
"881",
"883",
"929",
"937",
"941",
"947",
"977",
"991",
"1009",
"1013",
"1019",
"1033",
"1039",
"1049",
"1051",
"1097",
"1129",
"1153",
"1171"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A034794",
"A034795",
"A359633"
]
| null | Robert Israel, Jan 07 2023 | 2023-01-15T15:23:09 | oeisdata/seq/A359/A359633.seq | 68f59bc41810e74a6997778bfb00e352 |
A359634 | a(0)=1 and thereafter a(n) is the length of the longest contiguous group of terms in the sequence thus far that add up to n; if no such group exists, set a(n)=0. | [
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"3",
"4",
"5",
"4",
"5",
"6",
"4",
"5",
"6",
"7",
"6",
"7",
"8",
"5",
"7",
"8",
"9",
"7",
"6",
"8",
"9",
"10",
"6",
"9",
"10",
"11",
"9",
"8",
"10",
"11",
"12",
"9",
"10",
"9",
"11",
"12",
"13",
"7",
"12",
"13",
"14",
"12",
"11",
"13",
"14",
"15",
"11",
"13",
"11",
"14",
"15",
"16",
"13",
"6",
"14",
"13",
"15",
"16",
"17",
"13",
"15",
"12",
"16",
"17",
"18",
"15",
"8",
"16",
"14",
"17",
"18",
"19",
"15",
"16",
"12",
"17",
"14",
"18",
"19",
"20"
]
| [
"nonn"
]
| 25 | 0 | 3 | [
"A138099",
"A331614",
"A358537",
"A359634"
]
| null | Neal Gersh Tolunsky, Jan 08 2023 | 2023-03-09T04:21:11 | oeisdata/seq/A359/A359634.seq | 11373a5a3bf28a29c9d15d3e524e5c92 |
A359635 | a(n) = A162657(n)/n. | [
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"4",
"1",
"8",
"3",
"1",
"1",
"26",
"1",
"24",
"1",
"4",
"1",
"3",
"1",
"2",
"1",
"7",
"1",
"6",
"1",
"1",
"3",
"2",
"1",
"1",
"1",
"4",
"1",
"2",
"1",
"32",
"1",
"4",
"18",
"8",
"1",
"4",
"1",
"1",
"9",
"2",
"1",
"3",
"1",
"8",
"1",
"2",
"1",
"156",
"1",
"32",
"1",
"1",
"1",
"312",
"1",
"2",
"3",
"14",
"1",
"26",
"1",
"2",
"1",
"4",
"1",
"8",
"1",
"2",
"1",
"2",
"1",
"21",
"1",
"4",
"3",
"4",
"1",
"792"
]
| [
"nonn"
]
| 10 | 1 | 6 | [
"A162657",
"A359635"
]
| null | Michel Marcus, Jan 09 2023 | 2023-01-09T13:02:45 | oeisdata/seq/A359/A359635.seq | 9fe75d14bc8c5cc0819545d3bd405c75 |
A359636 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n distinct prime factors. | [
"7",
"19",
"643",
"51427",
"8083633",
"1077940147",
"75582271489",
"34710483181813"
]
| [
"nonn",
"hard",
"more"
]
| 25 | 1 | 1 | [
"A001359",
"A075590",
"A185032",
"A359636"
]
| null | Hugo Pfoertner, Jan 12 2023 | 2023-11-03T06:29:58 | oeisdata/seq/A359/A359636.seq | e1e2690058681b49da401bdf5e3f060a |
A359637 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n prime factors, counted with multiplicity. | [
"7",
"97",
"349",
"13309",
"33613",
"5594749",
"84477247",
"1524981247",
"60924074749"
]
| [
"nonn",
"hard",
"more"
]
| 5 | 2 | 1 | [
"A001222",
"A001359",
"A062502",
"A359636",
"A359637"
]
| null | Hugo Pfoertner, Jan 16 2023 | 2023-01-21T09:32:32 | oeisdata/seq/A359/A359637.seq | 9f6af0aacb4d938897f4c2a573b6e1c9 |
A359638 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have exactly n prime factors, counted with multiplicity. | [
"601",
"1429",
"81547",
"248749",
"27140749",
"310314157",
"3566181247"
]
| [
"nonn",
"more",
"hard"
]
| 4 | 3 | 1 | [
"A001222",
"A001359",
"A062502",
"A359636",
"A359637",
"A359638"
]
| null | Hugo Pfoertner, Jan 16 2023 | 2023-01-28T12:12:41 | oeisdata/seq/A359/A359638.seq | ba747aea1f183ec5cbc0dc0908475062 |
A359639 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n odd prime factors, counted with multiplicity. | [
"97",
"1999",
"101527",
"6666547",
"272572999",
"3819770107",
"410274361249"
]
| [
"nonn",
"hard",
"more"
]
| 4 | 2 | 1 | [
"A001222",
"A001359",
"A087436",
"A359637",
"A359639",
"A359640"
]
| null | Hugo Pfoertner, Jan 16 2023 | 2023-01-30T12:30:03 | oeisdata/seq/A359/A359639.seq | e55127ffef60f7aa5f584a344ff601ef |
A359640 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have exactly n odd prime factors, counted with multiplicity. | [
"307",
"1999",
"101527",
"7146697",
"272572999",
"4809363523"
]
| [
"nonn",
"hard",
"more"
]
| 4 | 2 | 1 | [
"A001222",
"A001359",
"A087436",
"A359637",
"A359639",
"A359640"
]
| null | Hugo Pfoertner, Jan 16 2023 | 2023-01-30T12:29:56 | oeisdata/seq/A359/A359640.seq | 85d6b38fd80f6a81d90224a3e226b458 |
A359641 | a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have exactly n odd prime factors, all with exponent 1. | [
"307",
"8929",
"992263",
"229658167",
"28674536239"
]
| [
"nonn",
"hard",
"more"
]
| 10 | 2 | 1 | [
"A001222",
"A001359",
"A087436",
"A285800",
"A359640",
"A359641"
]
| null | Hugo Pfoertner, Jan 17 2023 | 2023-02-21T17:17:26 | oeisdata/seq/A359/A359641.seq | 7c56289a624cb33c941918e937fb4613 |
A359642 | Number of numbers <= 10^n that are products of 4 distinct primes. | [
"0",
"0",
"16",
"429",
"7039",
"92966",
"1103888",
"12364826",
"133702610",
"1413227318",
"14709861824",
"151469044739",
"1547593008310",
"15721130285808",
"159006397271949",
"1602820838558101",
"16114386617828822",
"161673560523193369",
"1619352576852638084",
"16197963371445222701"
]
| [
"nonn"
]
| 15 | 1 | 3 | [
"A006880",
"A036351",
"A046386",
"A215218",
"A359642"
]
| null | Peter Dolland, Jan 09 2023 | 2025-01-31T16:11:13 | oeisdata/seq/A359/A359642.seq | abb54d9005481e6d6ca479f13b95fc66 |
A359643 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*k,k). | [
"1",
"5",
"37",
"317",
"2885",
"27105",
"259765",
"2523813",
"24768069",
"244941833",
"2437083697",
"24367722725",
"244639635749",
"2464477467769",
"24899468129405",
"252202062544617",
"2560119328830725",
"26038134699958233",
"265278657849511561",
"2706809063101138409",
"27657194997231516145",
"282941098708193905485"
]
| [
"nonn"
]
| 25 | 0 | 2 | [
"A026375",
"A156887",
"A188686",
"A346646",
"A346664",
"A359643"
]
| null | Vaclav Kotesovec, Jan 09 2023 | 2025-04-17T09:34:55 | oeisdata/seq/A359/A359643.seq | 84ce94adda12fa34522940980df03c52 |
A359644 | Number of numbers <= 10^n that are products of 5 distinct primes. | [
"0",
"0",
"0",
"24",
"910",
"18387",
"286758",
"3884936",
"48396263",
"571221133",
"6499261245",
"72047682376",
"783561421371",
"8399470576016",
"89038389261794",
"935562667202846",
"9761003371437806",
"101253973351371824",
"1045354835981786609"
]
| [
"nonn",
"more"
]
| 19 | 1 | 4 | [
"A006880",
"A036351",
"A046387",
"A215218",
"A359642",
"A359644"
]
| null | Peter Dolland, Jan 09 2023 | 2025-06-27T17:28:32 | oeisdata/seq/A359/A359644.seq | d1be1d87010f2b2f9950ded7db503a1c |
A359645 | Number of numbers <= 10^n that are products of 6 distinct primes. | [
"0",
"0",
"0",
"0",
"20",
"1235",
"32396",
"605939",
"9446284",
"131733664",
"1706815354",
"21008871506",
"249145286508",
"2873325692759",
"32433194803107",
"359960491516138",
"3941261642520039",
"42679704453671033",
"457980431402674541"
]
| [
"nonn",
"more"
]
| 18 | 1 | 5 | [
"A006880",
"A036351",
"A067885",
"A215218",
"A359642",
"A359644",
"A359645"
]
| null | Peter Dolland, Jan 09 2023 | 2025-06-27T17:28:17 | oeisdata/seq/A359/A359645.seq | 10c328527858c47243317905d9c48ac2 |
A359646 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial(5*n+k,k). | [
"1",
"7",
"89",
"1273",
"19181",
"297662",
"4707971",
"75459496",
"1221388525",
"19919031781",
"326797222834",
"5387618403526",
"89178832899887",
"1481143718244912",
"24671054686539336",
"411966653603163008",
"6894167059382069485",
"115593504497163747167",
"1941434442814233362939",
"32656575110841643234631"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A001850",
"A114496",
"A156886",
"A156887",
"A359646"
]
| null | Vaclav Kotesovec, Jan 09 2023 | 2023-01-09T21:30:47 | oeisdata/seq/A359/A359646.seq | 7946199dc3356d16b363d5a56bc4cb4e |
A359647 | a(n) = [x^n] hypergeom([1/4, 3/4], [2], 64*x). The central terms of the Motzkin triangle A359364 without zeros. | [
"1",
"6",
"140",
"4620",
"180180",
"7759752",
"356948592",
"17210021400",
"859544957700",
"44123307828600",
"2315270298060720",
"123691561681243920",
"6707888537328997200",
"368417878127146461600",
"20455964090297751153600",
"1146556787261188952159280",
"64797319609481605046295780"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000108",
"A001006",
"A001448",
"A359364",
"A359647"
]
| null | Peter Luschny, Jan 09 2023 | 2023-08-02T09:23:36 | oeisdata/seq/A359/A359647.seq | c0146927ed89e067437b4fa6daad518c |
A359648 | Triangle read by rows. T(n, k) = (n!)^2 / (k! * (n - k)! * (floor(n/2)!)^2 * (floor(n/2) + 1)). | [
"1",
"1",
"1",
"1",
"2",
"1",
"3",
"9",
"9",
"3",
"2",
"8",
"12",
"8",
"2",
"10",
"50",
"100",
"100",
"50",
"10",
"5",
"30",
"75",
"100",
"75",
"30",
"5",
"35",
"245",
"735",
"1225",
"1225",
"735",
"245",
"35",
"14",
"112",
"392",
"784",
"980",
"784",
"392",
"112",
"14",
"126",
"1134",
"4536",
"10584",
"15876",
"15876",
"10584",
"4536",
"1134",
"126"
]
| [
"nonn",
"tabl"
]
| 8 | 0 | 5 | [
"A000007",
"A057977",
"A063549",
"A240558",
"A359648"
]
| null | Peter Luschny, Jan 09 2023 | 2023-01-18T09:34:23 | oeisdata/seq/A359/A359648.seq | 3310c8787e2c56f63b827eb99360fd6d |
A359649 | a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n^2). | [
"1",
"1",
"5",
"28",
"609",
"6501",
"272701",
"4286815",
"272156417",
"5648748355",
"484054204501",
"12482361156398",
"1351553781736225",
"41650209565275195",
"5460281206077347469",
"195722005810272604876",
"30156361094764202326017",
"1232550298298392183231275",
"218366864894707599746619685"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A359364",
"A359649"
]
| null | Peter Luschny, Jan 10 2023 | 2024-01-08T07:58:41 | oeisdata/seq/A359/A359649.seq | 91e76eae5db34bff124c1d6ed16f2cff |
A359650 | Smallest prime factor q of (2^(p-1)-1) / (3*p) with prime p such that q is greater than p (increasing p, cf. A359387). | [
"31",
"89",
"178481",
"233",
"13367",
"6361",
"499",
"62020897",
"3391",
"1049",
"4153",
"1433",
"7068569257",
"1327",
"1399",
"1913",
"54217",
"80929",
"26371",
"7753",
"855857",
"5867",
"3449",
"48731",
"7707719",
"12619129",
"104369",
"32051",
"78557207",
"67219",
"1676083",
"34513",
"22291",
"4567",
"14563",
"830833",
"2731",
"343081"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A000720",
"A020639",
"A096060",
"A359387",
"A359650"
]
| null | Alain Rocchelli, Jan 09 2023 | 2023-01-21T02:42:41 | oeisdata/seq/A359/A359650.seq | 0884824bbb65186435b443e1ef65fb34 |
A359651 | Numbers with exactly three nonzero decimal digits and not ending with 0. | [
"111",
"112",
"113",
"114",
"115",
"116",
"117",
"118",
"119",
"121",
"122",
"123",
"124",
"125",
"126",
"127",
"128",
"129",
"131",
"132",
"133",
"134",
"135",
"136",
"137",
"138",
"139",
"141",
"142",
"143",
"144",
"145",
"146",
"147",
"148",
"149",
"151",
"152",
"153",
"154",
"155",
"156",
"157",
"158",
"159",
"161",
"162",
"163",
"164",
"165",
"166",
"167",
"168",
"169",
"171",
"172",
"173",
"174",
"175"
]
| [
"nonn",
"base",
"easy"
]
| 14 | 1 | 1 | [
"A359098",
"A359651"
]
| null | Charles R Greathouse IV, Jan 09 2023 | 2023-01-15T02:37:05 | oeisdata/seq/A359/A359651.seq | 41887e31c07aad8e8c8352ba09e72874 |
A359652 | Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic or geometric progression. | [
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"5",
"5",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"5",
"5",
"2",
"5",
"5",
"6",
"6",
"10",
"6",
"6",
"11",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"5",
"5",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"5",
"5",
"2",
"5",
"5",
"6",
"6",
"10",
"6",
"6",
"11",
"11",
"5",
"5",
"6",
"6",
"12",
"6",
"6",
"12",
"2",
"12",
"14",
"13",
"13",
"3",
"13",
"12",
"12",
"15",
"13",
"12",
"12",
"13",
"15",
"13",
"17"
]
| [
"nonn",
"look"
]
| 16 | 1 | 3 | [
"A229037",
"A268811",
"A359652"
]
| null | Neal Gersh Tolunsky, Jan 09 2023 | 2023-01-10T20:00:55 | oeisdata/seq/A359/A359652.seq | d44f2fec43d28e9da91f140e95a590f5 |
A359653 | Number of regions formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | [
"1",
"4",
"96",
"728",
"7840",
"17744",
"104136",
"246108",
"681704",
"1187200",
"3719496",
"5396692",
"14149896"
]
| [
"nonn",
"more"
]
| 8 | 1 | 2 | [
"A005728",
"A006842",
"A006843",
"A355798",
"A358882",
"A358886",
"A358948",
"A359653",
"A359654",
"A359655",
"A359656"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 09 2023 | 2023-01-10T18:21:25 | oeisdata/seq/A359/A359653.seq | d00841d2fa0daebf5d0145d0ad2c6e7b |
A359654 | Number of vertices formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | [
"4",
"9",
"77",
"593",
"6749",
"15569",
"93281",
"222933",
"623409",
"1087393",
"3453289",
"5011009",
"13271517"
]
| [
"nonn",
"more"
]
| 8 | 1 | 1 | [
"A005728",
"A006842",
"A006843",
"A355799",
"A358883",
"A358887",
"A358949",
"A359653",
"A359654",
"A359655",
"A359656"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 10 2023 | 2023-01-10T18:22:29 | oeisdata/seq/A359/A359654.seq | ea0aabc2291ddb465ee8188733ff6eff |
A359655 | Number of edges formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | [
"4",
"12",
"172",
"1320",
"14588",
"33312",
"197416",
"469040",
"1305112",
"2274592",
"7172784",
"10407700",
"27421412"
]
| [
"nonn",
"more"
]
| 6 | 1 | 1 | [
"A005728",
"A006842",
"A006843",
"A355800",
"A358884",
"A358888",
"A358950",
"A359653",
"A359654",
"A359655",
"A359656"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 10 2023 | 2023-01-10T18:22:47 | oeisdata/seq/A359/A359655.seq | efabb567fdbde8d3f1b83a5bfcb68d2f |
A359656 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square. | [
"0",
"1",
"0",
"4",
"56",
"40",
"368",
"300",
"48",
"12",
"3376",
"3408",
"960",
"96",
"7536",
"7524",
"2240",
"436",
"8",
"42048",
"45112",
"13912",
"2868",
"168",
"28",
"97720",
"105980",
"34496",
"7020",
"832",
"52",
"8",
"267240",
"290456",
"100560",
"20576",
"2688",
"160",
"24",
"461800",
"509824",
"174400",
"36228",
"4608",
"324",
"16",
"1411272",
"1594296",
"569152",
"126408",
"16856",
"1408",
"104"
]
| [
"nonn",
"tabf"
]
| 12 | 1 | 4 | [
"A005728",
"A006842",
"A006843",
"A355801",
"A358885",
"A358889",
"A358951",
"A359653",
"A359654",
"A359655",
"A359656"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 10 2023 | 2023-01-11T08:47:49 | oeisdata/seq/A359/A359656.seq | 98569bb6443f313416c166b2753c21af |
A359657 | Least k such that A359247(k) = n, or 0 if no such k exists. | [
"5",
"1",
"136",
"168",
"141",
"424",
"1867",
"680",
"3981",
"5800",
"2216",
"13648",
"5763",
"2728",
"8872",
"11944",
"15752",
"6824",
"15219",
"8352",
"17064",
"10920",
"10400",
"38407",
"25105",
"27304",
"36879",
"40501",
"37077",
"20323",
"25635",
"29073",
"57611",
"45795",
"90197",
"61741",
"68735",
"55319",
"46645",
"42549",
"95412"
]
| [
"nonn"
]
| 11 | 0 | 1 | [
"A070165",
"A187203",
"A359247",
"A359657"
]
| null | Michel Lagneau, Jan 10 2023 | 2023-01-25T10:01:37 | oeisdata/seq/A359/A359657.seq | d4ebef1f9b92fb6d2bd5d622bf33a29e |
A359658 | a(n) = Sum_{k=0..n} k^(k * (n-k) + 1). | [
"0",
"1",
"3",
"12",
"118",
"3345",
"337337",
"117813304",
"182877273548",
"1095343802746641",
"33833602932485958015",
"4588786457956655542361532",
"3347980595386754115503487966082",
"13023291362471615806961306534915589217"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A349893",
"A359658",
"A359659"
]
| null | Seiichi Manyama, Jan 10 2023 | 2023-01-10T06:44:13 | oeisdata/seq/A359/A359658.seq | 6a37d154c069937d66e2cd6f33519daa |
A359659 | a(n) = Sum_{k=0..n} k^(k * (n-k+1)). | [
"1",
"2",
"6",
"45",
"1051",
"88602",
"27121964",
"37004504305",
"198705527223757",
"5595513387083114570",
"686714367475480207331582",
"468422339816915120237104999421",
"1664212116512828935888786624225704855"
]
| [
"nonn"
]
| 18 | 0 | 2 | [
"A003101",
"A026898",
"A031971",
"A349836",
"A349882",
"A349883",
"A349893",
"A359658",
"A359659"
]
| null | Seiichi Manyama, Jan 10 2023 | 2023-01-12T06:44:30 | oeisdata/seq/A359/A359659.seq | beb9364ec8e2f47776c4c715f90a426b |
A359660 | a(n) = Sum_{k=0..n} k^(2 * (n-k) + 1). | [
"0",
"1",
"3",
"12",
"64",
"441",
"3855",
"41464",
"533736",
"8071785",
"141351715",
"2829417276",
"64038928728",
"1624347614737",
"45822087138879",
"1427872211276376",
"48858282302548240",
"1826209988254883889",
"74216973833968292451",
"3265676709281560408780"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 3 | [
"A000217",
"A003101",
"A234568",
"A349882",
"A359660"
]
| null | Seiichi Manyama, Jan 10 2023 | 2023-01-10T06:44:44 | oeisdata/seq/A359/A359660.seq | 0916423e64b08c6e0c56c3c760161f9e |
A359661 | a(n) is the number of free convex polyominoes of n cells. | [
"1",
"1",
"2",
"5",
"11",
"29",
"72",
"191",
"478",
"1211",
"2973",
"7274",
"17455",
"41645",
"98271",
"230848",
"539000",
"1254936"
]
| [
"nonn",
"more"
]
| 9 | 1 | 3 | [
"A000105",
"A001169",
"A067675",
"A359661"
]
| null | John Mason, Jan 10 2023 | 2023-01-10T11:38:15 | oeisdata/seq/A359/A359661.seq | 7a44de231d31409b0277d0d03e23e9ae |
A359662 | Number of (3-dimensional) cells of regular m-polytopes for m >= 3. | [
"1",
"5",
"8",
"15",
"16",
"24",
"35",
"40",
"70",
"80",
"120",
"126",
"160",
"210",
"240",
"330",
"495",
"560",
"600",
"715",
"1001",
"1120",
"1365",
"1792",
"1820",
"2016",
"2380",
"3060",
"3360",
"3876",
"4845",
"5280",
"5376",
"5985",
"7315",
"7920",
"8855",
"10626",
"11440",
"12650",
"14950",
"15360",
"16016",
"17550",
"20475",
"21840",
"23751"
]
| [
"easy",
"nonn"
]
| 12 | 1 | 2 | [
"A000332",
"A001789",
"A063924",
"A130810",
"A359201",
"A359202",
"A359662"
]
| null | Marco Ripà, Jan 10 2023 | 2023-01-12T23:01:41 | oeisdata/seq/A359/A359662.seq | a380f18bb123e22d8f93fd6d8053c3df |
A359663 | a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n terms of the Champernowne string starting from 1. | [
"1",
"3",
"2",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"47",
"14",
"21",
"15",
"13",
"11",
"16",
"18",
"61",
"20",
"67",
"73",
"22",
"24",
"26",
"25",
"28",
"30",
"17",
"27",
"32",
"33",
"107",
"109",
"36",
"19",
"29",
"34",
"38",
"127",
"39",
"35",
"137",
"40",
"42",
"44",
"45",
"48",
"46",
"49",
"51",
"43",
"50",
"54",
"52",
"57",
"31",
"55",
"193",
"56",
"60",
"23",
"58",
"62",
"64",
"63",
"66",
"65",
"68",
"70",
"72",
"69",
"77",
"75",
"37"
]
| [
"nonn",
"base"
]
| 7 | 1 | 2 | [
"A027749",
"A033307",
"A065648",
"A359114",
"A359663"
]
| null | Scott R. Shannon, Jan 10 2023 | 2023-01-10T07:59:05 | oeisdata/seq/A359/A359663.seq | 54e77f421554c694088a24ccf4e73cbf |
A359664 | Prime Maze Room 11, opposite parity of A059459 starting from prime room 11. | [
"11",
"43",
"41",
"2089",
"2081",
"2083",
"2087",
"10889035741470030830827987437816582768679",
"10889035741470030830827987437816582768647"
]
| [
"nonn",
"less"
]
| 79 | 1 | 1 | [
"A059459",
"A359664"
]
| null | Gregory Allen, Jan 10 2023 | 2023-02-03T16:25:28 | oeisdata/seq/A359/A359664.seq | a3800feecacc5abb50416f18a9187cbe |
A359665 | a(n) = Sum_{k=0..n} binomial(k^3, k). | [
"1",
"2",
"30",
"2955",
"638331",
"235169606",
"131748994154",
"104332124742623",
"110963563379491743",
"152605484049946645638",
"263562165946020159478038",
"558488792578762177358255808",
"1424733420462958066911824023728",
"4307309064570490624823548890385698",
"15228800547242034570505949850130312826"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A005809",
"A107444",
"A188675",
"A295773",
"A359665"
]
| null | Vaclav Kotesovec, Jan 10 2023 | 2023-01-10T08:32:34 | oeisdata/seq/A359/A359665.seq | 92bd6a862b88b4524e25c4baa3da2ad7 |
A359666 | Integers k such that sigma(k) <= sigma(k+1) <= sigma(k+2) <= sigma(k+3), where sigma is the sum of divisors. | [
"1",
"13",
"61",
"73",
"133",
"145",
"193",
"205",
"253",
"397",
"457",
"481",
"493",
"553",
"565",
"613",
"625",
"661",
"673",
"733",
"757",
"793",
"817",
"853",
"913",
"973",
"997",
"1033",
"1093",
"1213",
"1237",
"1285",
"1321",
"1333",
"1453",
"1513",
"1537",
"1633",
"1645",
"1657",
"1681",
"1813",
"1825",
"1873",
"1933",
"2077",
"2113",
"2173",
"2233",
"2245",
"2293",
"2413",
"2497"
]
| [
"nonn",
"easy"
]
| 61 | 1 | 2 | [
"A000203",
"A053224",
"A323726",
"A359666",
"A364662"
]
| null | Alexandru Petrescu, Feb 28 2023 | 2023-08-01T10:55:53 | oeisdata/seq/A359/A359666.seq | 558281cd784bbf327611c06e46aa0f01 |
A359667 | a(n) is the number of minimally prolific free polyominoes, i.e., that can generate the least possible number of children by adding a square. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"5",
"1",
"1",
"3",
"1",
"1",
"5",
"1",
"1",
"2",
"2"
]
| [
"nonn",
"more"
]
| 6 | 1 | 8 | [
"A000105",
"A255890",
"A359667"
]
| null | John Mason, Jan 10 2023 | 2023-01-10T13:04:58 | oeisdata/seq/A359/A359667.seq | 7a953767994dedf2c159b9b10392f110 |
A359668 | Triangle read by rows. Each term of the triangle is positive and distinct. In row k are the next k least numbers such that the sum of any one number from each of the first k rows is a prime number. | [
"2",
"3",
"5",
"6",
"12",
"24",
"18030",
"97830",
"165690",
"392250"
]
| [
"nonn",
"tabl",
"more",
"hard"
]
| 55 | 1 | 1 | [
"A000040",
"A000142",
"A000217",
"A001097",
"A359668"
]
| null | Tamas Sandor Nagy, Mar 14 2023 | 2023-11-06T07:16:24 | oeisdata/seq/A359/A359668.seq | 74d98098ffddc69a0d87cc5fda0f7185 |
A359669 | a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^(n*(n+1)) * A(x)^(n^2). | [
"1",
"1",
"0",
"3",
"6",
"13",
"55",
"142",
"429",
"1495",
"4538",
"14894",
"50279",
"164189",
"554402",
"1883870",
"6371434",
"21854442",
"75183191",
"259137380",
"899092908",
"3127293679",
"10907931688",
"38188033950",
"133998312862",
"471339759941",
"1662075700667",
"5872497411731",
"20790187564837",
"73741279736768"
]
| [
"nonn"
]
| 7 | 0 | 4 | [
"A359669",
"A359672"
]
| null | Paul D. Hanna, Jan 17 2023 | 2023-01-18T14:54:17 | oeisdata/seq/A359/A359669.seq | a0312fbb54fbbde641bc0208547b9026 |
A359670 | Triangle of coefficients T(n,k) of x^n*y^k in g.f. A(x,y) satisfying y = Sum_{n=-oo..+oo} (-1)^n * x^n * (y*A(x,y) + x^(n-1))^(n+1). | [
"1",
"2",
"1",
"4",
"6",
"1",
"8",
"21",
"12",
"1",
"14",
"62",
"68",
"20",
"1",
"24",
"162",
"284",
"170",
"30",
"1",
"40",
"384",
"998",
"970",
"360",
"42",
"1",
"64",
"855",
"3092",
"4410",
"2720",
"679",
"56",
"1",
"100",
"1806",
"8724",
"17172",
"15627",
"6608",
"1176",
"72",
"1",
"154",
"3648",
"22904",
"59545",
"74682",
"47089",
"14392",
"1908",
"90",
"1",
"232",
"7110",
"56679",
"188700",
"311530",
"271698",
"125160",
"28764",
"2940",
"110",
"1"
]
| [
"nonn",
"tabl"
]
| 44 | 0 | 2 | [
"A293600",
"A359670",
"A359711",
"A359712",
"A359713",
"A359714",
"A359715",
"A359718",
"A359720",
"A361770",
"A363104",
"A363105",
"A363135",
"A363136",
"A363137",
"A363142",
"A363182",
"A363183",
"A363184",
"A363185"
]
| null | Paul D. Hanna, Jan 17 2023 | 2023-05-26T13:45:38 | oeisdata/seq/A359/A359670.seq | a7f95c026006d6e4b763b9450a78c188 |
A359671 | a(n) = coefficient of x^n in A(x) where 1 = Sum_{n=-oo..+oo} (x^n - x*A(x))^n. | [
"2",
"4",
"6",
"6",
"10",
"78",
"412",
"1394",
"3312",
"6416",
"17454",
"83334",
"384284",
"1377888",
"3931286",
"10234748",
"31776266",
"127848076",
"527518582",
"1910397078",
"6035143914",
"18202417974",
"60151348904",
"226355566282",
"874920531958",
"3166323335574",
"10599244540550",
"34588365630694",
"118339356017608"
]
| [
"nonn"
]
| 9 | 0 | 1 | [
"A355868",
"A359671"
]
| null | Paul D. Hanna, Jan 10 2023 | 2023-10-13T11:11:48 | oeisdata/seq/A359/A359671.seq | 833818952454e945bf05ebf8fc8c4155 |
A359672 | a(n) = coefficient of x^n in A(x) where x = Sum_{n=-oo..+oo} (-1)^(n-1) * x^n * (1 + x^n*A(x)^n)^n. | [
"1",
"1",
"2",
"5",
"21",
"72",
"257",
"998",
"3988",
"16064",
"65734",
"273541",
"1151184",
"4886946",
"20916523",
"90181047",
"391230537",
"1706503782",
"7480000600",
"32930469730",
"145546039760",
"645574246834",
"2872745389578",
"12821285282360",
"57377599801569",
"257416078950987",
"1157519956026736",
"5216112572700566"
]
| [
"nonn"
]
| 16 | 0 | 3 | [
"A357399",
"A357791",
"A357797",
"A359672"
]
| null | Paul D. Hanna, Jan 10 2023 | 2023-01-11T11:09:33 | oeisdata/seq/A359/A359672.seq | 8b6b52eba487a06c901c35c1b8b0ad5a |
A359673 | a(n) = coefficient of x^n in A(x) where 1 = Sum_{n=-oo..+oo} (2*x + (-x)^n*A(x)^n)^n. | [
"1",
"2",
"5",
"13",
"30",
"74",
"202",
"616",
"2126",
"7828",
"29366",
"110398",
"414214",
"1556848",
"5892713",
"22524354",
"86954484",
"338421674",
"1324660464",
"5204326208",
"20498580511",
"80907096678",
"320002290542",
"1268500509496",
"5040195484362",
"20073242195580",
"80120884387322",
"320442284717582",
"1283939790460139"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A355868",
"A359673"
]
| null | Paul D. Hanna, Jan 10 2023 | 2023-10-13T11:09:03 | oeisdata/seq/A359/A359673.seq | a1d73160a71af9625691638f71414491 |
A359674 | Zero-based weighted sum of the prime indices of n in weakly increasing order. | [
"0",
"0",
"0",
"1",
"0",
"2",
"0",
"3",
"2",
"3",
"0",
"5",
"0",
"4",
"3",
"6",
"0",
"6",
"0",
"7",
"4",
"5",
"0",
"9",
"3",
"6",
"6",
"9",
"0",
"8",
"0",
"10",
"5",
"7",
"4",
"11",
"0",
"8",
"6",
"12",
"0",
"10",
"0",
"11",
"8",
"9",
"0",
"14",
"4",
"9",
"7",
"13",
"0",
"12",
"5",
"15",
"8",
"10",
"0",
"14",
"0",
"11",
"10",
"15",
"6",
"12",
"0",
"15",
"9",
"11",
"0",
"17",
"0",
"12",
"9",
"17",
"5",
"14",
"0",
"18"
]
| [
"nonn"
]
| 9 | 1 | 6 | [
"A001222",
"A001248",
"A008578",
"A029931",
"A053632",
"A055932",
"A056239",
"A112798",
"A124757",
"A231204",
"A243055",
"A304818",
"A318283",
"A358136",
"A358137",
"A358194",
"A359043",
"A359360",
"A359361",
"A359497",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359755"
]
| null | Gus Wiseman, Jan 13 2023 | 2023-01-14T22:00:30 | oeisdata/seq/A359/A359674.seq | 33ce869506afb3b6b04805d374a6e68a |
A359675 | Positions of first appearances in the sequence of zero-based weighted sums of prime indices (A359674). | [
"1",
"4",
"6",
"8",
"12",
"14",
"16",
"20",
"24",
"30",
"32",
"36",
"40",
"48",
"52",
"56",
"72",
"80",
"92",
"96",
"100",
"104",
"112",
"124",
"136",
"148",
"152",
"172",
"176",
"184",
"188",
"212",
"214",
"236",
"244",
"248",
"262",
"268",
"272",
"284",
"292",
"304",
"316",
"328",
"332",
"346",
"356",
"376",
"386",
"388",
"398",
"404",
"412",
"428",
"436",
"452",
"458"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A001222",
"A001248",
"A029931",
"A053632",
"A055932",
"A056239",
"A089633",
"A112798",
"A124757",
"A231204",
"A243055",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359043",
"A359360",
"A359361",
"A359497",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359683",
"A359754",
"A359755",
"A359756"
]
| null | Gus Wiseman, Jan 13 2023 | 2023-01-15T09:51:00 | oeisdata/seq/A359/A359675.seq | 150a6fc22f447bc604304f0387cb87c4 |
A359676 | Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674). | [
"1",
"4",
"6",
"8",
"14",
"12",
"16",
"20",
"30",
"24",
"32",
"36",
"40",
"52",
"48",
"56",
"100",
"72",
"80",
"92",
"96",
"104",
"112",
"124",
"136",
"148",
"176",
"152",
"214",
"172",
"184",
"188",
"262",
"212",
"272",
"236",
"248",
"244",
"304",
"268",
"346",
"284",
"328",
"292",
"386",
"316",
"398",
"332",
"376",
"356",
"458",
"388",
"478",
"404",
"472",
"412",
"526"
]
| [
"nonn",
"look"
]
| 6 | 1 | 2 | [
"A001222",
"A001248",
"A029931",
"A053632",
"A055932",
"A056239",
"A089633",
"A112798",
"A124757",
"A231204",
"A243055",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359043",
"A359361",
"A359497",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359683",
"A359754",
"A359755",
"A359756"
]
| null | Gus Wiseman, Jan 14 2023 | 2023-01-15T09:51:05 | oeisdata/seq/A359/A359676.seq | de22a005fd1c64ac4dc85e8569668c0f |
A359677 | Zero-based weighted sum of the reversed (weakly decreasing) prime indices of n. | [
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"3",
"2",
"1",
"0",
"3",
"0",
"1",
"2",
"6",
"0",
"4",
"0",
"3",
"2",
"1",
"0",
"6",
"3",
"1",
"6",
"3",
"0",
"4",
"0",
"10",
"2",
"1",
"3",
"7",
"0",
"1",
"2",
"6",
"0",
"4",
"0",
"3",
"6",
"1",
"0",
"10",
"4",
"5",
"2",
"3",
"0",
"9",
"3",
"6",
"2",
"1",
"0",
"7",
"0",
"1",
"6",
"15",
"3",
"4",
"0",
"3",
"2",
"5",
"0",
"11",
"0",
"1",
"7",
"3",
"4",
"4",
"0",
"10",
"12",
"1",
"0",
"7",
"3"
]
| [
"nonn"
]
| 5 | 1 | 8 | [
"A001222",
"A001248",
"A008578",
"A029931",
"A053632",
"A055932",
"A056239",
"A100484",
"A112798",
"A124757",
"A231204",
"A243055",
"A304818",
"A318283",
"A358136",
"A358137",
"A358194",
"A359042",
"A359043",
"A359361",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359683",
"A359754",
"A359755"
]
| null | Gus Wiseman, Jan 13 2023 | 2023-01-15T09:51:09 | oeisdata/seq/A359/A359677.seq | bc6ad72f52e14ac7f2e98d7c9a6406ab |
A359678 | Number of multisets (finite weakly increasing sequences of positive integers) with zero-based weighted sum (A359674) equal to n > 0. | [
"1",
"2",
"4",
"4",
"6",
"9",
"8",
"10",
"14",
"13",
"16",
"21",
"17",
"22",
"28",
"23",
"30",
"37",
"30",
"38",
"46",
"38",
"46",
"59",
"46",
"55",
"70",
"59",
"70",
"86",
"67",
"81",
"96",
"84",
"98",
"115",
"95",
"114",
"135",
"114",
"132",
"158",
"127",
"156",
"178",
"148",
"176",
"207",
"172",
"201",
"227",
"196",
"228",
"270",
"222",
"255",
"296",
"255",
"295",
"338",
"278"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A029931",
"A053632",
"A124757",
"A231204",
"A243055",
"A304818",
"A320387",
"A358194",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359680",
"A359681",
"A359757"
]
| null | Gus Wiseman, Jan 15 2023 | 2023-01-22T11:33:55 | oeisdata/seq/A359/A359678.seq | 6505d51b620258b9d6dfa7835230d218 |
A359679 | Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n. | [
"1",
"2",
"3",
"4",
"6",
"10",
"8",
"12",
"19",
"18",
"16",
"24",
"27",
"36",
"43",
"32",
"48",
"59",
"61",
"67",
"71",
"64",
"79",
"83",
"89",
"97",
"101",
"103",
"107",
"109",
"113",
"127",
"131",
"137",
"139",
"149",
"151",
"157",
"163",
"167",
"173",
"179",
"181",
"191",
"193",
"197",
"199",
"211",
"223",
"227",
"229",
"233",
"239",
"241",
"251",
"257",
"263",
"269"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A001222",
"A001248",
"A029931",
"A053632",
"A055932",
"A056239",
"A089633",
"A112798",
"A231204",
"A243055",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359043",
"A359360",
"A359361",
"A359497",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359683",
"A359754",
"A359755",
"A359756"
]
| null | Gus Wiseman, Jan 14 2023 | 2023-01-15T09:51:20 | oeisdata/seq/A359/A359679.seq | a0fabc4c6080394f6120578d5be661c6 |
A359680 | Positions of first appearances in the sequence of zero-based weighted sums of reversed prime indices (A359677). | [
"1",
"4",
"8",
"9",
"16",
"18",
"32",
"36",
"50",
"54",
"64",
"72",
"81",
"100",
"108",
"128",
"144",
"216",
"243",
"256",
"288",
"300",
"400",
"432",
"486",
"512",
"576",
"600",
"648",
"729",
"800",
"864",
"1024",
"1152",
"1296",
"1350",
"1728",
"1944",
"2048",
"2187",
"2304",
"2400",
"2916",
"3375",
"3456",
"3600",
"4096",
"4374",
"4608",
"4800",
"5184"
]
| [
"nonn"
]
| 5 | 1 | 2 | [
"A001222",
"A029931",
"A053632",
"A055932",
"A056239",
"A089633",
"A112798",
"A124757",
"A231204",
"A243055",
"A296150",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359043",
"A359361",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359683",
"A359754",
"A359755",
"A359756"
]
| null | Gus Wiseman, Jan 15 2023 | 2023-01-16T11:14:55 | oeisdata/seq/A359/A359680.seq | dfbf8d1864f28b25a6ed74228f91a4a1 |
A359681 | Least positive integer whose reversed (weakly decreasing) prime indices have zero-based weighted sum (A359677) equal to n. | [
"1",
"4",
"9",
"8",
"18",
"50",
"16",
"36",
"100",
"54",
"32",
"72",
"81",
"108",
"300",
"64",
"144",
"400",
"216",
"600",
"243",
"128",
"288",
"800",
"432",
"486",
"1350",
"648",
"256",
"576",
"729",
"864",
"2400",
"3375",
"1296",
"3600",
"512",
"1152",
"1944",
"1728",
"4800",
"9000",
"2187",
"2916",
"8100",
"1024",
"2304",
"6400",
"3456",
"4374",
"12150"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A001222",
"A001248",
"A029931",
"A053632",
"A055932",
"A056239",
"A089633",
"A112798",
"A124757",
"A231204",
"A243055",
"A304818",
"A318283",
"A320387",
"A358194",
"A359043",
"A359360",
"A359361",
"A359497",
"A359674",
"A359675",
"A359676",
"A359677",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359683",
"A359754",
"A359755"
]
| null | Gus Wiseman, Jan 15 2023 | 2023-01-15T09:51:40 | oeisdata/seq/A359/A359681.seq | 661b1c121a6cdb60ecc8009b093f9ccd |
A359682 | Least positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n. | [
"1",
"2",
"3",
"4",
"7",
"6",
"8",
"10",
"15",
"12",
"16",
"18",
"20",
"26",
"24",
"28",
"50",
"36",
"40",
"46",
"48",
"52",
"56",
"62",
"68",
"74",
"88",
"76",
"107",
"86",
"92",
"94",
"131",
"106",
"136",
"118",
"124",
"122",
"152",
"134",
"173",
"142",
"164",
"146",
"193",
"158",
"199",
"166",
"188",
"178",
"229",
"194",
"239",
"202",
"236",
"206",
"263",
"214",
"271",
"218"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A001222",
"A001248",
"A029931",
"A055932",
"A056239",
"A089633",
"A112798",
"A243055",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359043",
"A359360",
"A359361",
"A359497",
"A359675",
"A359676",
"A359678",
"A359679",
"A359680",
"A359681",
"A359682",
"A359683",
"A359754",
"A359755",
"A359756"
]
| null | Gus Wiseman, Jan 15 2023 | 2023-01-15T09:51:36 | oeisdata/seq/A359/A359682.seq | 1cc128ecbfbcd041d056bea45b9d5264 |
A359683 | Greatest positive integer whose reversed (weakly decreasing) prime indices have weighted sum (A318283) equal to n. | [
"1",
"2",
"3",
"5",
"7",
"11",
"14",
"22",
"26",
"34",
"44",
"55",
"68",
"85",
"110",
"130",
"170",
"190",
"242",
"290",
"374",
"418",
"506",
"638",
"748",
"836",
"1012",
"1276",
"1364",
"1628",
"1914",
"2090",
"2552",
"3190",
"3410",
"4070",
"4510",
"5060",
"6380",
"7018",
"8140",
"9020",
"9922",
"11396",
"14036",
"15004",
"17908",
"19844",
"21692",
"23452"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A001222",
"A001248",
"A029931",
"A055932",
"A056239",
"A089633",
"A112798",
"A243055",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359043",
"A359361",
"A359497",
"A359676",
"A359678",
"A359679",
"A359681",
"A359682",
"A359683",
"A359755"
]
| null | Gus Wiseman, Jan 15 2023 | 2023-01-28T12:15:05 | oeisdata/seq/A359/A359683.seq | 6edb9d7c6cdabe253aabf9e2ccf783d2 |
A359684 | Greatest prime dividing 2^n - n for n>=2; a(1) = 1. | [
"1",
"2",
"5",
"3",
"3",
"29",
"11",
"31",
"503",
"13",
"97",
"1021",
"8179",
"1637",
"4679",
"13",
"8737",
"131063",
"524269",
"262139",
"2097131",
"2003",
"1423",
"2713",
"123817",
"170327",
"577",
"14983",
"564533",
"87481",
"318949",
"262657",
"209510599",
"157109",
"344117",
"2473",
"2255501",
"26861",
"49977801259",
"24481"
]
| [
"nonn"
]
| 22 | 1 | 2 | [
"A000040",
"A000325",
"A006530",
"A359684"
]
| null | Philippe Deléham, Jan 11 2023 | 2023-03-30T02:32:03 | oeisdata/seq/A359/A359684.seq | 4560fc7f78280988f2f5d66a01f36a34 |
A359685 | Greatest prime dividing 2^n + n. | [
"3",
"3",
"11",
"5",
"37",
"7",
"5",
"11",
"521",
"47",
"71",
"79",
"547",
"911",
"32783",
"241",
"307",
"6899",
"24967",
"87383",
"457",
"4799",
"270601",
"7109",
"3728273",
"12497",
"1201",
"100613",
"2017",
"17318417",
"859",
"87211",
"47491",
"8589934609",
"195329",
"1483453",
"320370521",
"8191129",
"549755813927",
"478881371"
]
| [
"nonn"
]
| 18 | 1 | 1 | [
"A000040",
"A006127",
"A006530",
"A359685"
]
| null | Philippe Deléham, Jan 11 2023 | 2023-03-30T02:31:08 | oeisdata/seq/A359/A359685.seq | bd94de8ad294c9a3542cf76866cef591 |
A359686 | Triangle read by rows: T(n,k) is the minimum number of connected endofunctions that are spanning subgraphs of a semi-regular loopless digraph on n vertices each with out-degree k. | [
"1",
"1",
"8",
"0",
"14",
"78",
"0",
"22",
"213",
"944",
"0",
"0",
"529",
"3400",
"13800",
"0",
"0"
]
| [
"nonn",
"tabl",
"more"
]
| 16 | 2 | 3 | [
"A000435",
"A359628",
"A359686"
]
| null | Yali Harrary, Jan 11 2023 | 2024-01-04T14:31:09 | oeisdata/seq/A359/A359686.seq | 859c04e1d1b77137406f0cdfeee677d8 |
A359687 | Numbers k for which rank of the elliptic curve y^2 = x^3 - 432*k^2 is 5. | [
"489489",
"525698",
"526535",
"763002",
"903210",
"1423214"
]
| [
"nonn",
"more"
]
| 39 | 1 | 1 | [
"A060748",
"A060838",
"A159843",
"A309960",
"A309961",
"A309962",
"A309963",
"A309964",
"A359687"
]
| null | Maksym Voznyy and Charles R Greathouse IV, Jan 25 2023 | 2023-01-25T09:08:36 | oeisdata/seq/A359/A359687.seq | 578678cf9875ea1aed249b53c4441918 |
A359688 | a(n) is the number of asymmetrical polyiamonds of n cells. | [
"0",
"0",
"0",
"0",
"4",
"10",
"36",
"94",
"294",
"794",
"2300",
"6394",
"18266",
"51592",
"147426",
"420512",
"1206740",
"3466876"
]
| [
"nonn",
"more"
]
| 5 | 1 | 5 | [
"A000577",
"A359688"
]
| null | John Mason, Jan 11 2023 | 2023-01-11T13:13:53 | oeisdata/seq/A359/A359688.seq | 9feb0bf979af1ec15044c8ad45b9cb88 |
A359689 | a(n) is the number of free polyiamonds of n cells with chessboard coloring. | [
"2",
"1",
"2",
"4",
"8",
"19",
"48",
"120",
"320",
"864",
"2372",
"6581",
"18470",
"52094",
"147966",
"421931",
"1208214",
"3470789",
"10001186",
"28892674",
"83671476",
"242823392",
"706090582",
"2056861981",
"6001601254",
"17538308071",
"51323923796",
"150389970179",
"441211039118",
"1295886198194",
"3810209524640",
"11214075937205",
"33035791339150"
]
| [
"nonn"
]
| 19 | 1 | 1 | [
"A000577",
"A001933",
"A359689"
]
| null | John Mason, Jan 11 2023 | 2023-10-28T23:54:14 | oeisdata/seq/A359/A359689.seq | 2a23a0e642e096d9e080ffbe77a1578b |
A359690 | Number of vertices in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | [
"5",
"13",
"69",
"289",
"1971",
"3997",
"20371",
"45751",
"120957",
"205299",
"629847",
"897801",
"2334409",
"3461459",
"5517131",
"8468061"
]
| [
"nonn",
"more"
]
| 14 | 1 | 1 | [
"A005728",
"A006842",
"A006843",
"A331755",
"A358883",
"A358887",
"A359654",
"A359690",
"A359691",
"A359692",
"A359693",
"A359694"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 11 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359690.seq | 3900db77cf0be527e6ef8aff80d568b9 |
A359691 | Number of crossings in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | [
"1",
"7",
"59",
"275",
"1949",
"3971",
"20333",
"45705",
"120899",
"205233",
"629761",
"897707",
"2334291",
"3461329",
"5516985",
"8467899"
]
| [
"nonn",
"more"
]
| 8 | 1 | 2 | [
"A005728",
"A006842",
"A006843",
"A159065",
"A331755",
"A358883",
"A358887",
"A359654",
"A359690",
"A359691",
"A359692",
"A359693",
"A359694"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 11 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359691.seq | 2cf8d263598578318aedbf247f87f6fa |
A359692 | Number of regions in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | [
"2",
"12",
"94",
"382",
"2486",
"4946",
"24100",
"53152",
"138158",
"233254",
"700720",
"999364",
"2559344",
"3785044",
"6027148",
"9210820"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A005728",
"A006842",
"A006843",
"A290131",
"A358882",
"A358886",
"A359653",
"A359690",
"A359691",
"A359692",
"A359693",
"A359694"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 11 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359692.seq | 237dc4f1bae4961b63fc27b393434a03 |
A359693 | Number of edges in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | [
"6",
"24",
"162",
"670",
"4456",
"8942",
"44470",
"98902",
"259114",
"438552",
"1330566",
"1897164",
"4893752",
"7246502",
"11544278",
"17678880"
]
| [
"nonn",
"more"
]
| 9 | 1 | 1 | [
"A005728",
"A006842",
"A006843",
"A290132",
"A358884",
"A358888",
"A359655",
"A359690",
"A359691",
"A359692",
"A359693",
"A359694"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 11 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359693.seq | 181f4bc82d384ff4cd4fd34af95e511f |
A359694 | Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n. | [
"2",
"10",
"2",
"70",
"24",
"218",
"160",
"4",
"1254",
"1068",
"148",
"16",
"2254",
"2414",
"252",
"26",
"10082",
"11760",
"1980",
"266",
"12",
"21410",
"25958",
"5096",
"648",
"36",
"4",
"53422",
"68208",
"14360",
"1980",
"168",
"20",
"86986",
"118922",
"24028",
"3056",
"248",
"12",
"0",
"2",
"255678",
"346676",
"84344",
"12774",
"1132",
"110",
"4",
"2",
"365674",
"493530",
"119820",
"18600",
"1624",
"112",
"4"
]
| [
"nonn",
"tabf"
]
| 13 | 1 | 1 | [
"A005728",
"A006842",
"A006843",
"A290131",
"A358882",
"A358886",
"A359653",
"A359690",
"A359691",
"A359692",
"A359693",
"A359694"
]
| null | Scott R. Shannon and N. J. A. Sloane, Jan 11 2023 | 2025-02-16T08:34:04 | oeisdata/seq/A359/A359694.seq | 796ecf895960bf9264afa1e71f08f7b3 |
A359695 | Numbers k such that 29^k - 2 is prime. | [
"2",
"4",
"8",
"14",
"42",
"420",
"1344"
]
| [
"nonn",
"more"
]
| 33 | 1 | 1 | [
"A087886",
"A090669",
"A105772",
"A109076",
"A109080",
"A128457",
"A128459",
"A128460",
"A359695"
]
| null | Arsen Vardanyan, Mar 07 2023 | 2024-09-15T01:58:50 | oeisdata/seq/A359/A359695.seq | 46b76233f5171d7a3c6e5ceaf832c6b0 |
A359696 | a(n) is the number of points with integer coordinates located between the x-axis and the graph of the function y = n^3 / (n^2 + x^2). | [
"1",
"6",
"15",
"28",
"49",
"72",
"103",
"138",
"177",
"228",
"275",
"330",
"397",
"464",
"543",
"620",
"707",
"800",
"891",
"1002",
"1105",
"1220",
"1341",
"1468",
"1605",
"1740",
"1883",
"2032",
"2187",
"2356",
"2517",
"2694",
"2869",
"3058",
"3249",
"3444",
"3645",
"3856",
"4075",
"4294",
"4519",
"4748",
"4987",
"5230"
]
| [
"nonn"
]
| 44 | 1 | 2 | null | null | Nicolay Avilov, Mar 07 2023 | 2024-03-08T01:02:35 | oeisdata/seq/A359/A359696.seq | 283587cb031f7745d6e02a7485779b18 |
A359697 | Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) is carryless product n X k base 10. | [
"1",
"2",
"4",
"3",
"6",
"9",
"4",
"8",
"2",
"6",
"5",
"0",
"5",
"0",
"5",
"6",
"2",
"8",
"4",
"0",
"6",
"7",
"4",
"1",
"8",
"5",
"2",
"9",
"8",
"6",
"4",
"2",
"0",
"8",
"6",
"4",
"9",
"8",
"7",
"6",
"5",
"4",
"3",
"2",
"1",
"10",
"20",
"30",
"40",
"50",
"60",
"70",
"80",
"90",
"100",
"11",
"22",
"33",
"44",
"55",
"66",
"77",
"88",
"99",
"110",
"121",
"12",
"24",
"36",
"48",
"50",
"62",
"74",
"86",
"98",
"120",
"132",
"144"
]
| [
"nonn",
"tabl",
"base",
"look"
]
| 43 | 1 | 2 | [
"A001477",
"A004520",
"A008592",
"A055120",
"A059691",
"A059729",
"A359697"
]
| null | Seiichi Manyama, Mar 08 2023 | 2023-03-08T23:17:35 | oeisdata/seq/A359/A359697.seq | 0dbf990778703f0150765c7638cfbd78 |
A359698 | Least k > 0 such that the first n digits of 2^k and 3^k are identical. | [
"1",
"17",
"193",
"619",
"2016",
"91958",
"91958",
"8186278",
"45392361",
"977982331",
"26450915298",
"91600221212",
"196425900073",
"14810317269038",
"44430951807114",
"626642721222487",
"626642721222487",
"102882886570917135",
"874191214492184404",
"3830977578643912683",
"86801197487071715103"
]
| [
"base",
"nonn"
]
| 57 | 0 | 2 | [
"A000079",
"A000244",
"A088995",
"A359698"
]
| null | Keith F. Lynch, May 20 2023 | 2023-06-04T08:56:10 | oeisdata/seq/A359/A359698.seq | fc73360730ef17000a49d55fc140185b |
A359699 | Decimal expansion of x such that Gamma(t) and t^x*e^-t are tangent at one point. | [
"2",
"8",
"8",
"5",
"1",
"8",
"2",
"1",
"2",
"2",
"4",
"9",
"9",
"9",
"9",
"3",
"1",
"7",
"5",
"5",
"1",
"9",
"7",
"9",
"6",
"2",
"2",
"4",
"3",
"7",
"3",
"8",
"5",
"1",
"2",
"3",
"5",
"1",
"4",
"1",
"3",
"7",
"0",
"2",
"7",
"4",
"3",
"2",
"4",
"7",
"8",
"1",
"8",
"3",
"4",
"7",
"2",
"6",
"3",
"1",
"5",
"9",
"0",
"8",
"1",
"7",
"8",
"8",
"2",
"0",
"8",
"0",
"8",
"3",
"8",
"3",
"3",
"5",
"6",
"1",
"4",
"9",
"3",
"6",
"3",
"1",
"4",
"1",
"5",
"9",
"8",
"4",
"1",
"3",
"6",
"3",
"4",
"1",
"3",
"7",
"6",
"2",
"2",
"4",
"5",
"4"
]
| [
"cons",
"nonn"
]
| 26 | 1 | 1 | null | null | Jodi Spitz, Mar 07 2023 | 2023-11-10T10:42:37 | oeisdata/seq/A359/A359699.seq | 32d30ccc279da825d20342bae89c7a02 |
A359700 | a(n) = Sum_{d|n} d^(d + n/d - 1). | [
"1",
"5",
"28",
"265",
"3126",
"46754",
"823544",
"16778273",
"387420733",
"10000015690",
"285311670612",
"8916100733146",
"302875106592254",
"11112006831323074",
"437893890380939688",
"18446744073843786241",
"827240261886336764178",
"39346408075300026047027"
]
| [
"nonn"
]
| 19 | 1 | 2 | [
"A014566",
"A055225",
"A087909",
"A294956",
"A353013",
"A353014",
"A359700"
]
| null | Seiichi Manyama, Jan 11 2023 | 2023-08-14T01:59:57 | oeisdata/seq/A359/A359700.seq | 4d9448ef1a72af9fb426662f636e6dfc |
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