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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A381833
k/25 is in this list if k > 5 and A053824(k) = A112765(k), i.e. if digitsum(k, 5) = valuation(k, 5).
[ "2", "6", "15", "26", "35", "55", "100", "126", "135", "155", "200", "255", "300", "400", "626", "635", "655", "700", "755", "800", "900", "1125", "1255", "1300", "1400", "1625", "1900", "2125", "2625", "3126", "3135", "3155", "3200", "3255", "3300", "3400", "3625", "3755", "3800", "3900", "4125", "4400", "4625", "5125", "6255", "6300", "6400", "6625", "6900", "7125" ]
[ "nonn", "base" ]
6
1
1
[ "A053824", "A112765", "A381833", "A381834", "A381835", "A381836" ]
null
Peter Luschny, Mar 09 2025
2025-03-09T12:57:22
oeisdata/seq/A381/A381833.seq
460a8c2c0322eef4a1673bcbe4e3719d
A381834
k/16 is in this list if k > 4 and A053737(k) = A235127(k), i.e. if digitsum(k, 4) = valuation(k, 4).
[ "2", "5", "12", "17", "24", "36", "65", "72", "84", "112", "132", "160", "208", "257", "264", "276", "304", "324", "352", "400", "516", "544", "592", "704", "784", "896", "1025", "1032", "1044", "1072", "1092", "1120", "1168", "1284", "1312", "1360", "1472", "1552", "1664", "1856", "2052", "2080", "2128", "2240", "2320", "2432", "2624", "3088", "3200", "3392" ]
[ "nonn", "base" ]
5
1
1
[ "A053737", "A235127", "A381833", "A381834", "A381835", "A381837" ]
null
Peter Luschny, Mar 09 2025
2025-03-09T12:57:29
oeisdata/seq/A381/A381834.seq
1e9867f46fc735091908d8b130b9d3b7
A381835
k/9 is in this list if k > 3 and A053735(k) = A007949(k), i.e. if digitsum(k, 3) = valuation(k, 3).
[ "2", "4", "10", "15", "21", "28", "33", "39", "57", "72", "82", "87", "93", "111", "126", "144", "165", "180", "198", "244", "249", "255", "273", "288", "306", "327", "342", "360", "414", "459", "489", "504", "522", "576", "621", "675", "730", "735", "741", "759", "774", "792", "813", "828", "846", "900", "945", "975", "990", "1008", "1062", "1107", "1161", "1224", "1269", "1323" ]
[ "nonn", "base" ]
6
0
1
[ "A007949", "A053735", "A381833", "A381834", "A381835", "A381838" ]
null
Peter Luschny, Mar 09 2025
2025-03-09T12:57:40
oeisdata/seq/A381/A381835.seq
2ac8cfe36a18765e9e59c16499f00e9d
A381836
k/25 is in this list if A053824(k) < A112765(k), i.e. if digitsum(k, 5) < valuation(k, 5).
[ "1", "5", "10", "25", "30", "50", "75", "125", "130", "150", "175", "250", "275", "375", "500", "625", "630", "650", "675", "750", "775", "875", "1000", "1250", "1275", "1375", "1500", "1875", "2000", "2500", "3125", "3130", "3150", "3175", "3250", "3275", "3375", "3500", "3750", "3775", "3875", "4000", "4375", "4500", "5000", "5625", "6250", "6275", "6375" ]
[ "nonn", "base" ]
10
1
2
[ "A053824", "A112765", "A371176", "A381836", "A381837", "A381838" ]
null
Peter Luschny, Mar 08 2025
2025-03-09T12:57:47
oeisdata/seq/A381/A381836.seq
c6454c1c1e37d143c26d7e5ad19ad393
A381837
k/16 is in this list if A053737(k) < A235127(k), i.e. if digitsum(k, 4) < valuation(k, 4).
[ "1", "4", "8", "16", "20", "32", "48", "64", "68", "80", "96", "128", "144", "192", "256", "260", "272", "288", "320", "336", "384", "448", "512", "528", "576", "640", "768", "832", "1024", "1028", "1040", "1056", "1088", "1104", "1152", "1216", "1280", "1296", "1344", "1408", "1536", "1600", "1792", "2048", "2064", "2112", "2176", "2304", "2368", "2560", "2816" ]
[ "nonn", "base" ]
10
1
2
[ "A053737", "A235127", "A371176", "A381836", "A381837", "A381838" ]
null
Peter Luschny, Mar 08 2025
2025-03-09T12:57:56
oeisdata/seq/A381/A381837.seq
bf639f5098a9ec19c6f130a9cb154444
A381838
k/9 is in this list if A053735(k) < A007949(k), i.e. if digitsum(k, 3) < valuation(k, 3).
[ "1", "3", "6", "9", "12", "18", "27", "30", "36", "45", "54", "63", "81", "84", "90", "99", "108", "117", "135", "162", "171", "189", "216", "243", "246", "252", "261", "270", "279", "297", "324", "333", "351", "378", "405", "432", "486", "495", "513", "540", "567", "594", "648", "729", "732", "738", "747", "756", "765", "783", "810", "819", "837", "864", "891", "918", "972", "981", "999" ]
[ "nonn", "base" ]
11
1
2
[ "A007949", "A053735", "A371176", "A381836", "A381837", "A381838" ]
null
Peter Luschny, Mar 08 2025
2025-03-09T12:58:26
oeisdata/seq/A381/A381838.seq
b3725485dfeade84769faf92bc824503
A381839
In the binary expansion of n (without leading zeros): complement the bits strictly between the leftmost and the rightmost 0's, if any.
[ "0", "1", "2", "3", "4", "5", "6", "7", "10", "9", "8", "11", "12", "13", "14", "15", "22", "21", "20", "19", "18", "17", "16", "23", "26", "25", "24", "27", "28", "29", "30", "31", "46", "45", "44", "43", "42", "41", "40", "39", "38", "37", "36", "35", "34", "33", "32", "47", "54", "53", "52", "51", "50", "49", "48", "55", "58", "57", "56", "59", "60", "61", "62", "63", "94", "93", "92", "91" ]
[ "nonn", "base", "easy" ]
14
0
3
[ "A000225", "A030130", "A122155", "A381839", "A381852" ]
null
Rémy Sigrist, Mar 08 2025
2025-03-10T11:11:50
oeisdata/seq/A381/A381839.seq
9ec0e945aeb3809568901ce60d16cd77
A381840
G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 - x^2*A(x)^7.
[ "1", "1", "3", "11", "42", "153", "469", "690", "-5967", "-82708", "-700876", "-4989894", "-32082336", "-190742496", "-1053280998", "-5347579160", "-24162468390", "-88249158963", "-157067396045", "1334548659436", "20996875910808", "194476989681546", "1491599102987040", "10232074769143770", "64440205192609155" ]
[ "sign" ]
7
0
3
[ "A103779", "A367027", "A368971", "A381840" ]
null
Seiichi Manyama, Mar 08 2025
2025-03-08T09:39:24
oeisdata/seq/A381/A381840.seq
f97a792f5a360777436332c0f6a097f3
A381841
Position of the n-th occurrence of the digit 3 in A105083(n-1) for n>=1.
[ "3", "9", "12", "16", "22", "28", "31", "37", "40", "44", "50", "53", "57", "63", "69", "72", "76", "82", "88", "91", "97", "100", "104", "110", "116", "119", "125", "128", "132", "138", "141", "145", "151", "157", "160", "166", "169", "173", "179", "182", "186", "192", "198", "201", "205", "211", "217", "220", "226", "229", "233", "239", "242", "246", "252", "258" ]
[ "nonn" ]
11
1
1
[ "A064105", "A105083", "A136495", "A136496", "A202342", "A381841" ]
null
Jeffrey Shallit, Mar 08 2025
2025-03-09T12:51:57
oeisdata/seq/A381/A381841.seq
f9497f9c3e0b36b380354f856e78a2af
A381842
Triangle read by rows: T(n,k) is the number of non-equivalent subsets of size k in S_n, 0 <= k <= n!.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "1", "1", "1", "1", "4", "10", "41", "103", "309", "691", "1458", "2448", "3703", "4587", "5050", "4587", "3703", "2448", "1458", "691", "309", "103", "41", "10", "4", "1", "1", "1", "1", "6", "37", "715", "13710", "256751", "4140666", "58402198", "726296995", "8060937770", "80604620206", "732149722382" ]
[ "nonn", "tabf" ]
65
0
10
[ "A000041", "A362763", "A381842" ]
null
Raghavendra Tripathi, Mar 09 2025
2025-04-09T11:21:13
oeisdata/seq/A381/A381842.seq
4bc45806876495e1cfb2cefdd21b6054
A381843
Decimal expansion of (40320*e^9 - 322560*e^8 + 987840*e^7 - 1451520*e^6 + 1050000*e^5 - 344064*e^4 + 40824*e^3 - 1024*e^2 + e) / 40320.
[ "1", "8", "6", "6", "6", "6", "6", "6", "6", "6", "5", "2", "7", "0", "3", "2", "1", "3", "4", "8", "9", "5", "5", "5", "2", "1", "7", "2", "2", "9", "4", "8", "5", "6", "9", "6", "1", "0", "0", "2", "7", "8", "4", "8", "3", "5", "6", "2", "1", "5", "5", "0", "7", "6", "9", "8", "4", "1", "6", "0", "8", "4", "6", "7", "9", "9", "2", "7", "1", "6", "2", "2", "2", "5", "3", "5", "9", "5", "2", "6", "2", "6", "5", "8", "1", "1", "3" ]
[ "nonn", "cons", "easy" ]
30
2
2
[ "A001113", "A089087", "A089139", "A090142", "A090143", "A090611", "A379601", "A381673", "A381843", "A382020", "A382026" ]
null
Daniel Mondot, Mar 12 2025
2025-03-23T05:29:15
oeisdata/seq/A381/A381843.seq
ccd79adce917fd403f73ac8549b2a80a
A381844
Quotients of A380487.
[ "1", "3", "5", "7", "11", "19", "23", "34", "91", "105", "209", "221", "231", "385", "399", "429", "481", "609", "665", "715", "805", "897", "1001", "1105", "1430", "1729", "1870", "2046", "2233", "2261", "3094", "3230", "3553", "3565", "3774", "4278", "4862", "4921", "4945", "5270", "5358", "5365", "6409", "6670", "7429", "7462", "7657", "7990", "8041", "8569" ]
[ "nonn" ]
32
1
2
[ "A007947", "A008472", "A380487", "A381844" ]
null
Torlach Rush, Mar 10 2025
2025-04-02T22:06:22
oeisdata/seq/A381/A381844.seq
a42ae5933ead91a7a006a2141b30eef7
A381845
a(n) = denominator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ).
[ "1", "1", "8", "48", "192", "3840", "46080", "322560", "10321920", "26542080", "1857945600", "11678515200", "1961990553600", "25505877196800", "1428329123020800", "42849873690624000", "8903869857792000", "46620662575398912000", "2634762720116736000", "31888533201572855808000", "196237127394294497280000" ]
[ "nonn", "frac" ]
13
1
3
[ "A061360", "A061382", "A143991", "A381845" ]
null
Stefano Spezia, Mar 12 2025
2025-03-13T08:56:32
oeisdata/seq/A381/A381845.seq
ec27e632c5efe083f98d5501ae894dbe
A381852
In the binary expansion of n (without leading zeros): complement the bits strictly to the right of the leftmost zero digit, if any.
[ "0", "1", "2", "3", "5", "4", "6", "7", "11", "10", "9", "8", "13", "12", "14", "15", "23", "22", "21", "20", "19", "18", "17", "16", "27", "26", "25", "24", "29", "28", "30", "31", "47", "46", "45", "44", "43", "42", "41", "40", "39", "38", "37", "36", "35", "34", "33", "32", "55", "54", "53", "52", "51", "50", "49", "48", "59", "58", "57", "56", "61", "60", "62", "63", "95", "94", "93", "92" ]
[ "nonn", "base", "easy" ]
14
0
3
[ "A054429", "A063250", "A075427", "A381839", "A381852" ]
null
Rémy Sigrist, Mar 08 2025
2025-03-10T11:11:53
oeisdata/seq/A381/A381852.seq
0f6d827355c1baa0419de32d6fbe372f
A381854
Triangle read by rows: T(n, k) is the number of invertible n X n matrices over GF(2) that can be optimally row-reduced in k steps, n >= 0, k >= 0.
[ "1", "1", "1", "2", "2", "1", "1", "6", "24", "51", "60", "24", "2", "1", "12", "96", "542", "2058", "5316", "7530", "4058", "541", "6", "1", "20", "260", "2570", "19680", "117860", "540470", "1769710", "3571175", "3225310", "736540", "15740", "24", "1", "30", "570", "8415", "101610", "1026852", "8747890", "61978340", "355193925", "1561232840", "4753747050", "8111988473", "4866461728", "437272014", "949902", "120" ]
[ "nonn", "tabf", "hard" ]
40
0
4
[ "A002378", "A002884", "A172225", "A381854" ]
null
Søren Fuglede Jørgensen, Mar 08 2025
2025-03-09T16:21:26
oeisdata/seq/A381/A381854.seq
47368eb92436352616bc28167fbfc254
A381855
Starting from prime(n), a(n) is the minimum number > 1 of consecutive primes whose sum is the lesser of a twin prime pair.
[ "2", "95", "317", "23", "3", "5", "3", "3", "277", "7", "7", "25", "35", "237", "7", "5", "17", "41", "15", "33", "23", "7", "3", "111", "257", "3", "7", "57", "5", "11", "57", "13", "11", "79", "45", "67", "29", "97", "11", "15", "15", "21", "113", "19", "35", "15", "9", "5", "123", "29", "59", "27", "19", "227", "223", "37", "279", "53", "41", "3", "135", "53", "143", "81", "41", "29", "39", "63" ]
[ "nonn" ]
27
1
1
[ "A001359", "A381855" ]
null
Abhiram R Devesh, Mar 08 2025
2025-03-23T16:46:05
oeisdata/seq/A381/A381855.seq
48a1d07111f1e246c24ddcc7a35ca26b
A381856
Lexicographically earliest sequence of positive integers such that for any value k, no two sets of two or more indices at which k occurs have the same standard deviation.
[ "1", "1", "2", "1", "2", "2", "3", "1", "3", "2", "4", "3", "3", "4", "4", "1", "5", "2", "5", "3", "4", "5", "4", "6", "1", "5", "6", "6", "2", "3", "7", "5", "6", "4", "6", "1", "7", "7", "8", "5", "7", "8", "8", "9", "6", "9", "2", "8", "3", "7", "4", "5", "9", "9", "8", "10", "9", "10", "10", "11", "7", "1", "8", "10", "11", "11", "6", "11", "9", "12", "10", "2", "12", "8", "11", "13", "12", "12", "3", "10", "13", "13" ]
[ "nonn" ]
18
1
3
[ "A337226", "A380751", "A380783", "A380968", "A381856", "A382381" ]
null
Neal Gersh Tolunsky, Mar 08 2025
2025-03-29T15:44:30
oeisdata/seq/A381/A381856.seq
e6e9276fc24943a72d0eadca9a90270a
A381857
Number of n X n binary matrices with at least 2 adjacent 1's.
[ "0", "0", "9", "449", "64302", "33498985", "68713877875", "562948673292362", "18446743413061588661", "2417851638458709952150645", "1267650600226199352445557225326", "2658455991569819662405962686908743173", "22300745198530622979053904922855772969397419" ]
[ "nonn" ]
17
0
3
[ "A002416", "A006506", "A381857" ]
null
Benjamin Ghitterman, Mar 08 2025
2025-03-15T23:29:40
oeisdata/seq/A381/A381857.seq
0b575347fa772d2f7a447b5ea38d2cb5
A381858
a(n) is the number of permutations of [n] that avoid 312 and 4321 and whose square avoids 231.
[ "1", "1", "2", "5", "12", "26", "56", "125", "279", "618", "1367", "3030", "6720", "14896", "33013", "73173", "162198", "359525", "796900", "1766366", "3915256", "8678393", "19236131", "42637934", "94509351", "209485238", "464335636", "1029225640", "2281335673", "5056707001", "11208471338", "24844197877", "55068541516" ]
[ "nonn", "easy" ]
21
0
3
null
null
Kassie Archer, Mar 10 2025
2025-03-11T13:22:31
oeisdata/seq/A381/A381858.seq
2d311d7cd7b236bdf235beb4bf78ba5c
A381859
a(n) is the number of permutations that avoid 312 and 4321 and whose square avoids 321.
[ "1", "1", "2", "5", "11", "23", "50", "109", "236", "511", "1108", "2402", "5206", "11284", "24459", "53016", "114914", "249081", "539894", "1170243", "2536551", "5498082", "11917326", "25831309", "55990457", "121361689", "263056605", "570186341", "1235903062", "2678872272", "5806569196", "12585984849", "27280655629" ]
[ "nonn", "easy" ]
19
0
3
[ "A001590", "A381859" ]
null
Kassie Archer, Mar 10 2025
2025-03-18T15:29:21
oeisdata/seq/A381/A381859.seq
3196f314bed1f5d8f3a70550be0548be
A381860
G.f. A(x) satisfies A(x) = (1 + x)^3 * C(x*A(x)), where C(x) is the g.f. of A000108.
[ "1", "4", "12", "55", "327", "2157", "15141", "110853", "836790", "6465309", "50876776", "406335099", "3285202335", "26835060422", "221128733649", "1835973630276", "15344202894457", "128983332603009", "1089803313492966", "9250137181234430", "78837133437062307", "674408139329393187", "5788618956395607745" ]
[ "nonn" ]
10
0
2
[ "A000108", "A367640", "A381787", "A381860", "A381882" ]
null
Seiichi Manyama, Mar 08 2025
2025-03-10T10:37:18
oeisdata/seq/A381/A381860.seq
b8a01bfe5ff059299dd69f9de8e0de3a
A381861
G.f. A(x) satisfies A(x) = (1 + x*A(x))^4 * C(x), where C(x) is the g.f. of A000108.
[ "1", "5", "32", "231", "1797", "14715", "125064", "1093194", "9766783", "88793815", "818832674", "7640868924", "72014955566", "684551660324", "6555290711728", "63179148757584", "612376024087047", "5965515657187437", "58375460484257734", "573545171374958628", "5655759227878768987", "55957005428512022905" ]
[ "nonn" ]
14
0
2
[ "A000108", "A127632", "A153299", "A381861", "A381877" ]
null
Seiichi Manyama, Mar 08 2025
2025-03-09T09:55:26
oeisdata/seq/A381/A381861.seq
33494d2fbe6f2d5846d4caf71bee7203
A381862
Number of pairs of triangles that are pairwise edge-disjoint in the complete graph K_n.
[ "15", "100", "385", "1120", "2730", "5880", "11550", "21120", "36465", "60060", "95095", "145600", "216580", "314160", "445740", "620160", "847875", "1141140", "1514205", "1983520", "2567950", "3289000", "4171050", "5241600", "6531525", "8075340", "9911475", "12082560", "14635720", "17622880", "21101080", "25132800", "29786295" ]
[ "nonn", "easy" ]
45
5
1
[ "A054647", "A381862", "A381863" ]
null
Julian Allagan, Mar 08 2025
2025-03-28T08:35:45
oeisdata/seq/A381/A381862.seq
3a9110344adc8ef6fae5165a0de47200
A381863
Number of triples of triangles that are pairwise edge-disjoint in the complete graph K_n.
[ "120", "1575", "10080", "44380", "154000", "451990", "1170400", "2748460", "5965960", "12137125", "23383360", "43006600", "75988640", "129645740", "214472000", "345209480", "542187800", "832980995", "1254434720", "1855122500", "2698295600", "3865397250", "5460218400", "7613778900", "10490025000" ]
[ "nonn", "easy" ]
42
6
1
[ "A054647", "A381862", "A381863" ]
null
Julian Allagan, Mar 08 2025
2025-03-28T08:55:52
oeisdata/seq/A381/A381863.seq
4efbf9bd047621fcf2055659a40a156d
A381864
Numbers k in A024619 such that p^(m+1) == r (mod k) where r is also in A024619 for all p | n.
[ "15", "33", "35", "44", "45", "51", "63", "65", "66", "69", "70", "75", "76", "77", "80", "85", "87", "88", "90", "91", "92", "95", "99", "102", "104", "105", "115", "119", "123", "130", "133", "135", "138", "140", "141", "143", "144", "145", "152", "153", "154", "159", "160", "161", "170", "172", "174", "175", "176", "177", "180", "184", "185", "187", "188", "189", "190" ]
[ "nonn" ]
75
1
1
[ "A000961", "A024619", "A381750", "A381864", "A382120" ]
null
Michael De Vlieger, Apr 06 2025
2025-04-12T12:43:26
oeisdata/seq/A381/A381864.seq
2982c501942c322fc47cd5b76120357f
A381865
Number of sequences in which the matches of a fully symmetric single-elimination tournament with 3^n players can be played if arbitrarily many matches can occur simultaneously and each match involves 3 players.
[ "1", "1", "13", "308682013", "20447648974223714249697186722386536049691073" ]
[ "nonn", "more" ]
9
0
3
[ "A273723", "A379758", "A381865" ]
null
Noah A Rosenberg, Mar 08 2025
2025-03-19T10:25:12
oeisdata/seq/A381/A381865.seq
d85ffb704327ad24c4fe3de2833fba5f
A381866
Number of labeled histories for rooted 5-furcating trees with 4n+1 leaves if simultaneous 5-furcations are not allowed.
[ "1", "1", "126", "162162", "1003458456", "20419376121144", "1084881453316380720", "128835096988586792403600", "30577206578883234961900809600", "13328512616115465470187677202211200", "9988360697491697592427704919982668857600", "12203369577406758958826880335333105520792518400" ]
[ "nonn" ]
14
0
3
[ "A006472", "A007696", "A339411", "A381533", "A381536", "A381866" ]
null
Noah A Rosenberg, Mar 08 2025
2025-03-12T13:13:01
oeisdata/seq/A381/A381866.seq
5519293914efac175fe6c5c93b7284bd
A381867
G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x)^2, where C(x) is the g.f. of A000108.
[ "1", "3", "10", "44", "239", "1464", "9610", "65946", "466951", "3385259", "24999475", "187385168", "1421901090", "10901237530", "84312106160", "657031204068", "5153954345309", "40663760712441", "322478148002872", "2569086552458460", "20551321340065924", "165009872444132477", "1329352163579556971", "10742386009423170696" ]
[ "nonn" ]
10
0
2
[ "A000108", "A188687", "A366034", "A381867" ]
null
Seiichi Manyama, Mar 08 2025
2025-03-09T09:55:33
oeisdata/seq/A381/A381867.seq
0625bd2f87db20c8783ef85d71e348f9
A381868
Starting from the n-th prime, a(n) is the minimum number > 1 of consecutive primes whose sum is the greater of a twin prime pair.
[ "2", "137", "95", "3", "339", "93", "51", "5", "49", "5", "3", "115", "91", "35", "331", "7", "11", "3", "19", "29", "5", "187", "515", "15", "13", "79", "203", "11", "3", "69", "9", "93", "7", "13", "13", "5", "189", "71", "289", "419", "35", "239", "11", "9", "9", "33", "3", "129", "57", "75", "71", "53", "23", "121", "523", "13", "11", "3", "9", "11", "3", "193", "87", "5", "23", "181", "115", "3" ]
[ "nonn" ]
20
1
1
[ "A006512", "A381766", "A381855", "A381868" ]
null
Abhiram R Devesh, Mar 08 2025
2025-04-07T21:54:39
oeisdata/seq/A381/A381868.seq
73e382cf6fbf592af4a1672bd1701973
A381869
The smallest starting prime for which the sum of 2*n consecutive primes is 0 modulo 10, or -1 if no such prime exists.
[ "13", "11", "7", "7", "13", "17", "7", "17", "37", "3", "7", "41", "7", "7", "11", "11", "11", "11", "11", "13", "11", "13", "11", "7", "7", "17", "7", "43", "41", "3", "3", "13", "11", "7", "13", "19", "7", "11", "11", "29", "7", "43", "3", "7", "11", "13", "23", "29", "3", "7", "7", "11", "11", "11", "19", "13", "5", "5", "13", "37", "17", "3", "3", "7", "17", "17", "3", "11", "19", "13", "3", "7", "23" ]
[ "nonn" ]
20
1
1
[ "A007652", "A111324", "A381869" ]
null
Jean-Marc Rebert, Mar 09 2025
2025-03-23T13:41:05
oeisdata/seq/A381/A381869.seq
45af1b9662ceccb736ded3a374ac14d4
A381870
Numbers whose prime indices have a unique multiset partition into sets with distinct sums.
[ "1", "2", "3", "5", "7", "11", "12", "13", "17", "18", "19", "20", "23", "28", "29", "31", "36", "37", "41", "43", "44", "45", "47", "50", "52", "53", "59", "61", "63", "67", "68", "71", "73", "75", "76", "79", "83", "89", "92", "97", "98", "99", "100", "101", "103", "107", "109", "113", "116", "117", "120", "124", "127", "131", "137", "139", "147", "148", "149", "151", "153" ]
[ "nonn" ]
7
1
2
[ "A000720", "A000961", "A001055", "A001222", "A003963", "A005117", "A045778", "A050320", "A050326", "A055396", "A056239", "A061395", "A066328", "A089259", "A112798", "A116540", "A122111", "A166684", "A265947", "A270995", "A279785", "A293243", "A293511", "A296119", "A299202", "A300383", "A300385", "A317141", "A318360", "A321469", "A381633", "A381634", "A381635", "A381718", "A381806", "A381870", "A381990", "A381991" ]
null
Gus Wiseman, Mar 12 2025
2025-03-13T08:55:19
oeisdata/seq/A381/A381870.seq
30d6bef107752c89309da348a253cd7e
A381871
Numbers whose prime indices cannot be partitioned into constant blocks having a common sum.
[ "6", "10", "14", "15", "18", "20", "21", "22", "24", "26", "28", "30", "33", "34", "35", "38", "39", "42", "44", "45", "46", "50", "51", "52", "54", "55", "56", "57", "58", "60", "62", "65", "66", "68", "69", "70", "72", "74", "75", "76", "77", "78", "80", "82", "84", "85", "86", "87", "88", "90", "91", "92", "93", "94", "95", "96", "98", "99", "100", "102", "104", "105", "106", "110" ]
[ "nonn", "changed" ]
9
1
1
[ "A000688", "A000720", "A000961", "A001055", "A001222", "A006171", "A045778", "A050361", "A055396", "A056239", "A061395", "A112798", "A265947", "A279784", "A295935", "A300383", "A317141", "A321469", "A381453", "A381455", "A381633", "A381635", "A381636", "A381715", "A381716", "A381717", "A381719", "A381806", "A381871", "A381993", "A381995", "A383093" ]
null
Gus Wiseman, Mar 13 2025
2025-04-27T09:09:27
oeisdata/seq/A381/A381871.seq
3da6b3bac8f876503c47d4b8bd00ef7b
A381872
Number of multisets that can be obtained by taking the sum of each block of a multiset partition of the prime indices of n into blocks having a common sum.
[ "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "3", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "4", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1" ]
[ "nonn" ]
6
1
4
[ "A000005", "A000009", "A000041", "A000688", "A000720", "A000961", "A001055", "A001222", "A050361", "A055396", "A056239", "A061395", "A089723", "A112798", "A265947", "A279787", "A279789", "A300383", "A305551", "A306017", "A317141", "A321451", "A321452", "A321453", "A321454", "A321455", "A321469", "A381453", "A381455", "A381635", "A381636", "A381637", "A381715", "A381716", "A381872" ]
null
Gus Wiseman, Mar 14 2025
2025-03-14T17:10:14
oeisdata/seq/A381/A381872.seq
e3df823b187e051baac475e33436c256
A381873
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) while containing at most two distinct prime factors.
[ "1", "2", "4", "6", "3", "9", "12", "8", "10", "5", "15", "18", "14", "7", "21", "24", "16", "20", "22", "11", "33", "27", "36", "26", "13", "39", "45", "25", "35", "28", "32", "34", "17", "51", "48", "38", "19", "57", "54", "40", "44", "46", "23", "69", "63", "49", "56", "50", "52", "58", "29", "87", "72", "62", "31", "93", "75", "55", "65", "80", "64", "68", "74", "37", "111", "81" ]
[ "nonn", "look" ]
17
1
2
[ "A000977", "A027748", "A064413", "A070915", "A381873" ]
null
Scott R. Shannon, Mar 09 2025
2025-03-10T11:01:29
oeisdata/seq/A381/A381873.seq
59a110f6e1f2823797e950258ed488b3
A381874
Numbers whose set of divisors can be partitioned: a) into two disjoint subsets with equal sums and cardinalities, and b) into two disjoint subsets with equal products and cardinalities.
[ "24", "30", "42", "54", "60", "66", "78", "84", "90", "96", "102", "108", "114", "120", "126", "132", "138", "140", "150", "156", "160", "168", "174", "186", "198", "204", "210", "216", "220", "222", "224", "228", "240", "246", "258", "260", "264", "270", "276", "280", "282", "306", "308", "312", "318", "330", "336", "340", "342", "348", "352", "354", "360", "364", "366", "372", "378", "380", "384", "390", "402" ]
[ "nonn" ]
4
1
1
[ "A083207", "A347063", "A381874" ]
null
Ivan N. Ianakiev, Mar 09 2025
2025-03-12T08:40:15
oeisdata/seq/A381/A381874.seq
26b71edcad384dea766fb408eb1752a4
A381875
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^2, where C(x) is the g.f. of A000108.
[ "1", "3", "13", "66", "368", "2185", "13570", "87147", "574241", "3861286", "26390591", "182798850", "1280387583", "9053335674", "64534088960", "463249047099", "3345832486407", "24296575830677", "177286818019264", "1299208549351640", "9557974679439901", "70563100013789595", "522608148884843970" ]
[ "nonn" ]
9
0
2
[ "A000108", "A129442", "A381875", "A381876", "A381877" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T09:55:38
oeisdata/seq/A381/A381875.seq
86b19ed4e2b2462f087da811a7ddfff0
A381876
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108.
[ "1", "4", "23", "156", "1167", "9311", "77710", "670294", "5928183", "53467931", "489904745", "4547296624", "42667426369", "404044679434", "3856480309376", "37062228265769", "358330619946164", "3482936427997599", "34014454418349579", "333598711996924548", "3284326412065118717", "32446900771699499147" ]
[ "nonn" ]
10
0
2
[ "A000108", "A129442", "A381875", "A381876", "A381877", "A381880" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T09:55:42
oeisdata/seq/A381/A381876.seq
2582e5ec137d434fbe586cbe68b3a165
A381877
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^4, where C(x) is the g.f. of A000108.
[ "1", "5", "36", "307", "2891", "29029", "304716", "3303712", "36708842", "415818822", "4783832314", "55743318579", "656528284027", "7802975428711", "93467830304056", "1127239608233884", "13676060532043690", "166800618473750824", "2043978275887704674", "25152767272402722288", "310703538187552229521" ]
[ "nonn" ]
10
0
2
[ "A000108", "A129442", "A381861", "A381875", "A381876", "A381877" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T12:26:15
oeisdata/seq/A381/A381877.seq
effab6b95e3e0b6138641dbc45b833e3
A381878
Prime numbers p such that the sum of the d_i-th prime numbers, where (d_i) are the nonzero digits of p, is also a prime.
[ "2", "3", "5", "7", "13", "17", "31", "71", "103", "107", "181", "211", "223", "227", "229", "233", "239", "257", "277", "293", "347", "383", "389", "433", "443", "449", "467", "479", "487", "499", "523", "563", "569", "587", "647", "653", "659", "677", "683", "701", "727", "743", "769", "787", "811", "839", "857", "859", "863", "877", "883", "947", "967", "983" ]
[ "nonn", "base", "less" ]
15
1
1
[ "A046704", "A052034", "A381878" ]
null
Jean-Marc Rebert, Mar 09 2025
2025-03-19T10:30:26
oeisdata/seq/A381/A381878.seq
b710a5b654768f5311afcc55eaa97534
A381879
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / C(x) ), where C(x) is the g.f. of A000108.
[ "1", "3", "16", "106", "788", "6292", "52743", "457946", "4083328", "37174786", "344142192", "3229827900", "30661272627", "293907951057", "2840826401664", "27657352868946", "270968414904700", "2669604470832568", "26431802684789970", "262864480970961882", "2624640191306617088", "26301183967687772360" ]
[ "nonn" ]
10
0
2
[ "A000108", "A381817", "A381879", "A381880", "A381881" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T12:29:03
oeisdata/seq/A381/A381879.seq
27ba4e3d6094948586ba8bd94c7c35c6
A381880
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / C(x) ), where C(x) is the g.f. of A000108.
[ "1", "4", "27", "223", "2052", "20199", "208205", "2219149", "24261279", "270581313", "3066581130", "35216499786", "408919039968", "4792955710138", "56633333886618", "673881539636365", "8067939162382594", "97117925556632184", "1174721577627568371", "14270877151754826473", "174044527062280321368" ]
[ "nonn" ]
9
0
2
[ "A000108", "A381817", "A381879", "A381880", "A381882" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T12:29:00
oeisdata/seq/A381/A381880.seq
6d31ff055a1d3342103a6444a8e5771d
A381881
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * C(x)) ), where C(x) is the g.f. of A000108.
[ "1", "3", "14", "82", "547", "3958", "30249", "240362", "1966235", "16449495", "140093989", "1210575512", "10587490383", "93540456103", "833619150838", "7484887130882", "67645312129491", "614872423359187", "5617522739173495", "51556112664387720", "475105557839611760", "4394434006611790855" ]
[ "nonn" ]
11
0
2
[ "A000108", "A054727", "A381879", "A381881", "A381882" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T12:26:20
oeisdata/seq/A381/A381881.seq
a5c0d6f28310195a5eb67388520b6ae0
A381882
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * C(x)) ), where C(x) is the g.f. of A000108.
[ "1", "4", "24", "175", "1428", "12525", "115468", "1103777", "10844715", "108860766", "1111722956", "11514401451", "120666441067", "1277161022725", "13633269293868", "146606818816257", "1586739194404521", "17271207134469417", "188942438655850740", "2076317084779878706", "22909617070555385010" ]
[ "nonn" ]
10
0
2
[ "A000108", "A054727", "A381880", "A381881", "A381882" ]
null
Seiichi Manyama, Mar 09 2025
2025-03-09T12:26:24
oeisdata/seq/A381/A381882.seq
4e46a69e01d6912c9eb0478c4c5ec684
A381883
Triangle read by rows: T(n, k) = binomial(2*n - 1, k).
[ "1", "1", "1", "1", "3", "3", "1", "5", "10", "10", "1", "7", "21", "35", "35", "1", "9", "36", "84", "126", "126", "1", "11", "55", "165", "330", "462", "462", "1", "13", "78", "286", "715", "1287", "1716", "1716", "1", "15", "105", "455", "1365", "3003", "5005", "6435", "6435", "1", "17", "136", "680", "2380", "6188", "12376", "19448", "24310", "24310" ]
[ "nonn", "tabl", "easy" ]
10
0
5
[ "A007318", "A088218", "A114121", "A262977", "A381883" ]
null
Peter Luschny, Mar 15 2025
2025-04-03T09:58:47
oeisdata/seq/A381/A381883.seq
adf858376f6e0855245e6fd59fb87b77
A381884
Triangle read by rows: T(n, k) = 0 if n = 0 or k is not a quadratic residue modulo n, otherwise T(n, k) = k.
[ "0", "0", "1", "0", "1", "2", "0", "1", "0", "3", "0", "1", "0", "0", "4", "0", "1", "0", "0", "4", "5", "0", "1", "0", "3", "4", "0", "6", "0", "1", "2", "0", "4", "0", "0", "7", "0", "1", "0", "0", "4", "0", "0", "0", "8", "0", "1", "0", "0", "4", "0", "0", "7", "0", "9", "0", "1", "0", "0", "4", "5", "6", "0", "0", "9", "10", "0", "1", "0", "3", "4", "5", "0", "0", "0", "9", "0", "11", "0", "1", "0", "0", "4", "0", "0", "0", "0", "9", "0", "0", "12" ]
[ "nonn", "tabl" ]
15
0
6
[ "A057125", "A057126", "A057762", "A262931", "A262932", "A381884" ]
null
Peter Luschny, Mar 17 2025
2025-03-18T12:23:15
oeisdata/seq/A381/A381884.seq
6896fbdd5d9505609c22aee035659e47
A381885
a(n) = Product_{k=2..n-1} k^ord(n, k) where ord(n, k) = 0 if k does not divide n, otherwise is the exponent of the highest power of k that divides n.
[ "1", "1", "1", "4", "1", "6", "1", "32", "9", "10", "1", "288", "1", "14", "15", "2048", "1", "972", "1", "800", "21", "22", "1", "55296", "25", "26", "243", "1568", "1", "27000", "1", "65536", "33", "34", "35", "10077696", "1", "38", "39", "256000", "1", "74088", "1", "3872", "6075", "46", "1", "169869312", "49", "12500", "51", "5408", "1", "1417176", "55", "702464", "57" ]
[ "nonn" ]
13
1
4
[ "A005451", "A364813", "A381885" ]
null
Peter Luschny, Apr 01 2025
2025-04-01T08:55:35
oeisdata/seq/A381/A381885.seq
27edb8677fdb23ac57634eae0438d0d9
A381886
Triangle read by rows: T(n, k) = Sum_{j=1..floor(log[k](n))} floor(n / k^j) if k >= 2, T(n, 1) = n, T(n, 0) = 0^n.
[ "1", "0", "1", "0", "2", "1", "0", "3", "1", "1", "0", "4", "3", "1", "1", "0", "5", "3", "1", "1", "1", "0", "6", "4", "2", "1", "1", "1", "0", "7", "4", "2", "1", "1", "1", "1", "0", "8", "7", "2", "2", "1", "1", "1", "1", "0", "9", "7", "4", "2", "1", "1", "1", "1", "1", "0", "10", "8", "4", "2", "2", "1", "1", "1", "1", "1", "0", "11", "8", "4", "2", "2", "1", "1", "1", "1", "1", "1", "0", "12", "10", "5", "3", "2", "2", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "tabl" ]
21
0
5
[ "A011371", "A027868", "A054861", "A054893", "A054895", "A054896", "A054897", "A054898", "A078567", "A078632", "A078651", "A153216", "A366471", "A381886" ]
null
Peter Luschny, Apr 03 2025
2025-04-04T13:56:16
oeisdata/seq/A381/A381886.seq
e84f35c3cb2e25c335fb0da513864068
A381887
a(n) = 1 if n != p^m*(p-1) for any prime p and any m >= 0, otherwise Product_{p in W} p, where W are the primes such that n = p^m*(p-1) for some m >= 0.
[ "2", "6", "1", "10", "1", "21", "1", "2", "1", "11", "1", "13", "1", "1", "1", "34", "1", "57", "1", "5", "1", "23", "1", "1", "1", "1", "1", "29", "1", "31", "1", "2", "1", "1", "1", "37", "1", "1", "1", "41", "1", "301", "1", "1", "1", "47", "1", "1", "1", "1", "1", "53", "1", "3", "1", "1", "1", "59", "1", "61", "1", "1", "1", "2", "1", "67", "1", "1", "1", "71", "1", "73", "1", "1", "1", "1", "1", "79", "1" ]
[ "nonn" ]
9
1
1
[ "A155457", "A381887" ]
null
Peter Luschny, Apr 05 2025
2025-04-06T14:58:11
oeisdata/seq/A381/A381887.seq
2c70a75a03173f9450a51bc1b7435cb6
A381888
Triangle read by rows: T(n, k) = (n + 1) * Sum_{j=k..n} binomial(n, j) * Eulerian1(j, j - k).
[ "1", "2", "2", "3", "9", "3", "4", "28", "28", "4", "5", "75", "165", "75", "5", "6", "186", "786", "786", "186", "6", "7", "441", "3311", "6181", "3311", "441", "7", "8", "1016", "12888", "40888", "40888", "12888", "1016", "8", "9", "2295", "47529", "241191", "404361", "241191", "47529", "2295", "9", "10", "5110", "168670", "1312750", "3445510", "3445510", "1312750", "168670", "5110", "10" ]
[ "nonn", "tabl" ]
20
0
2
[ "A007526", "A046802", "A058877", "A122045", "A173018", "A381706", "A381888" ]
null
Peter Luschny, Mar 11 2025
2025-03-15T09:30:06
oeisdata/seq/A381/A381888.seq
c35ad7bd457c9353ef39b42c7e4e63f0
A381889
Expansion of e.g.f.: (BesselI(0, 2*x) + BesselI(1, 2*x))^2*exp(2*x).
[ "1", "4", "18", "86", "428", "2192", "11468", "60986", "328532", "1788368", "9819128", "54302712", "302157424", "1690193728", "9497996152", "53588976802", "303434431108", "1723578967056", "9818195961512", "56071829010968", "320970950634288", "1841213871449152", "10582333064327824", "60929582362628968", "351385363433883472" ]
[ "nonn" ]
14
0
2
[ "A001405", "A001700", "A005566", "A151093", "A381889" ]
null
Mélika Tebni, Mar 09 2025
2025-03-19T10:16:56
oeisdata/seq/A381/A381889.seq
fc53d4126d5cf30a946dfce43c5f4a11
A381891
Triangle read by rows: T(n,k) is the number of partitions of a 2-colored set of n objects into at most k parts with 0 <= k <= n.
[ "1", "0", "2", "0", "3", "6", "0", "4", "10", "14", "0", "5", "19", "28", "33", "0", "6", "28", "52", "64", "70", "0", "7", "44", "93", "127", "142", "149", "0", "8", "60", "152", "228", "272", "290", "298", "0", "9", "85", "242", "404", "507", "561", "582", "591", "0", "10", "110", "370", "672", "904", "1034", "1098", "1122", "1132", "0", "11", "146", "546", "1100", "1568", "1870", "2027", "2101", "2128", "2139" ]
[ "nonn", "tabl" ]
30
0
3
[ "A005380", "A026820", "A381891" ]
null
Peter Dolland, Mar 09 2025
2025-03-26T15:27:10
oeisdata/seq/A381/A381891.seq
c20069787367360591492f10a6e4f77d
A381892
Numbers k such that A381781(k) is negative.
[ "99", "260515", "18997153", "37362253", "50601157", "122925461", "534483448" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A381781", "A381892", "A381893" ]
null
Simcha Z. Katzoff, Mar 09 2025
2025-03-19T10:38:26
oeisdata/seq/A381/A381892.seq
93d8e660acd8c00aff0b09668fc26ebc
A381893
Negative values of A381781.
[ "-810", "-39184", "-4396135", "-124970", "-61325522", "-64927344", "-439288021" ]
[ "sign", "hard", "more" ]
19
1
1
[ "A381781", "A381892", "A381893" ]
null
Simcha Z. Katzoff, Mar 09 2025
2025-03-19T10:38:38
oeisdata/seq/A381/A381893.seq
789cd674d375e4b12212dbc0659834ef
A381894
Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same sum.
[ "1", "2", "2", "1", "1", "3", "5", "2", "2", "2", "3", "3", "3", "3", "3", "4", "4", "5", "5", "6", "6", "3", "3", "3", "6", "6", "6", "7", "7", "7", "8", "8", "8", "9", "9", "9", "4", "4", "4", "4", "5", "5", "5", "5", "6", "6", "6", "6", "6", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "11", "11", "11", "13", "13", "13", "15", "15", "15", "8", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9" ]
[ "nonn" ]
15
1
2
[ "A000002", "A331910", "A381894", "A382028" ]
null
Neal Gersh Tolunsky, Mar 09 2025
2025-03-21T17:10:57
oeisdata/seq/A381/A381894.seq
8b0bf551403c6a13c39643b9c821c465
A381895
Triangle read by rows: T(n, k) is the number of partitions of n with at most k parts where 0 <= k <= n, and each part is one of two kinds.
[ "1", "0", "2", "0", "2", "5", "0", "2", "6", "10", "0", "2", "9", "15", "20", "0", "2", "10", "22", "30", "36", "0", "2", "13", "31", "48", "58", "65", "0", "2", "14", "40", "68", "90", "102", "110", "0", "2", "17", "51", "97", "135", "162", "176", "185", "0", "2", "18", "64", "128", "194", "242", "274", "290", "300", "0", "2", "21", "77", "171", "271", "357", "415", "452", "470", "481" ]
[ "nonn", "tabl" ]
29
0
3
[ "A000712", "A026820", "A381895" ]
null
Peter Dolland, Mar 09 2025
2025-03-20T06:01:39
oeisdata/seq/A381/A381895.seq
7c010cc406174b16a8a0f87d5a33b595
A381896
Number of n X n Erdős matrices up to equivalence.
[ "1", "2", "6", "41" ]
[ "nonn", "hard", "more" ]
39
1
2
[ "A000041", "A381896" ]
null
Raghavendra Tripathi, Mar 09 2025
2025-03-25T21:10:56
oeisdata/seq/A381/A381896.seq
4009d867b5d301f60063c4cebc2d9dd1
A381897
a(n) = least integer m >= 2 such that prime(n) is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer h >= 1.
[ "3", "2", "3", "2", "2", "3", "3", "2", "2", "4", "2", "4", "2", "4", "2", "2", "3", "3", "2", "2", "2", "2", "5", "2", "2", "2", "3", "3", "2", "2", "2", "2", "2", "3", "2", "3", "3", "3", "3", "2", "3", "2", "2", "2", "2", "4", "3", "3", "3", "2", "3", "2", "4", "3", "3", "2", "3", "2", "2", "2", "3", "2", "4", "2", "3", "3", "3", "2", "4", "2", "2", "2", "2", "3", "3", "2", "2", "2", "2", "3", "3", "2", "2", "4", "2", "4" ]
[ "nonn" ]
14
1
1
[ "A000040", "A381239", "A381897", "A382278" ]
null
Clark Kimberling, Mar 09 2025
2025-03-22T18:50:42
oeisdata/seq/A381/A381897.seq
cdec63b0e095283b3e72de07ff65bfd2
A381898
Decimal expansion of exp(Sum_{k>=2} log_2(k)/(k * 2^k)).
[ "1", "2", "8", "3", "3", "0", "3", "1", "7", "1", "1", "8", "7", "4", "0", "6", "8", "1", "9", "3", "9", "2", "7", "9", "8", "8", "5", "0", "8", "1", "6", "1", "7", "3", "9", "2", "0", "7", "7", "4", "1", "3", "2", "4", "0", "1", "8", "8", "3", "0", "2", "5", "4", "6", "1", "6", "0", "5", "9", "1", "0", "8", "2", "3", "0", "8", "4", "4", "0", "4", "3", "2", "1", "7", "6", "6", "1", "1", "0", "1", "3", "3", "5", "2", "6", "9", "4", "7", "9", "9", "2", "8", "4", "0", "8", "1", "5", "5", "6", "3", "9", "3", "7", "1", "0", "9", "7", "6", "6", "1", "5", "3", "8", "0", "7", "7", "9", "6", "4", "4" ]
[ "nonn", "cons", "changed" ]
25
1
2
[ "A381456", "A381898", "A381900" ]
null
Jwalin Bhatt, Mar 09 2025
2025-04-14T17:31:50
oeisdata/seq/A381/A381898.seq
7ec5d261555e0cc9f069e11b8a4bb2c4
A381899
Irregular triangular array read by rows. T(n,k) is the number of length n words x on {0,1} such that I(x) + W(x)*(n-W(x)) = k, where I(x) is the number of inversions in x and W(x) is the number of 1's in x, n >= 0, 0 <= k <= floor(n^2/2).
[ "1", "2", "2", "1", "1", "2", "0", "2", "2", "2", "2", "0", "0", "2", "3", "3", "4", "1", "1", "2", "0", "0", "0", "2", "2", "4", "4", "6", "4", "4", "2", "2", "2", "0", "0", "0", "0", "2", "2", "2", "4", "5", "7", "6", "9", "7", "7", "5", "4", "1", "1", "2", "0", "0", "0", "0", "0", "2", "2", "2", "2", "4", "4", "8", "6", "10", "12", "14", "12", "14", "10", "10", "6", "4", "2", "2" ]
[ "nonn", "tabf" ]
29
0
2
[ "A000079", "A001788", "A053846", "A060546", "A083906", "A132186", "A226622", "A226635", "A381899" ]
null
Geoffrey Critzer, Mar 09 2025
2025-03-12T15:55:04
oeisdata/seq/A381/A381899.seq
314113b300b75ed244c19a3575950b82
A381900
Sequence where k is appended after every (2^(k-1))*k occurrences of 1, with multiple values following a 1 listed in order.
[ "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "4", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "4", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "5" ]
[ "nonn" ]
8
1
5
[ "A381522", "A381898", "A381900" ]
null
Jwalin Bhatt, Mar 09 2025
2025-03-25T00:40:41
oeisdata/seq/A381/A381900.seq
c0e40ae43911eb9ea6a6428767e718aa
A381901
Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product.
[ "1", "2", "4", "8", "14", "26", "46", "86", "166", "326", "634", "1262", "2518", "5006", "10006", "19946", "39874", "79738", "159398", "318778", "637502", "1274998", "2549978", "5099902", "10199786", "20399534", "40799062", "81598082", "163196134", "326392258", "652784498", "1305568942", "2611137838", "5222275634", "10444551254" ]
[ "nonn" ]
17
1
2
[ "A006992", "A090905", "A113117", "A113118", "A381901" ]
null
Andy Niedermaier, Mar 09 2025
2025-04-13T17:42:14
oeisdata/seq/A381/A381901.seq
9504b8c6bdc5a781bf663d48e65195a5
A381902
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) shares a factor with a(n-1), while the total number of prime factors, counted with multiplicity, of the form 4*k+1 and 4*k+3 for all terms a(1)..a(n) never differs by more than 1.
[ "1", "2", "4", "6", "8", "10", "5", "15", "3", "12", "16", "20", "14", "26", "13", "39", "9", "30", "25", "35", "7", "28", "32", "34", "17", "51", "18", "40", "22", "50", "24", "38", "52", "44", "55", "60", "58", "29", "87", "21", "70", "64", "68", "46", "74", "37", "111", "33", "75", "45", "65", "78", "36", "80", "48", "82", "41", "123", "42", "91", "104", "56", "100", "62", "31" ]
[ "nonn" ]
10
1
2
[ "A007350", "A027748", "A038698", "A064413", "A381902", "A382091" ]
null
Scott R. Shannon, Mar 09 2025
2025-04-01T08:53:43
oeisdata/seq/A381/A381902.seq
e7277018c8f5c9f88cc956021db1e1ac
A381905
Expansion of (1/x) * Series_Reversion( x / ((1+x) * B(x)) ), where B(x) is the g.f. of A001764.
[ "1", "2", "8", "47", "331", "2570", "21204", "182383", "1617163", "14675783", "135643839", "1272434069", "12083390801", "115934171020", "1122129142754", "10943574296787", "107433077283767", "1060800046515405", "10528321010319417", "104972259713887665", "1050936451974803973", "10560662821468607719" ]
[ "nonn" ]
8
0
2
[ "A001764", "A381905", "A381906", "A381907", "A381911" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T06:57:16
oeisdata/seq/A381/A381905.seq
ad8885ab3b1692f92ce5d8a54ad334e1
A381906
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A001764.
[ "1", "3", "15", "100", "787", "6848", "63583", "617350", "6191888", "63650430", "667043379", "7099806346", "76538663840", "833975952491", "9169925032189", "101616966476850", "1133736002540882", "12724529836447420", "143567856744995568", "1627454706916166076", "18526192807286106198", "211694470334287787868" ]
[ "nonn" ]
9
0
2
[ "A001764", "A381881", "A381905", "A381906", "A381907" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T06:58:10
oeisdata/seq/A381/A381906.seq
5657ab2036798af68ffce569e03e05c7
A381907
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A001764.
[ "1", "4", "25", "197", "1783", "17646", "185622", "2039617", "23149542", "269367631", "3196544816", "38539697456", "470773651286", "5813914938293", "72470441063067", "910587733474165", "11521140613913305", "146659482494039073", "1876975898990490298", "24137070792680577688", "311724732112458291945" ]
[ "nonn" ]
10
0
2
[ "A001764", "A381882", "A381905", "A381906", "A381907" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T06:59:29
oeisdata/seq/A381/A381907.seq
af1ae9e26c7b37a2495f50f00071679d
A381908
Expansion of (1/x) * Series_Reversion( x / ((1+x) * B(x)) ), where B(x) is the g.f. of A002293.
[ "1", "2", "9", "64", "556", "5351", "54818", "585941", "6459430", "72902748", "838174008", "9781930978", "115579403512", "1379879992445", "16620303073607", "201717610488447", "2464502123154530", "30286289207099652", "374115157763376043", "4642636869759251879", "57852132860181652189", "723592983110972398779" ]
[ "nonn" ]
10
0
2
[ "A002293", "A381908", "A381909", "A381910" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T07:02:32
oeisdata/seq/A381/A381908.seq
078e8cb4d2060da2b70a4a8fc933ae08
A381909
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A002293.
[ "1", "3", "16", "121", "1117", "11569", "128648", "1500054", "18091859", "223794730", "2823369749", "36185653049", "469808971400", "6165903108879", "81667617713170", "1090234962290114", "14654059445570507", "198151602861222385", "2693625234657193038", "36789566028850640226", "504600217464088999466" ]
[ "nonn" ]
12
0
2
[ "A002293", "A381908", "A381909", "A381910" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T07:01:08
oeisdata/seq/A381/A381909.seq
0ec9bf92078c6ed75176642c41a31756
A381910
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A002293.
[ "1", "4", "26", "222", "2243", "25243", "305217", "3878731", "51097713", "691596081", "9558970897", "134347855874", "1914131985782", "27582542400252", "401284140631911", "5886072268606617", "86951528919335670", "1292467847124221832", "19316795168721092789", "290107272994659617741", "4375905051887803660504" ]
[ "nonn" ]
12
0
2
[ "A002293", "A381908", "A381909", "A381910" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T07:03:49
oeisdata/seq/A381/A381910.seq
d93f88d5d2d2fddc53224750df10b571
A381911
Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A001764.
[ "1", "2", "9", "55", "394", "3102", "25969", "226891", "2045342", "18883205", "177640462", "1696658418", "16408796013", "160366113609", "1581329919636", "15713344659359", "157187582466527", "1581676730708500", "15998326150898211", "162571286470135097", "1658893916098102321", "16991130941208846890" ]
[ "nonn" ]
15
0
2
[ "A001764", "A381817", "A381911", "A381912", "A381913", "A381914" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-22T10:16:32
oeisdata/seq/A381/A381911.seq
0b9e2170e8c165e000e2418c9a05ceb6
A381912
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A001764.
[ "1", "3", "17", "124", "1038", "9470", "91586", "923542", "9608323", "102403921", "1112500651", "12275235274", "137193964646", "1549964417407", "17672282336488", "203092563108610", "2350061579393077", "27357919380212638", "320186582453226290", "3765185566095185740", "44465070300433434901", "527131055014319691537" ]
[ "nonn" ]
12
0
2
[ "A001764", "A381879", "A381911", "A381912", "A381913", "A381915" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T09:42:46
oeisdata/seq/A381/A381912.seq
d80ffcde8ecac2081fa1b6c8fc8cfe5d
A381913
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A001764.
[ "1", "4", "28", "245", "2422", "25860", "291106", "3405405", "41014131", "505344113", "6341182427", "80768735045", "1041645452650", "13575670575944", "178528253213469", "2366073408348545", "31571528771106126", "423794981085407622", "5718929869862880055", "77539914280883389432", "1055790501909183080512" ]
[ "nonn" ]
13
0
2
[ "A001764", "A381880", "A381911", "A381912", "A381913", "A381916" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T09:42:50
oeisdata/seq/A381/A381913.seq
b2cbee32ede105ab07abdfce8bce6df0
A381914
Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A002293.
[ "1", "2", "10", "72", "624", "6009", "61809", "664813", "7384613", "84045565", "974913510", "11483316680", "136974177209", "1651166320547", "20083352214058", "246168280262403", "3037682020219285", "37706043912831337", "470482875049515074", "5897864081341146065", "74243055437832292562", "938101296155866961124" ]
[ "nonn" ]
13
0
2
[ "A002293", "A381817", "A381911", "A381914", "A381915", "A381916" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T09:42:53
oeisdata/seq/A381/A381914.seq
c114bd55dd4d0fb3c35814adabb53f2f
A381915
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A002293.
[ "1", "3", "18", "145", "1378", "14515", "163700", "1936414", "23716654", "298216851", "3827542585", "49938733635", "660366743580", "8830549084588", "119205253249287", "1622258295003714", "22232669093660250", "306569446979862205", "4250285556933578693", "59210418891925845529", "828417259759216617257" ]
[ "nonn" ]
13
0
2
[ "A002293", "A381879", "A381912", "A381914", "A381915", "A381916" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T09:42:57
oeisdata/seq/A381/A381915.seq
52697b5357989f1d1684a075c211eb92
A381916
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A002293.
[ "1", "4", "29", "270", "2897", "34051", "426199", "5582619", "75660075", "1052748518", "14956346820", "216088986290", "3165555750458", "46912569559556", "702072705679590", "10595488626535181", "161071258091631337", "2464201011094137000", "37911236702465987337", "586166246311185676045", "9103432675706477369934" ]
[ "nonn" ]
12
0
2
[ "A002293", "A381880", "A381913", "A381914", "A381915", "A381916" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-10T09:43:02
oeisdata/seq/A381/A381916.seq
dde0505b2ac43e19183b6e95d903396e
A381917
Kaprekar numbers that are the concatenation of two equal numbers.
[ "55", "99", "5050", "7272", "7777", "9999", "500500", "648648", "851851", "999999", "13641364", "24752475", "25252525", "36363636", "50005000", "61116111", "88888888", "99999999", "1111111111", "3888938889", "4132841328", "5000050000", "5243952439", "9756097560", "9999999999", "159341159341", "175676175676", "233415233415" ]
[ "base", "nonn" ]
23
1
1
[ "A006886", "A020338", "A092118", "A381917" ]
null
Shyam Sunder Gupta, Mar 10 2025
2025-03-18T15:16:12
oeisdata/seq/A381/A381917.seq
1d7eecb7f99dffc77ce03b8d6e57f712
A381918
Kaprekar numbers that are the concatenation of two consecutive numbers.
[ "45", "2223", "2728", "4950", "148149", "351352", "499500", "11111112", "38883889", "49995000", "63636364", "74747475", "75247525", "86358636", "4756047561", "4999950000", "5867158672", "6111061111", "8888888889", "9132791328", "104247104248", "164983164984", "178321178322", "195156195157", "230769230770", "269230269231" ]
[ "base", "nonn" ]
20
1
1
[ "A001704", "A006886", "A030466", "A381918" ]
null
Shyam Sunder Gupta, Mar 10 2025
2025-03-18T15:25:48
oeisdata/seq/A381/A381918.seq
0ed7a1ea13587c0ae070e7a7e6988cdc
A381919
Pentagonal numbers which are products of four distinct primes.
[ "210", "330", "2262", "3290", "4030", "4510", "4845", "5370", "6902", "7315", "8855", "10542", "13490", "15555", "15862", "16485", "18095", "18426", "19437", "21182", "23002", "24130", "28497", "29330", "30602", "31465", "36426", "44290", "46905", "49595", "50142", "54626", "60501", "67310", "67947", "72490", "77862", "79235", "83426", "84135" ]
[ "nonn" ]
11
1
1
[ "A000326", "A046386", "A245365", "A381650", "A381919" ]
null
Massimo Kofler, Mar 10 2025
2025-03-16T22:18:59
oeisdata/seq/A381/A381919.seq
b2f507384b1b6d4a65e802d56a6b28c4
A381920
Hexagonal numbers that are products of exactly four distinct primes.
[ "1326", "1770", "2145", "2415", "3003", "3486", "4186", "5565", "6670", "7626", "8385", "8646", "9730", "13695", "17205", "17578", "24531", "25878", "27730", "28203", "35245", "35778", "37401", "42486", "47278", "47895", "51681", "59685", "60378", "63190", "63903", "66795", "72010", "74305", "75855", "81406", "84666", "87153", "91378", "95703" ]
[ "nonn" ]
9
1
1
[ "A000384", "A046386", "A129521", "A380007", "A381920" ]
null
Massimo Kofler, Mar 10 2025
2025-03-16T22:14:39
oeisdata/seq/A381/A381920.seq
adb0addc16c04ff641155ba418b1326d
A381921
Factorial numbers whose Hamming weight is also a factorial number.
[ "1", "2", "6", "24", "5040", "40320", "362880", "1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000", "126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000" ]
[ "nonn", "base" ]
15
1
2
[ "A000120", "A000142", "A381921", "A381922" ]
null
Ctibor O. Zizka, Mar 10 2025
2025-03-12T08:09:10
oeisdata/seq/A381/A381921.seq
f5f1a323d64fbbfbbb4b31df6a0dc436
A381922
Numbers k>0 such that the Hamming weight of k! is a factorial.
[ "1", "2", "3", "4", "7", "8", "9", "63", "64" ]
[ "nonn", "base", "more" ]
16
1
2
[ "A000120", "A000142", "A079584", "A381921", "A381922" ]
null
Ctibor O. Zizka, Mar 10 2025
2025-03-12T08:09:40
oeisdata/seq/A381/A381922.seq
519df8f42e7ee4fea21bdfed1a218d91
A381923
a(n) is the least k >= 2 such that (2^k - 1) mod (n*k - 1) = 0.
[ "2", "2", "12", "4", "24", "216", "792", "32", "144", "4410", "396", "108", "208", "1880", "3192", "16", "9240", "72", "24", "6048", "264", "2160", "1872", "270", "20916", "104", "5292", "940", "360", "1596", "756", "8", "132", "4620", "1260", "36", "1728", "12", "49500", "3024", "7560", "3168", "1440", "1080", "2688", "936", "1344", "1035", "44100", "28800" ]
[ "nonn" ]
20
1
1
[ "A000225", "A081856", "A087965", "A381923" ]
null
Ctibor O. Zizka, Mar 10 2025
2025-03-12T12:26:21
oeisdata/seq/A381/A381923.seq
33f27ac79f2f81994422b001397c836f
A381924
Multiplicative order of n mod prime(n).
[ "1", "2", "4", "3", "5", "12", "16", "6", "11", "28", "30", "9", "40", "21", "46", "13", "29", "60", "33", "7", "24", "13", "41", "88", "48", "100", "34", "106", "54", "7", "63", "26", "136", "23", "74", "75", "39", "9", "166", "86", "178", "5", "95", "192", "196", "99", "105", "222", "113", "228", "29", "34", "120", "250", "256", "262", "67", "270", "46", "8", "47", "292", "153", "155", "312" ]
[ "nonn" ]
23
1
2
[ "A014664", "A091185", "A226295", "A381924" ]
null
Giorgos Kalogeropoulos, Mar 12 2025
2025-03-26T19:15:05
oeisdata/seq/A381/A381924.seq
297839ae69eebe320625444cbb4498bb
A381925
Positive integers k which have at least one divisor d for which tau(k) = sigma(d).
[ "1", "4", "6", "15", "20", "21", "27", "33", "39", "42", "45", "50", "51", "56", "57", "60", "64", "69", "70", "72", "75", "84", "87", "90", "93", "96", "105", "108", "111", "123", "126", "129", "132", "141", "144", "150", "154", "156", "159", "175", "177", "180", "182", "183", "189", "198", "201", "204", "213", "219", "220", "228", "231", "234", "237", "238", "245", "249", "266" ]
[ "nonn", "changed" ]
25
1
2
[ "A000005", "A000203", "A000396", "A027750", "A381925", "A381926", "A381927" ]
null
Felix Huber, Mar 12 2025
2025-04-26T03:32:38
oeisdata/seq/A381/A381925.seq
8a838367ca91e021b145d98aed87f989
A381926
Smallest divisor d of A381925(n) for which sigma(d) = tau(A381925(n)).
[ "1", "2", "3", "3", "5", "3", "3", "3", "3", "7", "5", "5", "3", "7", "3", "6", "4", "3", "7", "6", "5", "6", "3", "6", "3", "6", "7", "6", "3", "3", "6", "3", "6", "3", "8", "6", "7", "6", "3", "5", "3", "10", "7", "3", "7", "6", "3", "6", "3", "3", "11", "6", "7", "6", "3", "7", "5", "3", "7", "3", "7", "5", "6", "3", "6", "10", "3", "6", "11", "3", "3", "7", "5", "3", "3", "6", "6", "11", "7", "15", "6", "3", "7", "3", "7", "8" ]
[ "nonn", "changed" ]
11
1
2
[ "A000005", "A000203", "A000396", "A027750", "A381925", "A381926", "A381927" ]
null
Felix Huber, Mar 12 2025
2025-04-26T03:32:41
oeisdata/seq/A381/A381926.seq
9fec4931bec2b6da267fc5bfe18f15fb
A381927
Least positive integer k which has at least n divisors d for which tau(k) = sigma(d).
[ "1", "132", "33660", "658812", "14982660", "119861280" ]
[ "nonn", "more", "changed" ]
12
1
2
[ "A000005", "A000203", "A000396", "A027750", "A381925", "A381926", "A381927" ]
null
Felix Huber, Mar 12 2025
2025-04-26T03:32:47
oeisdata/seq/A381/A381927.seq
7a02194d72061925fde840d3e1da7a54
A381928
Domination number of the n X n camel graph.
[ "1", "4", "9", "8", "8", "8", "9", "12", "16", "20", "25", "28", "31", "34", "40", "44", "50", "56", "61", "68" ]
[ "nonn", "more" ]
6
1
2
null
null
Eric W. Weisstein, Mar 10 2025
2025-03-10T11:02:40
oeisdata/seq/A381/A381928.seq
fabd897ef945fb1093909cc5e7c886e6
A381929
Ending positions of runs in the regular paperfolding sequence A034947.
[ "2", "3", "5", "7", "10", "12", "13", "15", "18", "19", "21", "24", "26", "28", "29", "31", "34", "35", "37", "39", "42", "44", "45", "48", "50", "51", "53", "56", "58", "60", "61", "63", "66", "67", "69", "71", "74", "76", "77", "79", "82", "83", "85", "88", "90", "92", "93", "96", "98", "99", "101", "103", "106", "108", "109", "112", "114", "115", "117", "120", "122", "124", "125" ]
[ "nonn" ]
8
1
1
[ "A034947", "A088431", "A371594", "A381929" ]
null
Jeffrey Shallit, Mar 10 2025
2025-03-11T22:06:58
oeisdata/seq/A381/A381929.seq
89385ed58f672d8e5d15c0533382a535
A381930
Irregular triangular array read by rows. T(n,k) is the number of length n words x on {0,1,2} such that I(x) + W_0(x)*W_1(x) + W_0(x)*W_2(x) + W_1(x)*W_2(x) = k where I(x) is the number of inversions in x and W_i(x) is the number of occurrences of the letter i in x for i={0,1,2}, n>=0, 0<=k<=floor(2n^2/3).
[ "1", "3", "3", "3", "3", "3", "0", "6", "7", "8", "2", "1", "3", "0", "0", "6", "9", "12", "18", "12", "12", "6", "3", "3", "0", "0", "0", "6", "6", "12", "15", "27", "27", "36", "33", "33", "21", "15", "6", "3", "3", "0", "0", "0", "0", "6", "6", "6", "12", "18", "27", "33", "52", "62", "77", "82", "86", "75", "68", "48", "35", "19", "11", "2", "1" ]
[ "nonn", "tabf" ]
17
0
2
[ "A000244", "A027472", "A056449", "A129529", "A342245", "A381899", "A381930" ]
null
Geoffrey Critzer, Mar 10 2025
2025-03-12T15:58:48
oeisdata/seq/A381/A381930.seq
1d2931fb578f1781bcf52caa126f1297
A381931
Triangular array T(n, k) read by rows: denominators of the coefficients for the iterated exponential F^{r}(x) = x + Sum_{n>=1} x^(n+1)*Sum_{k=1..n} r^(n+1-k)*A381932(n, k)/T(n, k) with F^{1}(x) = exp(x)-1 and F^{2}(x) = exp(exp(x)-1)-1.
[ "2", "4", "12", "8", "48", "48", "16", "144", "24", "180", "32", "1152", "1728", "5760", "8640", "64", "640", "3456", "5760", "17280", "6720", "128", "7680", "34560", "1152", "34560", "32256", "241920", "256", "26880", "82944", "414720", "41472", "580608", "107520", "1451520", "512", "430080", "645120", "622080", "4147200", "6967296", "21772800", "87091200", "43545600" ]
[ "nonn", "frac", "tabl" ]
23
1
1
[ "A052104", "A052105", "A052122", "A052123", "A144150", "A180609", "A184011", "A381931", "A381932" ]
null
Thomas Scheuerle, Mar 10 2025
2025-03-18T20:25:39
oeisdata/seq/A381/A381931.seq
1b54cf64d29acb9d364b8479bcec7a07
A381932
Triangular array T(n, k) read by rows: denominators of the coefficients for the iterated exponential F^{r}(x) = x + Sum_{n>=1} x^(n+1)*Sum_{k=1..n} r^(n+1-k)*T(n, k)/A381931(n, k) with F^{1}(x) = exp(x)-1 and F^{2}(x) = exp(exp(x)-1)-1.
[ "1", "1", "-1", "1", "-5", "1", "1", "-13", "1", "-1", "1", "-77", "89", "-91", "11", "1", "-29", "175", "-149", "91", "-1", "1", "-223", "1501", "-37", "391", "-43", "-11", "1", "-481", "2821", "-13943", "725", "-2357", "17", "29", "1", "-4609", "16099", "-19481", "91313", "-55649", "23137", "1727", "493", "1", "-4861", "89993", "-933293", "399637", "-1061231", "2035739", "-8189", "4897", "-2711" ]
[ "sign", "frac", "tabl" ]
9
1
5
[ "A052104", "A052105", "A052122", "A052123", "A064169", "A144150", "A180609", "A184011", "A381931", "A381932" ]
null
Thomas Scheuerle, Mar 12 2025
2025-03-18T20:25:49
oeisdata/seq/A381/A381932.seq
81c9a0fe148a5e65dc73f2aeed7259ea
A381933
a(n) is the number of occurrences of n in A350311.
[ "1", "1", "1", "2", "2", "2", "3", "3", "2", "4", "4", "3", "4", "5", "4", "5", "6", "4", "5", "7", "6", "5", "8", "7", "6", "8", "7", "5", "9", "9", "6", "9", "10", "8", "10", "11", "7", "10", "11", "8", "8", "12", "10", "10", "13", "10", "10", "14", "13", "9", "15", "14", "11", "14", "14", "10", "14", "15", "9", "12", "16", "13", "13", "18", "14", "14", "18", "15", "11", "19", "18", "13", "18", "19", "15" ]
[ "nonn", "base" ]
6
0
4
[ "A350311", "A381933" ]
null
Rémy Sigrist, Mar 10 2025
2025-03-11T08:23:54
oeisdata/seq/A381/A381933.seq
4763d26c29ad72a69116e44326058143
A381934
a(n) is the least k > 1 such that the binary expansions of n and n*k have the same number of nonleading zeros.
[ "2", "3", "3", "5", "3", "6", "5", "9", "3", "5", "6", "5", "5", "19", "9", "17", "3", "5", "5", "3", "6", "9", "5", "11", "5", "7", "19", "301", "9", "35", "17", "33", "3", "5", "5", "3", "5", "5", "3", "3", "6", "5", "9", "5", "5", "17", "11", "305", "5", "7", "7", "15", "19", "3", "301", "9", "9", "71", "35", "13", "17", "67", "33", "65", "3", "5", "5", "3", "5", "5", "3", "3", "5", "10", "5", "10", "3", "6" ]
[ "nonn", "base" ]
17
0
1
[ "A023416", "A292849", "A295827", "A352217", "A381934", "A381935" ]
null
Rémy Sigrist, Mar 10 2025
2025-03-30T20:27:37
oeisdata/seq/A381/A381934.seq
225bb59424be65af3dcf13aeaa21c288
A381935
For any n > 0, a(n) is the least nontrivial multiple of n whose binary expansion has the same number of nonleading zeros as that of n; a(0) = 0.
[ "0", "3", "6", "15", "12", "30", "30", "63", "24", "45", "60", "55", "60", "247", "126", "255", "48", "85", "90", "57", "120", "189", "110", "253", "120", "175", "494", "8127", "252", "1015", "510", "1023", "96", "165", "170", "105", "180", "185", "114", "117", "240", "205", "378", "215", "220", "765", "506", "14335", "240", "343", "350", "765", "988", "159", "16254" ]
[ "nonn", "base" ]
15
0
2
[ "A023416", "A161399", "A352217", "A381934", "A381935" ]
null
Rémy Sigrist, Mar 10 2025
2025-03-12T17:27:07
oeisdata/seq/A381/A381935.seq
bb3122fe4df3bacd8b88d5343680e08c
A381936
Number of primitive binary words of length n that avoid 11, start with 1 and end with 0.
[ "0", "1", "1", "1", "3", "3", "8", "11", "20", "30", "55", "83", "144", "224", "373", "597", "987", "1572", "2584", "4146", "6756", "10890", "17711", "28557", "46365", "74880", "121372", "196184", "317811", "513818", "832040", "1345659", "2178253", "3523590", "5702876", "9225784", "14930352", "24155232", "39088024", "63241794", "102334155", "165573148", "267914296" ]
[ "nonn" ]
31
1
5
[ "A000045", "A007436", "A008683", "A056267", "A113166", "A381936" ]
null
Aidan Diekmann, Mar 10 2025
2025-03-19T09:03:09
oeisdata/seq/A381/A381936.seq
a85d25752efbedada66ad7272e3f878c
A381937
G.f. A(x) satisfies A(x) = (1 + x) * B(x*A(x)), where B(x) is the g.f. of A001764.
[ "1", "2", "6", "35", "240", "1805", "14386", "119365", "1020136", "8918423", "79380514", "716911887", "6553219720", "60513355786", "563648995020", "5289485238552", "49963186247220", "474655663418546", "4532279676629700", "43473774550929628", "418706702628897708", "4047555977981218963" ]
[ "nonn" ]
11
0
2
[ "A001764", "A025227", "A346646", "A365178", "A381787", "A381937", "A381940" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-11T07:53:44
oeisdata/seq/A381/A381937.seq
55d8ee871f4a98d43b7aea16222583b4
A381938
G.f. A(x) satisfies A(x) = (1 + x)^2 * B(x*A(x)), where B(x) is the g.f. of A001764.
[ "1", "3", "9", "52", "380", "3066", "26304", "235314", "2170312", "20487963", "196988392", "1922327792", "18990571724", "189548947601", "1908604524752", "19364096602370", "197761735366804", "2031444188437719", "20974821788118024", "217561484977675026", "2265961977605950416", "23688432825547509283" ]
[ "nonn" ]
13
0
2
[ "A001764", "A366694", "A367640", "A381785", "A381938", "A381941" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-11T07:54:53
oeisdata/seq/A381/A381938.seq
c6315c2fb584bcff42535830de37f8a5
A381939
G.f. A(x) satisfies A(x) = (1 + x)^3 * B(x*A(x)), where B(x) is the g.f. of A001764.
[ "1", "4", "13", "74", "568", "4872", "44576", "425936", "4199616", "42404096", "436238592", "4556085248", "48179319808", "514825553408", "5550284218368", "60296483084288", "659417378381824", "7253858445852672", "80209754567786496", "891027699137609728", "9939286070426992640", "111286739309529858048" ]
[ "nonn" ]
14
0
2
[ "A001764", "A366695", "A367641", "A381860", "A381939", "A381942" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-11T07:56:10
oeisdata/seq/A381/A381939.seq
ea437277c99830e508126ddcc78d425a
A381940
G.f. A(x) satisfies A(x) = (1 + x) * B(x*A(x)), where B(x) is the g.f. of A002293.
[ "1", "2", "7", "51", "440", "4170", "41921", "438972", "4736281", "52286520", "587774685", "6705201456", "77426676892", "903251324476", "10629495065550", "126032922655030", "1504194199010435", "18056321542477095", "217859030049153565", "2640609137351540510", "32137554969392230950", "392580762083089376630" ]
[ "nonn" ]
13
0
2
[ "A002293", "A025227", "A346647", "A365184", "A381787", "A381937", "A381940" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-11T07:57:06
oeisdata/seq/A381/A381940.seq
ec65e78084106ebc1ce24c28e409536f
A381941
G.f. A(x) satisfies A(x) = (1 + x)^2 * B(x*A(x)), where B(x) is the g.f. of A002293.
[ "1", "3", "10", "71", "644", "6461", "68971", "768054", "8820281", "103694479", "1241799996", "15095075897", "185769856443", "2310006893997", "28978952155943", "366315306556482", "4661272734504606", "59659914501348239", "767539555514812321", "9920124234695256009", "128744011085858468131", "1677087982747514335025" ]
[ "nonn" ]
12
0
2
[ "A002293", "A366694", "A367640", "A381938", "A381941" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-11T07:59:16
oeisdata/seq/A381/A381941.seq
64326d17b59d0d6ffbd3c4a67c5b2288
A381942
G.f. A(x) satisfies A(x) = (1 + x)^3 * B(x*A(x)), where B(x) is the g.f. of A002293.
[ "1", "4", "14", "96", "905", "9550", "107552", "1265372", "15364920", "191090255", "2421646300", "31157939594", "405932855044", "5344301858465", "70990458721140", "950263442420120", "12805328720666376", "173574888045493536", "2365049262321662145", "32374714068988416170", "445017678283209218750", "6140131349497715896244" ]
[ "nonn" ]
11
0
2
[ "A002293", "A366695", "A381860", "A381939", "A381942" ]
null
Seiichi Manyama, Mar 10 2025
2025-03-11T08:00:14
oeisdata/seq/A381/A381942.seq
5f8158cdc9ac4cde3b1810407d9476a7