sequence_id stringlengths 7 7 | sequence_name stringlengths 4 573 | sequence listlengths 1 348 | keywords listlengths 1 7 | score int64 1 2.47k | offset_a int64 -14,827 666,262,453B | offset_b int64 0 635M ⌀ | cross_references listlengths 1 128 ⌀ | former_ids listlengths 1 3 ⌀ | author stringlengths 7 231 ⌀ | timestamp timestamp[us]date 1999-12-11 03:00:00 2026-01-19 02:46:49 | filename stringlengths 29 29 | hash stringlengths 32 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A391782 | Decimal expansion of Sum_{k>=1} eta(2*k) * Lucas(2*k) / 5^k, where eta is the Dirichlet eta function. | [
"1",
"0",
"5",
"8",
"0",
"6",
"0",
"1",
"1",
"8",
"9",
"7",
"8",
"4",
"3",
"7",
"3",
"1",
"3",
"7",
"5",
"2",
"7",
"1",
"6",
"0",
"8",
"8",
"6",
"2",
"3",
"6",
"7",
"4",
"9",
"5",
"6",
"1",
"5",
"6",
"1",
"2",
"1",
"9",
"3",
"... | [
"nonn",
"cons",
"changed"
] | 8 | 1 | 3 | [
"A000032",
"A005248",
"A350760",
"A391781",
"A391782"
] | null | Amiram Eldar, Dec 20 2025 | 2026-01-17T17:22:47 | oeisdata/seq/A391/A391782.seq | f20f959f69aafe7b274f0c8b32ddd172 |
A391783 | Decimal expansion of Sum_{k>=1} (-1)^(k+1) * log(1 + 1/k) / k. | [
"5",
"5",
"2",
"1",
"2",
"8",
"3",
"2",
"2",
"0",
"8",
"5",
"4",
"9",
"2",
"0",
"7",
"6",
"5",
"7",
"7",
"0",
"1",
"2",
"1",
"4",
"7",
"2",
"0",
"0",
"8",
"0",
"8",
"7",
"0",
"8",
"9",
"4",
"3",
"1",
"0",
"8",
"3",
"2",
"0",
"... | [
"nonn",
"cons",
"changed"
] | 8 | 0 | 1 | [
"A001008",
"A001620",
"A002805",
"A058312",
"A058313",
"A131688",
"A391783",
"A391784"
] | null | Amiram Eldar, Dec 20 2025 | 2026-01-17T17:22:14 | oeisdata/seq/A391/A391783.seq | 05c5ff90344d94d97583276674c8024b |
A391784 | Decimal expansion of Sum_{k>=1} log(1 + 1/(k+1)) / k. | [
"8",
"6",
"0",
"6",
"2",
"0",
"1",
"9",
"2",
"8",
"5",
"3",
"1",
"3",
"8",
"3",
"6",
"4",
"0",
"4",
"3",
"4",
"9",
"4",
"9",
"2",
"0",
"2",
"7",
"4",
"5",
"8",
"7",
"8",
"2",
"0",
"1",
"3",
"6",
"3",
"9",
"4",
"4",
"8",
"6",
"... | [
"nonn",
"cons"
] | 8 | 0 | 1 | [
"A001008",
"A001620",
"A002805",
"A006232",
"A006233",
"A058312",
"A058313",
"A391783",
"A391784"
] | null | Amiram Eldar, Dec 20 2025 | 2025-12-20T03:38:44 | oeisdata/seq/A391/A391784.seq | 196f2cdbe01c12d586678e990c6e5b38 |
A391785 | Decimal expansion of zeta(2) * Product_{p prime} (1 - 2/p^2 + 1/p^(2/5) - 1/p^(3/2) + 1/p^4). | [
"7",
"6",
"3",
"3",
"5",
"6",
"4",
"3",
"0",
"2",
"1",
"6",
"2",
"2",
"9",
"5",
"9",
"0",
"0",
"9",
"9",
"9",
"4",
"4",
"3",
"9",
"1",
"6",
"7",
"3",
"2",
"0",
"9",
"1",
"0",
"7",
"7",
"4",
"2",
"4",
"5",
"8",
"3",
"6",
"6",
"... | [
"nonn",
"cons"
] | 9 | 0 | 1 | [
"A013661",
"A391785"
] | null | Amiram Eldar, Dec 20 2025 | 2025-12-20T10:16:06 | oeisdata/seq/A391/A391785.seq | 7c216230dc7c5c67f0da91db8a4068b8 |
A391787 | a(n) is the least n-bit number k such that k has the maximum number of distinct (nonempty) substrings in the binary representation of k. | [
"0",
"2",
"4",
"9",
"19",
"35",
"70",
"139",
"278",
"558",
"1070",
"2140",
"4253",
"8503",
"17006",
"34007",
"68014",
"136028",
"272060",
"534204",
"1068408",
"2133369",
"4266362",
"8532669",
"17065338",
"34130555",
"68261103",
"136522206",
"273044399",
"546... | [
"nonn",
"base"
] | 30 | 1 | 2 | [
"A094913",
"A141297",
"A391787"
] | null | Ctibor O. Zizka, Dec 20 2025 | 2025-12-31T09:47:14 | oeisdata/seq/A391/A391787.seq | 010861b6a52144046ab4fd78283967b7 |
A391788 | Array read by antidiagonals: A(n,k) = phi(n+k) with k >= 0 and A(0,0) = 0. | [
"0",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"4",
"4",
"4",
"4",
"4",
"4",
"2",
"2",
"2",
"2",
"2",
"2",
"2",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"... | [
"nonn",
"easy",
"tabl"
] | 9 | 0 | 7 | [
"A000010",
"A002618",
"A062570",
"A391788",
"A391789",
"A391790"
] | null | Stefano Spezia, Dec 20 2025 | 2025-12-24T09:55:13 | oeisdata/seq/A391/A391788.seq | b67330822248b3070967c90b0f1ae981 |
A391789 | a(n) is the determinant of the n-th order Hankel matrix M(n) whose generic element is given by M(i,j) = phi(i+j) with i,j = 0, ..., n-1 and M(0,0) = 0. | [
"1",
"0",
"-1",
"1",
"-2",
"-20",
"-8",
"256",
"5920",
"24320",
"-385536",
"380928",
"109130240",
"1048645632",
"-26955161600",
"266634035200",
"3857663459328",
"28245816836096",
"-284017798938624",
"-3430335521030144",
"-27229528475172864",
"4759106956244811776",
"-16349... | [
"sign"
] | 14 | 0 | 5 | [
"A000010",
"A368025",
"A391788",
"A391789",
"A391790"
] | null | Stefano Spezia, Dec 20 2025 | 2025-12-24T09:55:08 | oeisdata/seq/A391/A391789.seq | 564d5e139a3418b596931f5fb6fd5877 |
A391790 | a(n) is the permanent of the n-th order Hankel matrix M(n) whose generic element is given by M(i,j) = phi(i+j) with i,j = 0, ..., n-1 and M(0,0) = 0. | [
"1",
"0",
"1",
"7",
"154",
"4860",
"265048",
"15959744",
"1702784480",
"174374326912",
"25548068301056",
"4392451231078400",
"975899333856328192",
"222438109032688009216",
"67405846484696921661440",
"20031561030571606152773632",
"7508762497888891587398205440",
"32611231980227966706... | [
"nonn"
] | 13 | 0 | 4 | [
"A000010",
"A368026",
"A391788",
"A391789",
"A391790"
] | null | Stefano Spezia, Dec 20 2025 | 2025-12-24T09:55:04 | oeisdata/seq/A391/A391790.seq | ba9dd3a645457ec76879284c77bbb73a |
A391791 | a(n)/2^(n-1) is the expected win if one of two baskets is chosen randomly and the player optimally chooses the coins with values from 1 to n (see Comments for details). | [
"1",
"5",
"20",
"65",
"190",
"530",
"1407",
"3585",
"8942",
"21819",
"52204",
"123190",
"287044",
"661329",
"1509949",
"3420580",
"7688444",
"17173896",
"38143782",
"84262365",
"185278522",
"405700861"
] | [
"nonn",
"hard",
"more",
"changed"
] | 16 | 1 | 2 | [
"A391537",
"A391538",
"A391791",
"A391792"
] | null | Ruediger Jehn, Dec 20 2025 | 2026-01-07T16:16:55 | oeisdata/seq/A391/A391791.seq | b04b5e6b8052e592d7f96969d7f029ae |
A391792 | a(n)/3^(n-1) is the expected win if one of three baskets is chosen randomly and the player optimally chooses the coins with values from 1 to n (see Comments for details). | [
"1",
"7",
"40",
"192",
"837",
"3423",
"13478",
"51396",
"190809",
"693595",
"2477822",
"8740848",
"30419671",
"104752091",
"357748926",
"1211285880",
"4074000387",
"13615817865"
] | [
"nonn",
"hard",
"more",
"new"
] | 6 | 1 | 2 | [
"A391537",
"A391538",
"A391791",
"A391792"
] | null | Ruediger Jehn, Dec 31 2025 | 2026-01-07T16:17:39 | oeisdata/seq/A391/A391792.seq | 5d345a6207eb6cc66bb569e101d0f93c |
A391793 | Multiplicative sequence a(n) with a(p^e) = ((e mod 5) * ((e mod 5) - 5) + 4) / 2 for prime p and e > 0. | [
"1",
"0",
"0",
"-1",
"0",
"0",
"0",
"-1",
"-1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"0",
"-1",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0"... | [
"sign",
"easy",
"mult"
] | 9 | 1 | 32 | null | null | Werner Schulte, Dec 20 2025 | 2025-12-28T20:36:24 | oeisdata/seq/A391/A391793.seq | c12c919bc11c60b954e9317cc304f2cc |
A391795 | Largest possible index of a topological sequence of three dimensional lattice points with depth n. | [
"1",
"0",
"2",
"5",
"7",
"11",
"17",
"23",
"31",
"40",
"47",
"56"
] | [
"nonn",
"more"
] | 11 | 0 | 3 | [
"A000219",
"A000293",
"A002836",
"A207542",
"A387672",
"A391795"
] | null | John Tyler Rascoe, Dec 20 2025 | 2025-12-21T10:47:14 | oeisdata/seq/A391/A391795.seq | 703a73f28bc9e61c27786fcd2f788686 |
A391796 | a(n) is the least k such that the residues mod 3 of the primes prime(k), prime(k+1), ... comprise a string of n 2's followed by 1. | [
"3",
"9",
"15",
"54",
"290",
"987",
"4530",
"21481",
"58554",
"60967",
"136457",
"136456",
"673393",
"1254204",
"1254203",
"7709873",
"21357254",
"21357253",
"25813465",
"25813464",
"39500858",
"39500857",
"947438661",
"947438660",
"947438659",
"5703167679",
"5703... | [
"nonn",
"new"
] | 17 | 1 | 1 | [
"A390511",
"A391796",
"A391807",
"A392104"
] | null | Clark Kimberling, Jan 05 2026 | 2026-01-17T12:56:04 | oeisdata/seq/A391/A391796.seq | 37517551777e80340e6ba270ee05ea96 |
A391797 | Numbers k such that prime(2*k + 2) - prime(2*k) < prime(2*k + 1) - prime(2*k - 1). | [
"6",
"8",
"12",
"16",
"20",
"24",
"27",
"28",
"31",
"34",
"37",
"40",
"44",
"46",
"50",
"51",
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"56",
"58",
"61",
"64",
"65",
"69",
"70",
"71",
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"79",
"81",
"84",
"85",
"89",
"90",
"95",
"97",
"99",
"100",
"103",
"104",
"107",
"1... | [
"nonn"
] | 9 | 1 | 1 | [
"A000027",
"A000040",
"A110854",
"A391797",
"A391798",
"A391799",
"A391800"
] | null | Clark Kimberling, Dec 23 2025 | 2025-12-30T15:33:13 | oeisdata/seq/A391/A391797.seq | 4ae705d268cba42f9c98c56c66c0137d |
A391798 | Numbers k such that prime(2*k + 2) - prime(2*k) = prime(2*k + 1) - prime(2*k - 1). | [
"2",
"3",
"5",
"11",
"13",
"14",
"15",
"17",
"19",
"21",
"22",
"32",
"36",
"39",
"41",
"47",
"52",
"53",
"63",
"74",
"75",
"76",
"77",
"83",
"86",
"88",
"91",
"93",
"96",
"106",
"118",
"122",
"124",
"125",
"128",
"136",
"137",
"143",
"151",... | [
"nonn"
] | 10 | 1 | 1 | [
"A000027",
"A000040",
"A022884",
"A110854",
"A391797",
"A391798",
"A391799",
"A391800"
] | null | Clark Kimberling, Dec 23 2025 | 2026-01-01T23:31:00 | oeisdata/seq/A391/A391798.seq | 84738173393ec2c159871c52063f51c5 |
A391799 | Numbers k such that prime(2*k + 2) - prime(2*k) > prime(2*k + 1) - prime(2*k - 1). | [
"1",
"4",
"7",
"9",
"10",
"18",
"23",
"25",
"26",
"29",
"30",
"33",
"35",
"38",
"42",
"43",
"45",
"48",
"49",
"55",
"57",
"59",
"60",
"62",
"66",
"67",
"68",
"72",
"78",
"80",
"82",
"87",
"92",
"94",
"98",
"101",
"102",
"105",
"108",
"110... | [
"nonn"
] | 6 | 1 | 2 | [
"A000040",
"A110854",
"A391797",
"A391798",
"A391799",
"A391800"
] | null | Clark Kimberling, Dec 29 2025 | 2026-01-04T19:51:35 | oeisdata/seq/A391/A391799.seq | c41b1453aa990ef63d9793159a9fcde0 |
A391800 | Primes indexed by A391797. | [
"13",
"19",
"37",
"53",
"71",
"89",
"103",
"107",
"127",
"139",
"157",
"173",
"193",
"199",
"229",
"233",
"251",
"263",
"271",
"283",
"311",
"313",
"347",
"349",
"353",
"367",
"401",
"419",
"433",
"439",
"461",
"463",
"499",
"509",
"523",
"541",
... | [
"nonn"
] | 4 | 1 | 1 | [
"A000027",
"A391797",
"A391800",
"A391801",
"A391802"
] | null | Clark Kimberling, Dec 30 2025 | 2026-01-04T22:12:00 | oeisdata/seq/A391/A391800.seq | f3ec5aa2f21f1ba662b5d3c904aaf7a5 |
A391801 | Primes indexed by A391798. | [
"3",
"5",
"11",
"31",
"41",
"43",
"47",
"59",
"67",
"73",
"79",
"131",
"151",
"167",
"179",
"211",
"239",
"241",
"307",
"373",
"379",
"383",
"389",
"431",
"443",
"457",
"467",
"487",
"503",
"577",
"647",
"673",
"683",
"691",
"719",
"769",
"773"... | [
"nonn"
] | 4 | 1 | 1 | [
"A000027",
"A391798",
"A391800",
"A391801",
"A391802"
] | null | Clark Kimberling, Dec 30 2025 | 2026-01-04T22:12:23 | oeisdata/seq/A391/A391801.seq | 8599160baf936dd5863bfb9fc345e213 |
A391802 | Primes indexed by A391799. | [
"2",
"7",
"17",
"23",
"29",
"61",
"83",
"97",
"101",
"109",
"113",
"137",
"149",
"163",
"181",
"191",
"197",
"223",
"227",
"257",
"269",
"277",
"281",
"293",
"317",
"331",
"337",
"359",
"397",
"409",
"421",
"449",
"479",
"491",
"521",
"547",
"5... | [
"nonn"
] | 4 | 1 | 1 | [
"A000027",
"A391799",
"A391800",
"A391801",
"A391802"
] | null | Clark Kimberling, Dec 30 2025 | 2026-01-04T22:12:44 | oeisdata/seq/A391/A391802.seq | 5237ee68ae3450bff052f696d6d4c136 |
A391803 | a(n) = floor(Sum_{k=1..n} n/prime(k)). | [
"0",
"1",
"3",
"4",
"6",
"8",
"9",
"11",
"13",
"15",
"17",
"19",
"21",
"22",
"24",
"26",
"28",
"30",
"32",
"34",
"36",
"38",
"40",
"43",
"45",
"47",
"49",
"51",
"53",
"55",
"57",
"59",
"61",
"63",
"66",
"68",
"70",
"72",
"74",
"76",
"78... | [
"nonn",
"new"
] | 14 | 1 | 3 | [
"A000040",
"A046024",
"A391803"
] | null | Clark Kimberling, Dec 31 2025 | 2026-01-05T15:00:48 | oeisdata/seq/A391/A391803.seq | 73273e61164cd50c539b125b3e1ac85b |
A391804 | a(n) = least prime greater than prime(n)*prime(n+1). | [
"7",
"17",
"37",
"79",
"149",
"223",
"331",
"439",
"673",
"907",
"1151",
"1523",
"1777",
"2027",
"2503",
"3137",
"3607",
"4091",
"4759",
"5189",
"5779",
"6563",
"7393",
"8641",
"9803",
"10427",
"11027",
"11677",
"12323",
"14369",
"16649",
"17957",
"190... | [
"nonn",
"easy",
"new"
] | 9 | 1 | 1 | [
"A000040",
"A006094",
"A151800",
"A391804",
"A391805"
] | null | Clark Kimberling, Jan 04 2026 | 2026-01-09T15:24:41 | oeisdata/seq/A391/A391804.seq | a1cfaa8ae0520c4bd6e197cc77df7a3f |
A391805 | a(n) = greatest prime less than prime(n)*prime(n+1). | [
"5",
"13",
"31",
"73",
"139",
"211",
"317",
"433",
"661",
"887",
"1129",
"1511",
"1759",
"2017",
"2477",
"3121",
"3593",
"4079",
"4751",
"5179",
"5749",
"6553",
"7369",
"8629",
"9791",
"10399",
"11003",
"11657",
"12301",
"14347",
"16633",
"17939",
"190... | [
"nonn",
"easy",
"new"
] | 10 | 1 | 1 | [
"A000040",
"A006094",
"A391804",
"A391805"
] | null | Clark Kimberling, Jan 04 2026 | 2026-01-09T15:24:05 | oeisdata/seq/A391/A391805.seq | 98a9f8bf0a344691ad954ff8f2cf4f4a |
A391806 | a(n) = least k such that the sum of the first k odd primes is divisible by n. | [
"1",
"2",
"1",
"2",
"3",
"16",
"6",
"2",
"13",
"20",
"44",
"40",
"4",
"6",
"3",
"38",
"33",
"42",
"25",
"60",
"60",
"44",
"24",
"40",
"7",
"4",
"100",
"6",
"89",
"60",
"13",
"38",
"44",
"40",
"60",
"42",
"27",
"60",
"5",
"186",
"157",
... | [
"nonn",
"new"
] | 11 | 1 | 2 | [
"A053050",
"A065091",
"A071148",
"A391806"
] | null | Clark Kimberling, Jan 05 2026 | 2026-01-17T16:13:48 | oeisdata/seq/A391/A391806.seq | 693b07b8bd726f0b7e20c4364c1ed2d1 |
A391807 | a(n) is the least k such that the residues mod 3 of the primes prime(k), prime(k+1),... include a string of n 1's followed by 2. | [
"4",
"11",
"36",
"273",
"272",
"271",
"2209",
"11199",
"13718",
"13717",
"34369",
"172147",
"172146",
"3094796",
"3094795",
"4308948",
"12762142",
"23902561",
"72084958",
"72084957",
"72084956",
"1052779162",
"1052779161",
"1857276774",
"1857276773",
"19398320447",
... | [
"nonn",
"new"
] | 20 | 1 | 1 | [
"A039701",
"A390511",
"A391796",
"A391807"
] | null | Clark Kimberling, Jan 05 2026 | 2026-01-18T23:45:46 | oeisdata/seq/A391/A391807.seq | 164d5388c37579117bfcf38039cf79dc |
A391808 | Number of topological sequences of three dimensional lattice points with depth n and the largest possible index. | [
"1",
"0",
"2",
"1",
"3",
"9",
"3",
"10",
"5",
"1",
"3",
"9"
] | [
"nonn",
"more"
] | 7 | 0 | 3 | [
"A000219",
"A000293",
"A002836",
"A207542",
"A387672",
"A391808"
] | null | John Tyler Rascoe, Dec 20 2025 | 2025-12-28T19:53:03 | oeisdata/seq/A391/A391808.seq | ff32c092b8938a69be9b961b307f4ab5 |
A391809 | A Beatty sequence: floor(n*x) for n >= 1 where x = Sum_{n>=0} 1/2^floor(n*x). | [
"1",
"3",
"5",
"6",
"8",
"10",
"11",
"13",
"15",
"16",
"18",
"20",
"21",
"23",
"25",
"26",
"28",
"30",
"31",
"33",
"35",
"36",
"38",
"40",
"41",
"43",
"45",
"46",
"48",
"50",
"51",
"53",
"55",
"57",
"58",
"60",
"62",
"63",
"65",
"67",
"... | [
"nonn",
"new"
] | 22 | 1 | 2 | [
"A329987",
"A391809",
"A391815"
] | null | Paul D. Hanna, Dec 31 2025 | 2026-01-05T09:59:56 | oeisdata/seq/A391/A391809.seq | 3fe2fac88a7598456e05100d466a5715 |
A391810 | Irregular triangle, read by rows, where row n lists the coefficients of nonpositive powers of x in the doubly infinite series Sum_{k=-oo..oo} x^k * (1 - x^k)^(n+k) for n >= 1. | [
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"2",
"-1",
"-1",
"1",
"-2",
"4",
"-2",
"-1",
"1",
"-3",
"7",
"-6",
"2",
"1",
"0",
"-2",
"1",
"-1",
"1",
"-4",
"11",
"-13",
"6",
"3",
"0",
"-6",
"3",
"-1",
"1",
"-5",
"16",
"-24",
"16",
"1",
"2",
... | [
"sign",
"tabf"
] | 37 | 1 | 8 | [
"A391810",
"A391811"
] | null | Paul D. Hanna, Dec 21 2025 | 2025-12-28T09:57:11 | oeisdata/seq/A391/A391810.seq | 6b311d18bccda053e77a05184d7a77cb |
A391811 | a(n) equals half the sum of the squares of the terms in row n of irregular triangle A391810. | [
"1",
"1",
"4",
"13",
"53",
"199",
"674",
"2313",
"8731",
"34453",
"135151",
"516056",
"1929917",
"7191767",
"27150041",
"104424657",
"407094655",
"1594363303",
"6233521880",
"24277356505",
"94261319494",
"365585759896",
"1419238266986",
"5523689999096",
"2157387579183... | [
"nonn"
] | 11 | 1 | 3 | [
"A391810",
"A391811"
] | null | Paul D. Hanna, Dec 21 2025 | 2025-12-28T09:56:55 | oeisdata/seq/A391/A391811.seq | 6209417e701a8e64eb2006720b195646 |
A391812 | Decimal expansion of the constant x where each term in the simple continued fraction of x equals 2 minus the respective bit in the binary expansion of x, with an initial term of '1'. | [
"1",
"3",
"8",
"6",
"7",
"5",
"0",
"5",
"0",
"6",
"8",
"3",
"7",
"5",
"1",
"7",
"5",
"6",
"7",
"9",
"9",
"4",
"1",
"6",
"8",
"2",
"5",
"7",
"8",
"0",
"4",
"5",
"2",
"2",
"3",
"3",
"2",
"4",
"5",
"1",
"4",
"0",
"1",
"5",
"9",
"... | [
"nonn",
"cons"
] | 13 | 1 | 2 | [
"A391812",
"A391813",
"A391814"
] | null | Paul D. Hanna, Dec 30 2025 | 2025-12-30T11:19:38 | oeisdata/seq/A391/A391812.seq | 9368d19127278dd8eca9d788283ed056 |
A391813 | Continued fraction of the constant x where a(n) = 2 - A391814(n+1) for n >= 0, and A391814 is the binary expansion of x starting with A391814(1) = 1. | [
"1",
"2",
"1",
"1",
"2",
"2",
"2",
"1",
"1",
"2",
"2",
"2",
"2",
"2",
"2",
"1",
"2",
"2",
"2",
"2",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"2",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"2",
"2",
"2",
"2",
"2",
"1",
"... | [
"nonn",
"cofr",
"new"
] | 17 | 0 | 2 | [
"A391812",
"A391813",
"A391814",
"A391873"
] | null | Paul D. Hanna, Dec 30 2025 | 2026-01-05T10:02:22 | oeisdata/seq/A391/A391813.seq | 0025bba2765117d1ff48e5f4deed3a03 |
A391814 | Binary expansion of the constant x where a(n) = 2 - A391813(n-1) for n >= 1, and A391813 is the continued fraction of x starting with A391813(0) = 1. | [
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"... | [
"nonn",
"base",
"new"
] | 15 | 1 | null | [
"A391812",
"A391813",
"A391814",
"A391872"
] | null | Paul D. Hanna, Dec 30 2025 | 2026-01-05T10:00:00 | oeisdata/seq/A391/A391814.seq | f27c511264aff1510686661c35fd0364 |
A391815 | Decimal expansion of the constant x that satisfies x = Sum_{n>=0} 1/2^floor(n*x). | [
"1",
"6",
"7",
"7",
"4",
"1",
"9",
"3",
"5",
"4",
"8",
"3",
"8",
"7",
"0",
"9",
"6",
"7",
"0",
"2",
"5",
"6",
"6",
"2",
"5",
"6",
"4",
"7",
"5",
"7",
"9",
"6",
"3",
"3",
"6",
"3",
"2",
"6",
"2",
"7",
"9",
"7",
"0",
"6",
"4",
"... | [
"nonn",
"cons",
"new"
] | 28 | 1 | 2 | [
"A119809",
"A119812",
"A329986",
"A391809",
"A391815"
] | null | Paul D. Hanna, Dec 30 2025 | 2026-01-05T10:00:04 | oeisdata/seq/A391/A391815.seq | e77419cadd91029c0c533c27d6a7956f |
A391817 | Number of topological sequences of three dimensional lattice points with index n and depth n - 2. | [
"1",
"9",
"25",
"61",
"125",
"252",
"472",
"872",
"1548"
] | [
"nonn",
"more"
] | 5 | 5 | 2 | [
"A000219",
"A000293",
"A002836",
"A207542",
"A387672",
"A391817"
] | null | John Tyler Rascoe, Dec 20 2025 | 2025-12-28T19:53:20 | oeisdata/seq/A391/A391817.seq | 1848c70192b5bbcf47c5a9709ede924a |
A391818 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from upper left corner to lower right corner, and no 1 having more than two 1's adjacent. | [
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"5",
"5",
"1",
"1",
"8",
"17",
"8",
"1",
"1",
"13",
"39",
"39",
"13",
"1",
"1",
"20",
"83",
"132",
"83",
"20",
"1",
"1",
"32",
"175",
"389",
"389",
"175",
"32",
"1",
"1",
"52",
"375",
"1095",
"1561",
... | [
"nonn",
"tabl"
] | 11 | 1 | 5 | [
"A000012",
"A163684",
"A163685",
"A163686",
"A163687",
"A163688",
"A163689",
"A163690",
"A163691",
"A163692",
"A163693",
"A359573",
"A391818",
"A391819",
"A391820",
"A391822"
] | null | Andrew Howroyd, Dec 20 2025 | 2025-12-21T17:31:24 | oeisdata/seq/A391/A391818.seq | 623890a6959a6ac8c14e99a21da6781e |
A391819 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, all corners 1, and no 1 having more than two 1's adjacent. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"5",
"2",
"1",
"1",
"4",
"9",
"9",
"4",
"1",
"1",
"6",
"17",
"13",
"17",
"6",
"1",
"1",
"10",
"39",
"29",
"29",
"39",
"10",
"1",
"1",
"16",
"95",
"87",
"73",
"87",
"95",
... | [
"nonn",
"tabl"
] | 9 | 1 | 8 | [
"A000012",
"A163732",
"A163733",
"A163734",
"A163735",
"A163736",
"A163737",
"A163738",
"A163739",
"A163740",
"A163741",
"A389687",
"A391818",
"A391819",
"A391820",
"A391822"
] | null | Andrew Howroyd, Dec 21 2025 | 2025-12-21T17:31:20 | oeisdata/seq/A391/A391819.seq | d4f0c533decac8f98424af775ed160f8 |
A391820 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected and no 1 having more than two 1's adjacent. | [
"1",
"3",
"3",
"6",
"13",
"6",
"10",
"33",
"33",
"10",
"15",
"69",
"108",
"69",
"15",
"21",
"131",
"291",
"291",
"131",
"21",
"28",
"235",
"710",
"1044",
"710",
"235",
"28",
"36",
"407",
"1635",
"3408",
"3408",
"1635",
"407",
"36",
"45",
"689... | [
"nonn",
"tabl"
] | 6 | 1 | 2 | [
"A360196",
"A360199",
"A391820",
"A391821",
"A391822"
] | null | Andrew Howroyd, Dec 21 2025 | 2025-12-21T17:31:16 | oeisdata/seq/A391/A391820.seq | 0e437fa6905896741bd5eadf1db8d014 |
A391821 | Number of n X n binary arrays with all 1's connected and no 1 having more than two 1's adjacent. | [
"1",
"13",
"108",
"1044",
"15118",
"338008",
"11612695",
"631125163",
"56172850171",
"8350747478181",
"2075606259753276",
"854387913414906842",
"578644663866606223343",
"646305755254714977651975",
"1200822615271663184220885305"
] | [
"nonn"
] | 5 | 1 | 2 | [
"A059525",
"A297664",
"A360200",
"A391820",
"A391821"
] | null | Andrew Howroyd, Dec 21 2025 | 2025-12-21T20:02:14 | oeisdata/seq/A391/A391821.seq | 2f844029d3627924f7381b2cb49ed263 |
A391822 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from top row to bottom row, and no 1 having more than two 1's adjacent. | [
"1",
"3",
"1",
"6",
"7",
"1",
"10",
"21",
"10",
"1",
"15",
"49",
"48",
"16",
"1",
"21",
"101",
"163",
"108",
"26",
"1",
"28",
"193",
"463",
"531",
"236",
"42",
"1",
"36",
"351",
"1186",
"2119",
"1611",
"506",
"68",
"1",
"45",
"617",
"2854",... | [
"nonn",
"tabl"
] | 5 | 1 | 2 | [
"A000012",
"A000217",
"A163713",
"A163714",
"A163715",
"A163716",
"A163717",
"A163718",
"A163719",
"A163720",
"A163721",
"A163722",
"A163723",
"A163724",
"A163725",
"A163726",
"A163727",
"A163728",
"A163729",
"A163730",
"A163731",
"A359574",
"A391818",
"A391819",
"A39... | null | Andrew Howroyd, Dec 21 2025 | 2025-12-21T20:02:01 | oeisdata/seq/A391/A391822.seq | 11312609e55c603906b86cc32ff76671 |
A391823 | Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from top row to lower right corner, and no 1 having more than two 1's adjacent. | [
"1",
"2",
"1",
"3",
"5",
"1",
"4",
"11",
"7",
"1",
"5",
"21",
"28",
"11",
"1",
"6",
"38",
"80",
"63",
"18",
"1",
"7",
"66",
"200",
"259",
"138",
"29",
"1",
"8",
"112",
"469",
"896",
"775",
"298",
"47",
"1",
"9",
"187",
"1064",
"2821",
"... | [
"nonn",
"tabl"
] | 6 | 1 | 2 | [
"A000012",
"A000027",
"A163694",
"A163695",
"A163696",
"A163697",
"A163698",
"A163699",
"A163700",
"A163701",
"A163702",
"A163703",
"A163704",
"A163705",
"A163706",
"A163707",
"A163708",
"A163709",
"A163710",
"A163711",
"A163712",
"A391489",
"A391818",
"A391819",
"A39... | null | Andrew Howroyd, Dec 22 2025 | 2025-12-22T22:07:05 | oeisdata/seq/A391/A391823.seq | e76f50c150ffb1d66c514b147c39f309 |
A391824 | Array read by antidiagonals: T(m,n) is the number of partitions of the vertices of the grid graph P_m X P_n into dominating sets. | [
"1",
"2",
"2",
"2",
"4",
"2",
"3",
"13",
"13",
"3",
"4",
"35",
"66",
"35",
"4",
"6",
"113",
"397",
"397",
"113",
"6",
"9",
"368",
"2436",
"4563",
"2436",
"368",
"9",
"14",
"1182",
"14785",
"52595",
"52595",
"14785",
"1182",
"14",
"22",
"3838"... | [
"nonn",
"tabl",
"new"
] | 9 | 1 | 2 | [
"A001611",
"A180771",
"A207868",
"A218354",
"A230819",
"A391824",
"A391825",
"A391826",
"A391827"
] | null | Andrew Howroyd, Jan 10 2026 | 2026-01-10T20:11:58 | oeisdata/seq/A391/A391824.seq | b310b4407aad8b76e24f8407613afe27 |
A391825 | Number of partitions of the vertices of the n X n grid graph into dominating sets. | [
"1",
"4",
"66",
"4563",
"1168506",
"1075501316",
"3576191040553",
"42884077247092791"
] | [
"nonn",
"more",
"new"
] | 4 | 1 | 2 | [
"A391824",
"A391825"
] | null | Andrew Howroyd, Jan 10 2026 | 2026-01-10T20:11:46 | oeisdata/seq/A391/A391825.seq | da26e5c9be57d81e57ee4b9fb00069ec |
A391826 | Number of partitions of the vertices of the n-ladder graph into dominating sets. | [
"2",
"4",
"13",
"35",
"113",
"368",
"1182",
"3838",
"12463",
"40429",
"131269",
"426262",
"1384198",
"4495620",
"14602111",
"47431703",
"154081177",
"500554852",
"1626190314",
"5283311170",
"17165381859",
"55771348385",
"181208069377",
"588777467930",
"1913070123762",... | [
"nonn",
"new"
] | 5 | 1 | 1 | [
"A180762",
"A230813",
"A391824",
"A391826",
"A391827"
] | null | Andrew Howroyd, Jan 10 2026 | 2026-01-10T20:11:37 | oeisdata/seq/A391/A391826.seq | ebd2812777d3ad7acf4c78d59005c813 |
A391827 | Number of partitions of the vertices of the n X 3 grid graph into dominating sets. | [
"2",
"13",
"66",
"397",
"2436",
"14785",
"90660",
"553739",
"3388938",
"20741171",
"126964984",
"777465223",
"4761197556",
"29162734671",
"178641529684",
"1094401625403",
"6705058123466",
"41082146261365",
"251723814381242",
"1542452107793101",
"9451751484893444",
"57919325... | [
"nonn",
"new"
] | 10 | 1 | 1 | [
"A180763",
"A230814",
"A391824",
"A391826",
"A391827"
] | null | Andrew Howroyd, Jan 10 2026 | 2026-01-10T20:11:26 | oeisdata/seq/A391/A391827.seq | 63442230bd5d8c9ffbce1a66c6cace79 |
A391828 | Numbers k such that the map k -> k' reaches a nonzero cycle, where k' is the arithmetic derivative. | [
"4",
"27",
"3125",
"823543",
"1647082",
"2238771",
"3358143",
"3793738",
"4425686",
"4452758",
"5682974",
"6716282",
"7251855",
"8322027",
"12974315",
"14415850",
"16650815",
"18968665",
"20182246",
"21005098",
"22838035",
"24924635",
"25650001",
"25901246",
"29126923... | [
"nonn",
"new"
] | 26 | 1 | 1 | [
"A003415",
"A051674",
"A099309",
"A348329",
"A391828"
] | null | Michael Adams, Dec 20 2025 | 2026-01-07T15:29:53 | oeisdata/seq/A391/A391828.seq | 0c4ffc68da369dae3e13401015fcc377 |
A391829 | a(n) = (1/4) * Sum_{k=0..n} (k+2) * binomial(2*k+2,2*n-2*k+1). | [
"1",
"3",
"9",
"30",
"91",
"271",
"801",
"2330",
"6710",
"19172",
"54386",
"153362",
"430257",
"1201685",
"3343079",
"9268130",
"25614741",
"70595817",
"194078465",
"532337092",
"1457119612",
"3980884648",
"10856936212",
"29562266740",
"80375490401",
"218228740855",... | [
"nonn"
] | 17 | 0 | 2 | [
"A381421",
"A391829",
"A391832",
"A391835"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T07:30:02 | oeisdata/seq/A391/A391829.seq | 7c416f80bd8a101526341b668e098e88 |
A391830 | a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * binomial(2*k+2,2*n-4*k+1). | [
"1",
"0",
"3",
"3",
"6",
"20",
"16",
"70",
"85",
"190",
"399",
"565",
"1429",
"2114",
"4425",
"8145",
"13877",
"28508",
"47243",
"92523",
"165512",
"297396",
"562390",
"982140",
"1843714",
"3292870",
"5975118",
"10938740",
"19496065",
"35751958",
"63998039... | [
"nonn"
] | 17 | 0 | 3 | [
"A391830",
"A391833",
"A391836"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T06:26:37 | oeisdata/seq/A391/A391830.seq | e4b3a5e3eb61c9ec2a947eb0fff2987f |
A391831 | a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * binomial(2*n-4*k+2,2*k+1). | [
"1",
"3",
"6",
"13",
"35",
"91",
"214",
"491",
"1151",
"2711",
"6290",
"14427",
"33010",
"75444",
"171786",
"389500",
"880533",
"1986357",
"4471290",
"10042661",
"22511404",
"50374282",
"112545858",
"251073154",
"559324988",
"1244426930",
"2765391188",
"61384448... | [
"nonn"
] | 17 | 0 | 2 | [
"A391831",
"A391834",
"A391837"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T06:26:41 | oeisdata/seq/A391/A391831.seq | 5b7fea828df900e0bafe3531bea746d6 |
A391832 | a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^k * binomial(2*k+2,2*n-2*k+1). | [
"1",
"6",
"30",
"160",
"824",
"4112",
"20240",
"98432",
"473648",
"2260000",
"10707872",
"50428928",
"236267264",
"1101967872",
"5119345152",
"23699419136",
"109371557120",
"503331831296",
"2310505584128",
"10581929451520",
"48363392444416",
"220617599430656",
"1004622677... | [
"nonn"
] | 17 | 0 | 2 | [
"A391829",
"A391832",
"A391835"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T07:30:05 | oeisdata/seq/A391/A391832.seq | e21cec260922a65a000edc2d969fa21d |
A391833 | a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * 2^k * binomial(2*k+2,2*n-4*k+1). | [
"1",
"0",
"6",
"6",
"24",
"80",
"104",
"560",
"800",
"2960",
"6720",
"15200",
"46384",
"90944",
"273184",
"601248",
"1525760",
"3863552",
"8808192",
"23230464",
"53175296",
"134251008",
"323028992",
"774392832",
"1920513280",
"4529858560",
"11176308224",
"266691... | [
"nonn"
] | 17 | 0 | 3 | [
"A391830",
"A391833",
"A391836"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T06:26:49 | oeisdata/seq/A391/A391833.seq | 19a9794f84b4d8fb33effd6b56f9520d |
A391834 | a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * 2^(n-2*k) * binomial(2*n-4*k+2,2*k+1). | [
"1",
"6",
"24",
"86",
"320",
"1232",
"4696",
"17488",
"64160",
"233872",
"848960",
"3067200",
"11026672",
"39468576",
"140761344",
"500445344",
"1774199808",
"6273738240",
"22132498176",
"77912939008",
"273744796672",
"960083626496",
"3361707657216",
"11753105758208",
... | [
"nonn",
"easy"
] | 20 | 0 | 2 | [
"A391831",
"A391834",
"A391837"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-02T15:47:23 | oeisdata/seq/A391/A391834.seq | b3f0935f0e317add651fe4ddaa5bee3d |
A391835 | a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^(n-k) * binomial(2*k+2,2*n-2*k+1). | [
"1",
"3",
"12",
"50",
"179",
"661",
"2390",
"8476",
"29909",
"104519",
"362672",
"1251478",
"4295783",
"14680713",
"49976442",
"169541536",
"573390953",
"1933856347",
"6505983668",
"21838288442",
"73152323803",
"244578237373",
"816308965214",
"2720178349156",
"9051042... | [
"nonn"
] | 17 | 0 | 2 | [
"A391829",
"A391832",
"A391835"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T07:30:09 | oeisdata/seq/A391/A391835.seq | fe8475352f5489995fb0be4270e291fa |
A391836 | a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * 2^(n-2*k) * binomial(2*k+2,2*n-4*k+1). | [
"1",
"0",
"3",
"6",
"6",
"40",
"34",
"140",
"295",
"440",
"1533",
"2210",
"5812",
"12544",
"22212",
"58104",
"103421",
"233296",
"499367",
"957246",
"2196050",
"4265208",
"9077206",
"19147812",
"38083843",
"82195784",
"165218433",
"343559002",
"715871584",
"... | [
"nonn",
"easy"
] | 21 | 0 | 3 | [
"A391830",
"A391833",
"A391836"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-02T15:47:18 | oeisdata/seq/A391/A391836.seq | 33c9d140d6cbe0cb42983155f62696f6 |
A391837 | a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * 2^k * binomial(2*n-4*k+2,2*k+1). | [
"1",
"3",
"6",
"16",
"55",
"161",
"412",
"1086",
"3013",
"8199",
"21602",
"56748",
"150163",
"395885",
"1034872",
"2695210",
"7014705",
"18219971",
"47176414",
"121863960",
"314305951",
"809367049",
"2080584852",
"5340057974",
"13687727069",
"35041285439",
"895992... | [
"nonn"
] | 17 | 0 | 2 | [
"A391831",
"A391834",
"A391837"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-03T07:29:59 | oeisdata/seq/A391/A391837.seq | b9a5dd8e8c3bc82e9f6eaa2b4ad28f8a |
A391839 | a(n) is the least prime that can be written as (product + sum) of n distinct composite numbers. | [
"79",
"383",
"3491",
"17317",
"207409",
"4976711",
"46448719",
"1088640103",
"25082265727",
"338610585739",
"6270566400157",
"147483721728181",
"2781121609728199",
"78219045273600227",
"2294425328025600257",
"70501432806604800289",
"1803968969906847744313",
"61225613524111196160347... | [
"nonn"
] | 7 | 2 | 1 | [
"A391772",
"A391839"
] | null | Robert Israel, Dec 21 2025 | 2025-12-23T09:41:17 | oeisdata/seq/A391/A391839.seq | fd57a9ab9a006387df77856aefb29928 |
A391840 | Base 16 sum of digits of prime(n). | [
"2",
"3",
"5",
"7",
"11",
"13",
"2",
"4",
"8",
"14",
"16",
"7",
"11",
"13",
"17",
"8",
"14",
"16",
"7",
"11",
"13",
"19",
"8",
"14",
"7",
"11",
"13",
"17",
"19",
"8",
"22",
"11",
"17",
"19",
"14",
"16",
"22",
"13",
"17",
"23",
"14",
"... | [
"nonn",
"base"
] | 21 | 1 | 1 | [
"A007605",
"A014499",
"A053836",
"A239690",
"A239694",
"A391840"
] | null | Kaloian Ivanov, Dec 21 2025 | 2025-12-30T13:31:44 | oeisdata/seq/A391/A391840.seq | cd29de062451e0af1c6f5369712d8371 |
A391841 | Positive integers k with exactly sqrt(tau(k)) square divisors. | [
"1",
"8",
"27",
"125",
"216",
"343",
"384",
"640",
"896",
"1000",
"1331",
"1408",
"1440",
"1664",
"2016",
"2176",
"2197",
"2400",
"2432",
"2744",
"2944",
"3168",
"3375",
"3712",
"3744",
"3968",
"4374",
"4704",
"4736",
"4860",
"4896",
"4913",
"5248",
... | [
"nonn"
] | 7 | 1 | 2 | [
"A000005",
"A036436",
"A046951",
"A391841"
] | null | Felix Huber, Dec 30 2025 | 2026-01-04T20:49:38 | oeisdata/seq/A391/A391841.seq | f99a963bec42615feee523293acdf6a9 |
A391842 | Integers k such that d(k)*d(k+1) is a divisor of k*(k+1) where d(k) = A000005(k) is the number of divisors of k. | [
"1",
"3",
"7",
"8",
"11",
"12",
"15",
"24",
"32",
"35",
"36",
"44",
"63",
"71",
"72",
"79",
"95",
"96",
"116",
"127",
"128",
"144",
"159",
"171",
"179",
"180",
"239",
"240",
"243",
"251",
"287",
"304",
"324",
"332",
"335",
"351",
"360",
"383"... | [
"nonn"
] | 30 | 1 | 2 | [
"A000005",
"A002378",
"A033950",
"A092517",
"A114617",
"A391842"
] | null | Hoàn Toán, Dec 21 2025 | 2025-12-29T19:28:40 | oeisdata/seq/A391/A391842.seq | d2d64316c67fd45bd931f4f930f05a7a |
A391844 | a(n) = 1 if the least prime not dividing the arithmetic derivative of n is equal to the least prime dividing n, otherwise 0. a(1) = 1 by convention. | [
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"... | [
"nonn",
"new"
] | 7 | 1 | null | [
"A003415",
"A020639",
"A053669",
"A370124",
"A391844",
"A391845"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-16T13:17:12 | oeisdata/seq/A391/A391844.seq | c259b0bdbd98ad8b8337e4f6aecb01c6 |
A391845 | Numbers k such that the least prime not dividing the arithmetic derivative of k is equal to the least prime dividing k. | [
"1",
"2",
"6",
"10",
"14",
"15",
"18",
"21",
"22",
"26",
"30",
"33",
"34",
"35",
"38",
"39",
"42",
"46",
"50",
"51",
"54",
"57",
"58",
"62",
"65",
"66",
"69",
"70",
"74",
"78",
"82",
"86",
"87",
"90",
"93",
"94",
"95",
"98",
"102",
"106",... | [
"nonn",
"new"
] | 14 | 1 | 2 | [
"A003415",
"A020639",
"A048103",
"A053669",
"A080364",
"A369650",
"A370125",
"A391844",
"A391845",
"A392592"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-17T16:41:03 | oeisdata/seq/A391/A391845.seq | 38f0d34f3b9ce8e01fa682c9810b2143 |
A391846 | Numbers k such that 11*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"6",
"8",
"12",
"15",
"16",
"17",
"24",
"27",
"30",
"31",
"32",
"33",
"34",
"48",
"51",
"54",
"60",
"62",
"63",
"64",
"65",
"66",
"68",
"96",
"102",
"108",
"120",
"124",
"126",
"127",
"128",
"129",
"130",
"132",
"... | [
"nonn",
"base"
] | 13 | 1 | 3 | [
"A048718",
"A048720",
"A115803",
"A280500",
"A391585",
"A391740",
"A391742",
"A391744",
"A391846",
"A391847",
"A391848",
"A391850",
"A391852",
"A391854",
"A391856",
"A391858",
"A391860",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-29T07:32:42 | oeisdata/seq/A391/A391846.seq | c55f7996164cd934363df181f274f7fb |
A391847 | Odd numbers k such that 11*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"15",
"17",
"27",
"31",
"33",
"51",
"63",
"65",
"127",
"129",
"195",
"207",
"219",
"243",
"255",
"257",
"273",
"387",
"403",
"411",
"415",
"435",
"499",
"511",
"513",
"529",
"545",
"771",
"783",
"819",
"831",
"963",
"975",
"1011",
"10... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A048720",
"A280500",
"A391584",
"A391725",
"A391741",
"A391743",
"A391745",
"A391846",
"A391847",
"A391849",
"A391851"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T14:41:40 | oeisdata/seq/A391/A391847.seq | 5fdfe82fffe86b9ccc2265d95d040ac7 |
A391848 | Numbers k such that 13*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"10",
"12",
"15",
"16",
"17",
"20",
"21",
"24",
"30",
"31",
"32",
"33",
"34",
"40",
"42",
"45",
"47",
"48",
"60",
"61",
"62",
"63",
"64",
"65",
"66",
"68",
"80",
"84",
"85",
"90",
"94",
"95",
"96"... | [
"nonn",
"base"
] | 12 | 1 | 3 | [
"A048718",
"A048720",
"A115772",
"A115805",
"A280500",
"A391585",
"A391740",
"A391742",
"A391744",
"A391846",
"A391848",
"A391849",
"A391850",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-29T07:32:45 | oeisdata/seq/A391/A391848.seq | c18946ca0f316834d7598deecc9e1988 |
A391849 | Odd numbers k such that 13*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"15",
"17",
"21",
"31",
"33",
"45",
"47",
"61",
"63",
"65",
"85",
"95",
"125",
"127",
"129",
"165",
"173",
"175",
"181",
"189",
"191",
"195",
"245",
"253",
"255",
"257",
"273",
"341",
"351",
"381",
"383",
"387",
"501",
"509",
"... | [
"nonn",
"base"
] | 6 | 1 | 2 | [
"A048720",
"A280500",
"A391584",
"A391725",
"A391741",
"A391743",
"A391745",
"A391847",
"A391848",
"A391849",
"A391851"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T14:42:48 | oeisdata/seq/A391/A391849.seq | 450fec726bac4ddec69da9641437ae18 |
A391850 | Numbers k such that 15*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"10",
"12",
"15",
"16",
"17",
"20",
"21",
"24",
"30",
"31",
"32",
"33",
"34",
"40",
"42",
"48",
"51",
"60",
"62",
"63",
"64",
"65",
"66",
"68",
"80",
"84",
"85",
"96",
"102",
"120",
"124",
"126",
... | [
"nonn",
"base"
] | 11 | 1 | 3 | [
"A048718",
"A048720",
"A115774",
"A115801",
"A115807",
"A280500",
"A391585",
"A391740",
"A391742",
"A391744",
"A391846",
"A391850",
"A391851",
"A391852",
"A391854",
"A391856",
"A391858",
"A391860",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-29T07:32:53 | oeisdata/seq/A391/A391850.seq | b760b8a64eb533ee8504d7272b7ab180 |
A391851 | Odd numbers k such that 15*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"15",
"17",
"21",
"31",
"33",
"51",
"63",
"65",
"85",
"127",
"129",
"195",
"255",
"257",
"273",
"341",
"387",
"511",
"513",
"529",
"545",
"645",
"771",
"819",
"1023",
"1025",
"1041",
"1057",
"1089",
"1285",
"1365",
"1539",
"2047",
... | [
"nonn",
"base"
] | 6 | 1 | 2 | [
"A048720",
"A280500",
"A391584",
"A391725",
"A391741",
"A391743",
"A391745",
"A391847",
"A391849",
"A391850",
"A391851"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T17:04:06 | oeisdata/seq/A391/A391851.seq | 268c8961c58ccb6ffcc88186a4161d04 |
A391852 | Numbers k such that 17*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"18",
"20",
"22",
"24",
"26",
"28",
"30",
"31",
"32",
"33",
"36",
"37",
"40",
"41",
"44",
"45",
"48",
"52",
"56",
"60",
"62",
"63",
"64",
"65",
... | [
"nonn",
"base"
] | 7 | 1 | 3 | [
"A048720",
"A115809",
"A115847",
"A280500",
"A391852",
"A391853"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T20:02:06 | oeisdata/seq/A391/A391852.seq | 920f2db2f2b2034ab37f748d605ec4ee |
A391853 | Odd numbers k such that 17*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"31",
"33",
"37",
"41",
"45",
"63",
"65",
"67",
"73",
"75",
"97",
"105",
"127",
"129",
"131",
"133",
"135",
"161",
"165",
"193",
"195",
"225",
"255",
"257",
"259",
"261",
"263",
"265",
"267",
"269",
... | [
"nonn",
"base"
] | 7 | 1 | 2 | [
"A048720",
"A280500",
"A391725",
"A391852",
"A391853"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T20:02:10 | oeisdata/seq/A391/A391853.seq | ddce0cc169aa87f1eee94db91c27ddc1 |
A391854 | Numbers k such that 19*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"10",
"12",
"14",
"16",
"20",
"24",
"28",
"31",
"32",
"33",
"40",
"48",
"56",
"62",
"63",
"64",
"65",
"66",
"80",
"96",
"112",
"119",
"124",
"126",
"127",
"128",
"129",
"130",
"132",
"133",
"16... | [
"nonn",
"base"
] | 9 | 1 | 3 | [
"A048720",
"A115805",
"A115874",
"A280500",
"A391854",
"A391855"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T20:02:17 | oeisdata/seq/A391/A391854.seq | e5545e3ecb4d3c89e6c913ddbf9a8d92 |
A391855 | Odd numbers k such that 19*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"7",
"31",
"33",
"63",
"65",
"119",
"127",
"129",
"133",
"161",
"195",
"255",
"257",
"261",
"321",
"387",
"455",
"511",
"513",
"517",
"641",
"645",
"771",
"1023",
"1025",
"1029",
"1057",
"1281",
"1285",
"1539",
"1799",
"1823",
"191... | [
"nonn",
"base"
] | 7 | 1 | 2 | [
"A048720",
"A280500",
"A391725",
"A391854",
"A391855"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T20:01:57 | oeisdata/seq/A391/A391855.seq | 47c5905ee49d4aacaa533495a1b35ca3 |
A391856 | Numbers k such that 21*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"12",
"16",
"18",
"20",
"21",
"24",
"31",
"32",
"33",
"36",
"40",
"42",
"48",
"62",
"63",
"64",
"65",
"66",
"67",
"72",
"73",
"80",
"84",
"85",
"96",
"97",
"124",
"126",
"127",
"128",
"... | [
"nonn",
"base"
] | 13 | 1 | 3 | [
"A048720",
"A115422",
"A115774",
"A115809",
"A280500",
"A391856",
"A391857",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-26T16:03:01 | oeisdata/seq/A391/A391856.seq | 0b094267d471ee20c287a5e06d64112a |
A391857 | Odd numbers k such that 21*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"9",
"21",
"31",
"33",
"63",
"65",
"67",
"73",
"85",
"97",
"127",
"129",
"131",
"193",
"195",
"255",
"257",
"259",
"265",
"289",
"341",
"385",
"387",
"511",
"513",
"515",
"521",
"577",
"579",
"585",
"645",
"769",
"771",
"777",
... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A048720",
"A280500",
"A391725",
"A391856",
"A391857"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T22:32:28 | oeisdata/seq/A391/A391857.seq | 11d3287558324923fabc47c1a6c92614 |
A391858 | Numbers k such that 25*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"10",
"12",
"14",
"16",
"20",
"24",
"28",
"31",
"32",
"33",
"40",
"48",
"51",
"56",
"62",
"63",
"64",
"65",
"66",
"80",
"93",
"95",
"96",
"102",
"112",
"124",
"125",
"126",
"127",
"128",
"129",... | [
"nonn",
"base"
] | 17 | 1 | 3 | [
"A048720",
"A280500",
"A391737",
"A391738",
"A391739",
"A391744",
"A391858",
"A391859",
"A391860",
"A391925"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-23T15:04:18 | oeisdata/seq/A391/A391858.seq | 84eb8b25747e7d2158f1ee82cb4eaff9 |
A391859 | Odd numbers k such that 25*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"7",
"31",
"33",
"51",
"63",
"65",
"93",
"95",
"125",
"127",
"129",
"133",
"161",
"191",
"253",
"255",
"257",
"261",
"321",
"381",
"383",
"387",
"509",
"511",
"513",
"517",
"641",
"645",
"765",
"767",
"771",
"775",
"819",
"899",
... | [
"nonn",
"base"
] | 6 | 1 | 2 | [
"A048720",
"A280500",
"A391725",
"A391745",
"A391858",
"A391859",
"A391861"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T22:31:55 | oeisdata/seq/A391/A391859.seq | 3aad8765619b9a5e77a2a5fb393a9f42 |
A391860 | Numbers k such that 49*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"14",
"15",
"16",
"18",
"20",
"21",
"24",
"28",
"30",
"32",
"36",
"40",
"42",
"48",
"56",
"60",
"63",
"64",
"65",
"72",
"73",
"80",
"84",
"85",
"96",
"99",
"112",
"120",
"126... | [
"nonn",
"base"
] | 7 | 1 | 3 | [
"A048720",
"A114384",
"A280500",
"A391744",
"A391858",
"A391860",
"A391861"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T22:32:24 | oeisdata/seq/A391/A391860.seq | c8bea68652de21c582a06a229ef9a165 |
A391861 | Odd numbers k such that 49*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"7",
"9",
"15",
"21",
"63",
"65",
"73",
"85",
"99",
"127",
"129",
"189",
"191",
"253",
"255",
"257",
"261",
"321",
"341",
"383",
"509",
"511",
"513",
"517",
"521",
"577",
"585",
"641",
"693",
"701",
"703",
"757",
"765",
"767",
... | [
"nonn",
"base"
] | 7 | 1 | 2 | [
"A048720",
"A280500",
"A391725",
"A391745",
"A391859",
"A391860",
"A391861"
] | null | Antti Karttunen, Dec 21 2025 | 2025-12-21T22:32:20 | oeisdata/seq/A391/A391861.seq | 174af854b368561565713d76b20631eb |
A391862 | Numbers k that are coprime to A276085(k), where A276085 is the primorial base log-function. | [
"1",
"2",
"3",
"5",
"7",
"8",
"9",
"10",
"11",
"13",
"14",
"15",
"17",
"18",
"19",
"21",
"22",
"23",
"24",
"25",
"26",
"29",
"31",
"32",
"33",
"34",
"35",
"37",
"39",
"40",
"41",
"43",
"46",
"47",
"49",
"50",
"51",
"53",
"54",
"55",
"56... | [
"nonn",
"new"
] | 8 | 1 | 2 | [
"A276085",
"A359794",
"A369650",
"A373361",
"A391862",
"A391863"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-16T19:12:40 | oeisdata/seq/A391/A391862.seq | d2727537508e85fab20e4a12a877c7fc |
A391863 | Numbers k that are coprime to A276085(k) and that are not divisible by p^p for any prime p, where A276085 is the primorial base log-function. | [
"1",
"2",
"3",
"5",
"7",
"9",
"10",
"11",
"13",
"14",
"15",
"17",
"18",
"19",
"21",
"22",
"23",
"25",
"26",
"29",
"31",
"33",
"34",
"35",
"37",
"39",
"41",
"43",
"46",
"47",
"49",
"50",
"51",
"53",
"55",
"57",
"58",
"59",
"61",
"62",
"6... | [
"nonn",
"new"
] | 9 | 1 | 2 | [
"A048103",
"A276085",
"A276086",
"A324583",
"A359550",
"A373361",
"A391862",
"A391863",
"A391866"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-16T19:12:17 | oeisdata/seq/A391/A391863.seq | 81d7295ce6a480f07dc543bf46d00398 |
A391864 | Numbers k such that A003415(k) == A276085(k) (mod 2310), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function. | [
"1",
"2",
"10",
"15",
"28",
"161",
"2189",
"2308",
"4618",
"5005",
"6924",
"6927",
"7917",
"9684",
"11024",
"11540",
"11548",
"11555",
"16331",
"18478",
"20772",
"20788",
"21147",
"23098",
"23105",
"24660",
"27717",
"27718",
"29861",
"30028",
"31065",
"3... | [
"nonn",
"new"
] | 24 | 1 | 2 | [
"A003415",
"A276085",
"A369650",
"A391864",
"A391865",
"A391946",
"A391947",
"A392593",
"A392598"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-18T15:40:34 | oeisdata/seq/A391/A391864.seq | b30e612aee0a579a84cefb12be5ce5bf |
A391865 | Numbers k such that A003415(k) == A276085(k) (mod 5^5), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function. | [
"1",
"2",
"10",
"15",
"28",
"2681",
"3828",
"5005",
"5239",
"10906",
"12768",
"13656",
"13761",
"16119",
"16591",
"22616",
"26318",
"26831",
"33881",
"37105",
"39477",
"40806",
"42638",
"54940",
"55228",
"62883",
"63957",
"64331",
"70119",
"76882",
"79199"... | [
"nonn",
"new"
] | 9 | 1 | 2 | [
"A003415",
"A276085",
"A369650",
"A377878",
"A391864",
"A391865"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-16T19:13:01 | oeisdata/seq/A391/A391865.seq | 8a893193239e91f655966459d12e03c4 |
A391866 | Nonsquarefree numbers k that are not divisible by p^p for any prime p, and for which A276085(k) is a multiple of A003557(k), where A276085 is the primorial base log-function. | [
"150",
"294",
"578",
"1050",
"1083",
"1650",
"1694",
"1950",
"2535",
"2550",
"2625",
"2850",
"3234",
"3450",
"3630",
"3822",
"4350",
"4650",
"4998",
"5145",
"5550",
"5586",
"6150",
"6375",
"6450",
"6762",
"7050",
"7942",
"7950",
"8526",
"8850",
"8918",
... | [
"nonn",
"new"
] | 10 | 1 | 1 | [
"A003557",
"A008966",
"A276085",
"A359550",
"A371083",
"A371086",
"A391866",
"A392592"
] | null | Antti Karttunen, Jan 16 2026 | 2026-01-17T16:41:07 | oeisdata/seq/A391/A391866.seq | 32b7d84e0f43f09d7152cbdc6b61e041 |
A391870 | Records in A210693. | [
"4",
"11",
"18",
"23",
"48",
"221",
"2003",
"2927",
"4256",
"10063",
"19296",
"23618",
"57576",
"70852",
"125558",
"181586",
"211101",
"593286",
"742861",
"1384104",
"1938665",
"2103883",
"2341224",
"2469308",
"2757948",
"3419961",
"4763217",
"8229111",
"93441... | [
"nonn"
] | 15 | 1 | 1 | [
"A210693",
"A391870",
"A391871"
] | null | Paolo Xausa, Dec 21 2025 | 2025-12-23T03:06:15 | oeisdata/seq/A391/A391870.seq | 239a32ff97abf7ede91731b859a8cdb9 |
A391871 | Indices of records in A210693. | [
"1",
"2",
"12",
"21",
"24",
"27",
"71",
"407",
"425",
"447",
"567",
"1073",
"1151",
"1643",
"2729",
"3947",
"5277",
"5393",
"9665",
"14123",
"17309",
"21827",
"28551",
"30113",
"33633",
"42749",
"45737",
"50177",
"75755",
"83213",
"126737",
"145577",
"... | [
"nonn"
] | 19 | 1 | 2 | [
"A210693",
"A391870",
"A391871"
] | null | Paolo Xausa, Dec 21 2025 | 2026-01-03T06:25:47 | oeisdata/seq/A391/A391871.seq | 3036b038eef5e42937b80aa782390af1 |
A391872 | Decimal expansion of the constant x where the terms in the simple continued fraction expansion of x equal 2 plus the respective bits in the binary expansion of x, after the initial constant term of '1'. | [
"1",
"4",
"3",
"4",
"0",
"5",
"7",
"5",
"3",
"6",
"1",
"6",
"6",
"2",
"2",
"9",
"0",
"9",
"0",
"1",
"9",
"9",
"5",
"8",
"5",
"3",
"9",
"2",
"4",
"8",
"7",
"9",
"5",
"1",
"1",
"3",
"5",
"9",
"1",
"7",
"8",
"5",
"6",
"0",
"1",
"... | [
"nonn",
"cons"
] | 15 | 1 | 2 | [
"A391872",
"A391873"
] | null | Paul D. Hanna, Dec 22 2025 | 2025-12-28T09:56:58 | oeisdata/seq/A391/A391872.seq | 155dc44f38cfd37819fb0cdc68cce1a3 |
A391873 | Continued fraction expansion of the constant x in which each term equals 2 plus the respective bit in the binary expansion of x, after the initial constant term of '1'. | [
"1",
"2",
"3",
"3",
"2",
"3",
"3",
"3",
"3",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"2",
"2",
"3",
"3",
"2",
"2",
"3",
"2",
"3",
"2",
"2",
"2",
"2",
"3",
"2",
"3",
"2",
"2",
"3",
"3",
"2",
"3",
"2",
"3",
"2",
"3",
"2",
"2",
"3",
"... | [
"nonn",
"cofr",
"cons",
"easy"
] | 15 | 0 | 2 | [
"A391872",
"A391873"
] | null | Paul D. Hanna, Dec 22 2025 | 2025-12-28T09:56:51 | oeisdata/seq/A391/A391873.seq | a341b3454a411b1e4bb4865d5ff97c07 |
A391874 | Nonsquare integers >= 2 for which the square of its largest prime factor equals the sum of the squares of its other prime factors, with multiplicity. | [
"240",
"2240",
"3402",
"21504",
"34650",
"80262",
"92664",
"145350",
"165000",
"185130",
"194922",
"332640",
"342342",
"382200",
"432630",
"505197",
"585728",
"640458",
"792918",
"909558",
"928200",
"1395360",
"1539384",
"1584000",
"1630200",
"1706922",
"1716858",... | [
"nonn",
"changed"
] | 28 | 1 | 1 | [
"A385967",
"A390574",
"A391874"
] | null | Charles L. Hohn, Dec 21 2025 | 2026-01-12T12:17:57 | oeisdata/seq/A391/A391874.seq | 27fed3b21de2f934c6def8963fee4bd8 |
A391875 | a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(2*k,2*(n-k)). | [
"1",
"6",
"30",
"224",
"1464",
"8592",
"48912",
"270720",
"1459248",
"7709216",
"40068000",
"205378560",
"1040357120",
"5216715264",
"25927942656",
"127867834368",
"626272781568",
"3048584609280",
"14758392452608",
"71091792715776",
"340910500030464",
"1628080470994944",
... | [
"nonn",
"easy"
] | 20 | 0 | 2 | [
"A108485",
"A390700",
"A391875"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-02T15:56:40 | oeisdata/seq/A391/A391875.seq | 829e542641423a22389a9bfd804e24a4 |
A391876 | a(n) = Sum_{k=0..n} 2^(n-k) * binomial(k+2,2) * binomial(2*k,2*(n-k)). | [
"1",
"3",
"12",
"82",
"339",
"1461",
"6198",
"24732",
"97557",
"377095",
"1431792",
"5370102",
"19904711",
"73046121",
"265779354",
"959669856",
"3441865065",
"12270185691",
"43506695476",
"153510593754",
"539253893883",
"1886647300701",
"6576263406270",
"22844885842020... | [
"nonn",
"easy"
] | 20 | 0 | 2 | [
"A108480",
"A390732",
"A391876"
] | null | Seiichi Manyama, Dec 21 2025 | 2026-01-02T15:56:45 | oeisdata/seq/A391/A391876.seq | db2ce1de87d7d94739f7fe7f727a2ee8 |
A391877 | Number of directed Hamiltonian cycles in the complete 5-partite graph K_{n,n,n,n,n}. | [
"24",
"112512",
"8730457344",
"3965523677282304",
"6602585886478172160000",
"30755963063492987269939200000",
"335936272110882930782166948249600000",
"7595808835329828456450518426001290035200000",
"324050343201501938055429125845935244614775603200000",
"2427896693981310120923718660456542234765474503... | [
"nonn"
] | 12 | 1 | 1 | [
"A010790",
"A234365",
"A378241",
"A391877"
] | null | Medet Jumadildayev, Dec 21 2025 | 2025-12-28T21:16:13 | oeisdata/seq/A391/A391877.seq | cd3c0a30edfb74618beaef19e970915a |
A391880 | Triangle T(n,k) read by rows, where the n-th row is the vector of n consecutive primes with minimum first element, such that the components of the sum of this vector and of this vector arranged in reverse order are all the same. | [
"2",
"2",
"3",
"3",
"5",
"7",
"5",
"7",
"11",
"13",
"18713",
"18719",
"18731",
"18743",
"18749",
"5",
"7",
"11",
"13",
"17",
"19",
"683747",
"683759",
"683777",
"683783",
"683789",
"683807",
"683819",
"17",
"19",
"23",
"29",
"31",
"37",
"41",
"43... | [
"nonn",
"tabl"
] | 10 | 1 | 1 | [
"A055382",
"A175309",
"A267028",
"A391880",
"A391881"
] | null | Hugo Pfoertner, Dec 22 2025 | 2025-12-22T10:40:23 | oeisdata/seq/A391/A391880.seq | 9a4eafe1de2f2ed9423a1885268adfa9 |
A391881 | a(n) = T(n,1) + T(n,n), where T(n,k) is A391880. | [
"4",
"5",
"10",
"18",
"37462",
"24",
"1367566",
"60",
"196607854",
"60",
"120670499918",
"330",
"2339539498438",
"16043622",
"7891538081398078",
"2142130380",
"318135617703221314",
"3227805300",
"13839880244194493194",
"3595191630030"
] | [
"nonn",
"more",
"hard"
] | 5 | 1 | 1 | [
"A175309",
"A391880",
"A391881"
] | null | Hugo Pfoertner, Dec 22 2025 | 2025-12-22T10:02:31 | oeisdata/seq/A391/A391881.seq | 737483e268c0d3e9cac19d132b45ab15 |
A391882 | a(n) is the least k > 0 such that n! + k is an odd nonsquare semiprime (A046388). | [
"14",
"14",
"13",
"9",
"9",
"3",
"1",
"5",
"1",
"5",
"1",
"3",
"17",
"1",
"1",
"7",
"7",
"3",
"23",
"1",
"1",
"11",
"29",
"3",
"1",
"1",
"1",
"37",
"1",
"41",
"47",
"19",
"11",
"11",
"1",
"7",
"3",
"41",
"1",
"13",
"127",
"47",
"59"... | [
"nonn"
] | 6 | 0 | 1 | [
"A046388",
"A131057",
"A356207",
"A391882"
] | null | Hugo Pfoertner, Dec 30 2025 | 2025-12-30T17:17:31 | oeisdata/seq/A391/A391882.seq | d8ebbf913aabe41520a18649cb2a5315 |
A391883 | a(n) = A000010(n) mod A048865(n). | [
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"1",
"2",
"2",
"0",
"3",
"4",
"1",
"4",
"2",
"0",
"4",
"6",
"1",
"4",
"5",
"2",
"5",
"1",
"1",
"0",
"6",
"2",
"7",
"6",
"3",
"3",
"8",
"4",
"6",
"4",
"2",
"3",
"8",
"0",
"10",
"4",
... | [
"nonn",
"look"
] | 18 | 3 | 9 | [
"A000010",
"A048865",
"A307712",
"A391883"
] | null | Ctibor O. Zizka, Dec 22 2025 | 2025-12-29T05:59:05 | oeisdata/seq/A391/A391883.seq | 030cda256471efbbd977f11d546e2400 |
A391885 | Numbers m such that the product m*(m+1) has a set of prime divisors, from greatest down to 2, that is missing exactly one prime divisor. | [
"4",
"6",
"21",
"27",
"44",
"48",
"49",
"54",
"55",
"63",
"65",
"77",
"90",
"98",
"99",
"104",
"120",
"175",
"195",
"350",
"363",
"560",
"594",
"935",
"1000",
"1155",
"1274",
"2430",
"2925",
"4095",
"4199",
"4224",
"5984",
"10647",
"10829",
"1436... | [
"nonn",
"fini",
"full"
] | 25 | 1 | 1 | [
"A059957",
"A252489",
"A391449",
"A391602",
"A391885",
"A391970"
] | null | Ken Clements, Dec 22 2025 | 2025-12-31T16:01:01 | oeisdata/seq/A391/A391885.seq | 9c083c8c60dc203e9b455c87ac3b3587 |
A391886 | Array read by downward antidiagonals: A(n,k) = A(n-1,k) + (k+1)*A(n-1,k+1) + k*A(n-1,k-1) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = 1. | [
"1",
"1",
"2",
"1",
"4",
"6",
"1",
"6",
"18",
"24",
"1",
"8",
"38",
"100",
"124",
"1",
"10",
"66",
"272",
"668",
"792",
"1",
"12",
"102",
"588",
"2236",
"5264",
"6056",
"1",
"14",
"146",
"1096",
"5788",
"20936",
"47928",
"53984",
"1",
"16",
... | [
"nonn",
"tabl"
] | 8 | 0 | 3 | [
"A201158",
"A391886"
] | null | Mikhail Kurkov, Dec 22 2025 | 2025-12-23T04:23:03 | oeisdata/seq/A391/A391886.seq | a285e6d5465d88619b74f5c9e8179508 |
A391887 | Alternately add and multiply the last two terms starting with 2, 1. | [
"2",
"1",
"3",
"3",
"6",
"18",
"24",
"432",
"456",
"196992",
"197448",
"38895676416",
"38895873864",
"1512881323731695591424",
"1512881323770591465288",
"2288809899755012359448064967916189926490112",
"2288809899755012359449577849239960517955400"
] | [
"nonn",
"easy"
] | 21 | 0 | 1 | [
"A000032",
"A000204",
"A039941",
"A077753",
"A265496",
"A391887"
] | null | Adolf Cusmariu, Dec 22 2025 | 2025-12-29T15:11:52 | oeisdata/seq/A391/A391887.seq | f95ee24b67746d21dd842d7b91029c78 |
A391890 | a(n) = Sum_{k=0..n} (k+1) * binomial(2*k+1,2*n-2*k+1). | [
"1",
"6",
"17",
"58",
"188",
"570",
"1715",
"5074",
"14787",
"42676",
"122104",
"346804",
"979013",
"2749150",
"7684437",
"21393326",
"59346996",
"164112814",
"452535543",
"1244660906",
"3415404295",
"9352256360",
"25559520752",
"69730069352",
"189923821833",
"51651... | [
"nonn"
] | 15 | 0 | 2 | [
"A381421",
"A391829",
"A391890",
"A391891"
] | null | Seiichi Manyama, Dec 22 2025 | 2026-01-01T15:17:01 | oeisdata/seq/A391/A391890.seq | 017c5e11bd2d18ddc7a973e615d9a10b |
A391891 | a(n) = Sum_{k=0..n} (k+1) * binomial(2*k+1,2*n-2*k). | [
"1",
"2",
"9",
"34",
"104",
"326",
"995",
"2954",
"8671",
"25156",
"72256",
"205948",
"583109",
"1641570",
"4598725",
"12827750",
"35646792",
"98726370",
"272611239",
"750730314",
"2062369787",
"5653126280",
"15464460608",
"42225863096",
"115102499721",
"31326414157... | [
"nonn"
] | 14 | 0 | 2 | [
"A381421",
"A391829",
"A391890",
"A391891"
] | null | Seiichi Manyama, Dec 22 2025 | 2026-01-01T15:16:11 | oeisdata/seq/A391/A391891.seq | 8d11b375af938927ba752da1e72b08df |
A391892 | a(n) = Sum_{k=0..n} (k+1) * 2^(n-k) * binomial(2*k+1,2*n-2*k+1). | [
"1",
"6",
"19",
"88",
"337",
"1242",
"4623",
"16652",
"59389",
"209902",
"734491",
"2553024",
"8819753",
"30306498",
"103669991",
"353201460",
"1199086357",
"4057965398",
"13694169715",
"46095091816",
"154799435457",
"518763845034",
"1735138977727",
"5793377734748",
"... | [
"nonn"
] | 15 | 0 | 2 | [
"A390732",
"A391835",
"A391892",
"A391893"
] | null | Seiichi Manyama, Dec 22 2025 | 2026-01-01T06:51:36 | oeisdata/seq/A391/A391892.seq | 5730dd3f84095308393962ac90c7ec5f |
A391893 | a(n) = Sum_{k=0..n} (k+1) * 2^(n-k) * binomial(2*k+1,2*n-2*k). | [
"1",
"2",
"15",
"64",
"233",
"926",
"3411",
"12380",
"44605",
"158074",
"555687",
"1938488",
"6715217",
"23135190",
"79313403",
"270741396",
"920731749",
"3120733874",
"10545871951",
"35542007920",
"119494151033",
"400860857358",
"1342044618659",
"4484767772876",
"149... | [
"nonn"
] | 14 | 0 | 2 | [
"A390732",
"A391835",
"A391892",
"A391893"
] | null | Seiichi Manyama, Dec 22 2025 | 2026-01-01T08:46:42 | oeisdata/seq/A391/A391893.seq | a0c2cacd34d3db61500fb4305ef64c1e |
A391894 | a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(2*k+1,2*n-2*k+1). | [
"1",
"12",
"64",
"344",
"1852",
"9504",
"47616",
"235072",
"1145104",
"5518400",
"26364928",
"125049984",
"589461440",
"2763899904",
"12899926016",
"59964819456",
"277750014208",
"1282419653632",
"5904300064768",
"27113852057600",
"124223466028032",
"567932306153472",
"25... | [
"nonn"
] | 15 | 0 | 2 | [
"A390700",
"A391832",
"A391894",
"A391895"
] | null | Seiichi Manyama, Dec 22 2025 | 2026-01-01T08:46:45 | oeisdata/seq/A391/A391894.seq | 5d2bb5b85fcac57ca2a87c0646eda35d |
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