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1999-12-11 03:00:00
2025-04-28 00:58:08
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A381529
T(n,k) is the number of permutations of [n] having exactly k pairs of integers i<j in [n] such that their cycle minima have opposite sorting order; triangle T(n,k), n>=0, 0<=k<=A125811(n)-1, read by rows.
[ "1", "1", "2", "5", "1", "15", "5", "4", "54", "21", "24", "16", "5", "235", "89", "118", "112", "101", "35", "28", "2", "1237", "408", "577", "633", "719", "585", "402", "239", "167", "59", "14", "7790", "2106", "3023", "3529", "4410", "4463", "4600", "3012", "2789", "1933", "1438", "629", "442", "122", "34", "57581", "12529", "17693", "20980", "27208", "30064", "35359", "33332", "28137", "24970", "22850", "17148", "14272", "8645", "5639", "3684", "1809", "664", "282", "34" ]
[ "nonn", "tabf" ]
34
0
3
[ "A000142", "A008302", "A051295", "A125810", "A125811", "A126673", "A381299", "A381529", "A381531", "A381539", "A381545" ]
null
Alois P. Heinz, Feb 26 2025
2025-02-27T17:05:26
oeisdata/seq/A381/A381529.seq
a58a5fcc06ef6ea262c7819e5b3a0015
A381530
a(n) is the least k > 0 such that n / k contains a digit 1 in its decimal representation.
[ "1", "2", "2", "3", "3", "4", "4", "5", "5", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "3", "1", "2", "2", "3", "3", "3", "3", "3", "3", "3", "1", "3", "3", "3", "3", "3", "3", "3", "3", "4", "1", "2", "2", "3", "3", "4", "4", "4", "4", "4", "1", "4", "4", "4", "4", "4", "4", "4", "4", "5", "1", "2", "2", "4", "4", "4", "4", "5", "5", "5", "1", "5", "3", "3", "3", "5", "5", "5", "5", "1" ]
[ "nonn", "base" ]
11
1
2
[ "A317173", "A371706", "A381530" ]
null
Ctibor O. Zizka, Feb 26 2025
2025-03-02T23:21:18
oeisdata/seq/A381/A381530.seq
ff55a5ca25c740f006db567d07d65461
A381531
Number of permutations of [n] having the maximal possible number of pairs of integers i<j in [n] such that their cycle minima have opposite sorting order.
[ "1", "1", "2", "1", "4", "5", "2", "14", "34", "34", "12", "132", "540", "1020", "888", "288", "4608", "28800", "89280", "143712", "113472", "34560", "760320", "6773760", "31449600", "81527040", "117089280", "85847040", "24883200", "721612800", "8709120000", "56783462400", "217205452800", "495200563200", "651939840000", "450584985600", "125411328000" ]
[ "nonn" ]
24
0
3
[ "A000178", "A000217", "A125811", "A381529", "A381531" ]
null
Alois P. Heinz, Feb 26 2025
2025-02-26T21:09:01
oeisdata/seq/A381/A381531.seq
26bc80d460fdb5dd9a2646fd893e6c2e
A381532
Smallest integer k>0 such that prime(n) + k*prime(n+1) is prime.
[ "1", "2", "2", "2", "2", "2", "6", "6", "4", "8", "4", "6", "2", "2", "10", "10", "2", "6", "12", "6", "4", "6", "4", "2", "14", "2", "2", "6", "6", "2", "2", "6", "6", "6", "20", "6", "4", "8", "4", "16", "2", "2", "2", "2", "8", "10", "4", "2", "6", "6", "6", "14", "2", "4", "10", "6", "2", "6", "2", "6", "18", "2", "2", "2", "2", "12", "10", "2", "6", "6", "4", "2", "22", "4", "6", "10", "12", "6", "8", "8", "12", "2" ]
[ "nonn" ]
71
1
2
[ "A129919", "A175914", "A368691", "A381532" ]
null
Jean-Marc Rebert, Mar 07 2025
2025-03-29T04:26:29
oeisdata/seq/A381/A381532.seq
4a2fdbee2e41445f50a495333f5278aa
A381533
Number of labeled histories for rooted 5-furcating trees with 4n+1 leaves if simultaneous 5-furcations are allowed.
[ "1", "1", "126", "198198", "1552358808", "41269930621920", "2917021792126858416", "466738566750935966462976", "150642168106131265276308435840", "89930728809765858827345682838905216", "92814015425659158860323886440105229380608", "156870775305420194841270876582071899442900414976", "415352074564676036635314305973768435826840253066044416" ]
[ "nonn" ]
8
0
3
[ "A317059", "A381486", "A381523", "A381533" ]
null
Noah A Rosenberg, Feb 26 2025
2025-03-08T20:48:57
oeisdata/seq/A381/A381533.seq
336bf64b5b4e8f7b7891897e7539a3d6
A381534
A084849 interleaved with positive even numbers.
[ "1", "2", "4", "4", "11", "6", "22", "8", "37", "10", "56", "12", "79", "14", "106", "16", "137", "18", "172", "20", "211", "22", "254", "24", "301", "26", "352", "28", "407", "30", "466", "32", "529", "34", "596", "36", "667", "38", "742", "40", "821", "42", "904", "44", "991", "46", "1082", "48", "1177", "50", "1276", "52" ]
[ "nonn", "easy" ]
21
1
2
[ "A000124", "A005843", "A354008", "A381534" ]
null
Ali Sada, Feb 26 2025
2025-03-01T12:13:58
oeisdata/seq/A381/A381534.seq
c23be87a68c823185bc511ede2284881
A381535
a(n) is the least nonnegative number that can be represented as the sum of two (not necessarily distinct) generalized pentagonal numbers in exactly n ways.
[ "11", "0", "2", "27", "92", "352", "1002", "16927", "2302", "7827", "25052", "220052", "13352", "1487552", "101752", "195677", "85177", "137532552", "173577" ]
[ "nonn", "more" ]
9
0
1
[ "A001318", "A093518", "A381535" ]
null
Robert Israel, Feb 26 2025
2025-03-01T12:18:43
oeisdata/seq/A381/A381535.seq
829d45f63583d003499c6dd6dd78b926
A381536
Number of labeled histories for rooted 4-furcating trees with 3n+1 leaves if simultaneous 4-furcations are not allowed.
[ "1", "1", "35", "7350", "5255250", "9564555000", "37072215180000", "271183254041700000", "3430468163627505000000", "70238835650273164875000000", "2210064963735845132791875000000", "102493972758213553878355995000000000", "6769214430816214165896021689775000000000", "618638506832293812621237422228537250000000000" ]
[ "nonn" ]
11
0
3
[ "A006472", "A339411", "A381523", "A381536" ]
null
Noah A Rosenberg, Feb 26 2025
2025-03-08T20:47:43
oeisdata/seq/A381/A381536.seq
dcb427532de637c14a7c26a4eb24c9a3
A381538
Numbers of the form m^(m^k).
[ "1", "4", "16", "27", "256", "3125", "19683", "46656", "65536", "823543", "16777216", "387420489", "4294967296", "10000000000", "285311670611", "7625597484987", "8916100448256", "302875106592253", "11112006825558016", "298023223876953125", "437893890380859375", "18446744073709551616" ]
[ "nonn" ]
19
1
2
[ "A000312", "A001597", "A067688", "A097374", "A257309", "A380760", "A381538" ]
null
Charles L. Hohn, Feb 26 2025
2025-03-09T13:09:49
oeisdata/seq/A381/A381538.seq
558e30bd2d715c8e6566bdc95e8c0e76
A381539
Number of permutations of [n] having exactly one pair of integers i<j in [n] such that their cycle minima have opposite sorting order.
[ "0", "0", "0", "1", "5", "21", "89", "408", "2106", "12529", "86579", "691287", "6296333", "64454418", "731532528", "9101244205", "122993164505", "1792140943473", "27987008885201", "466072881110268", "8241676745580774", "154187446760870761", "3042028843184493887", "63114652818792762987", "1373581948592359961909" ]
[ "nonn" ]
21
0
5
[ "A381529", "A381539" ]
null
Alois P. Heinz, Feb 26 2025
2025-02-26T21:09:54
oeisdata/seq/A381/A381539.seq
8368c5f14de096ad34ae7cb928f90a53
A381540
Numbers appearing only once in A048767 (Look-and-Say partition of prime indices).
[ "1", "2", "3", "4", "5", "7", "9", "11", "12", "13", "17", "18", "19", "20", "23", "24", "25", "28", "29", "31", "37", "40", "41", "43", "44", "45", "47", "48", "49", "50", "52", "53", "54", "56", "59", "61", "63", "67", "68", "71", "72", "73", "75", "76", "79", "80", "83", "88", "89", "92", "97", "98", "99", "101", "103", "104", "107", "108", "109", "112", "113", "116", "117", "121" ]
[ "nonn" ]
7
1
2
[ "A000005", "A000040", "A000720", "A000961", "A001222", "A003557", "A047966", "A048767", "A048768", "A051903", "A051904", "A055396", "A056239", "A061395", "A066328", "A071178", "A112798", "A116861", "A122111", "A130091", "A217605", "A239455", "A239964", "A351293", "A351294", "A351295", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381440", "A381540", "A381541" ]
null
Gus Wiseman, Mar 02 2025
2025-03-02T22:34:30
oeisdata/seq/A381/A381540.seq
68b8639fd22b95ff1cfa4681d67f21d5
A381541
Numbers appearing more than once in A048767 (Look-and-Say partition of prime indices).
[ "8", "16", "27", "32", "64", "81", "96", "125", "128", "144", "160", "192", "216", "224", "243", "256", "288" ]
[ "nonn", "more" ]
7
1
1
[ "A000005", "A000040", "A000720", "A000961", "A001222", "A003557", "A047966", "A048767", "A048768", "A051903", "A051904", "A055396", "A056239", "A061395", "A066328", "A071178", "A112798", "A116861", "A122111", "A130091", "A217605", "A239455", "A239964", "A351293", "A351294", "A351295", "A381431", "A381432", "A381433", "A381434", "A381435", "A381436", "A381440", "A381540", "A381541" ]
null
Gus Wiseman, Mar 02 2025
2025-03-02T22:45:57
oeisdata/seq/A381/A381541.seq
00a2a211dc3bbdcc903dbc1771caba62
A381542
Numbers > 1 whose greatest prime index equals their greatest prime multiplicity.
[ "2", "9", "12", "18", "36", "40", "112", "120", "125", "135", "200", "250", "270", "336", "352", "360", "375", "500", "540", "560", "567", "600", "675", "750", "784", "832", "1000", "1008", "1056", "1080", "1125", "1134", "1350", "1500", "1680", "1760", "1800", "2176", "2250", "2268", "2352", "2401", "2464", "2496", "2673", "2700", "2800", "2835", "3000" ]
[ "nonn" ]
6
1
1
[ "A000005", "A000040", "A000720", "A001221", "A001222", "A001223", "A008284", "A047966", "A047993", "A048767", "A051903", "A051904", "A055396", "A056239", "A061395", "A091602", "A106529", "A112798", "A122111", "A130091", "A212166", "A239964", "A240312", "A317090", "A381439", "A381542", "A381543", "A381544", "A381632", "A382302" ]
null
Gus Wiseman, Mar 24 2025
2025-03-24T22:35:24
oeisdata/seq/A381/A381542.seq
6357624d7a5022a46a64ddf56197456d
A381543
Numbers > 1 whose greatest prime index (A061395), number of distinct prime factors (A001221), and greatest prime multiplicity (A051903) are all equal.
[ "2", "12", "18", "36", "120", "270", "360", "540", "600", "750", "1080", "1350", "1500", "1680", "1800", "2250", "2700", "3000", "4500", "5040", "5400", "5670", "6750", "8400", "9000", "11340", "11760", "13500", "15120", "22680", "25200", "26250", "27000", "28350", "35280", "36960", "39690", "42000", "45360", "52500", "56700", "58800", "72030" ]
[ "nonn" ]
7
1
1
[ "A000009", "A000040", "A000720", "A001221", "A001222", "A001223", "A008284", "A047993", "A048767", "A051903", "A051904", "A055396", "A055932", "A056239", "A061395", "A062457", "A066328", "A091602", "A106529", "A112798", "A116608", "A122111", "A130091", "A212166", "A239964", "A240312", "A317090", "A363719", "A363740", "A365676", "A380955", "A381542", "A381543", "A381632", "A382302" ]
null
Gus Wiseman, Mar 24 2025
2025-03-24T22:35:15
oeisdata/seq/A381/A381543.seq
bc386d6a73a1e8dc4f6442232c543899
A381544
Number of integer partitions of n not containing more ones than any other part.
[ "0", "0", "1", "2", "3", "4", "7", "8", "13", "17", "24", "30", "45", "54", "75", "97", "127", "160", "212", "263", "342", "427", "541", "672", "851", "1046", "1307", "1607", "1989", "2428", "2993", "3631", "4443", "5378", "6533", "7873", "9527", "11424", "13752", "16447", "19701", "23470", "28016", "33253", "39537", "46801", "55428", "65408", "77238" ]
[ "nonn" ]
6
0
4
[ "A000009", "A000041", "A007814", "A008284", "A008289", "A047966", "A047993", "A051903", "A091602", "A091605", "A106529", "A116598", "A116861", "A212166", "A232697", "A237984", "A239964", "A240312", "A241131", "A360013", "A360014", "A360015", "A362608", "A363724", "A381079", "A381437", "A381438", "A381439", "A381542", "A381543", "A381544", "A382302", "A382303" ]
null
Gus Wiseman, Mar 24 2025
2025-03-25T08:57:42
oeisdata/seq/A381/A381544.seq
90f2e056e8fe103ea490df76faa511b9
A381545
Number of permutations of [n] having exactly n pairs of integers i<j in [n] such that their cycle minima have opposite sorting order.
[ "1", "0", "0", "0", "0", "0", "28", "239", "2789", "24970", "247089", "2289028", "23926282", "244031780", "2795283827", "32671509063", "426329260855", "5714045982473", "86176948036417", "1327311505233240", "22831768389870460", "401597165962560396", "7782893107559342148", "153285768850390602735", "3316598607281771351415" ]
[ "nonn" ]
10
0
7
[ "A381529", "A381545" ]
null
Alois P. Heinz, Feb 26 2025
2025-02-27T17:05:11
oeisdata/seq/A381/A381545.seq
3db50dd83808ad18cd5b39a5f2ee1052
A381546
Numbers with an odd number of abundant divisors.
[ "12", "18", "20", "30", "36", "42", "48", "56", "66", "70", "72", "78", "80", "84", "88", "90", "102", "104", "108", "114", "120", "126", "132", "138", "140", "144", "156", "162", "174", "186", "192", "196", "198", "204", "222", "224", "228", "234", "246", "252", "258", "270", "272", "276", "282", "288", "300", "304", "306", "308", "318", "320", "324", "330", "336", "342", "348" ]
[ "nonn", "easy" ]
8
1
1
[ "A005101", "A080224", "A091191", "A381546", "A381547", "A381548", "A381549" ]
null
Amiram Eldar, Feb 26 2025
2025-02-27T06:41:24
oeisdata/seq/A381/A381546.seq
079c6ad9b3448ac020cf36cd729dd002
A381547
Odd numbers with an odd number of abundant divisors.
[ "945", "1575", "2205", "3465", "4095", "4725", "5355", "5775", "5985", "6435", "6615", "6825", "7245", "7425", "8085", "8415", "8505", "8925", "9135", "9555", "9765", "10395", "11025", "11655", "12285", "12705", "12915", "13545", "14175", "14805", "15015", "16065", "16695", "17955", "18585", "19215", "19635", "19845", "21105", "21735", "21945" ]
[ "nonn", "easy" ]
7
1
1
[ "A005231", "A005408", "A006038", "A080224", "A187795", "A381546", "A381547", "A381548", "A381549" ]
null
Amiram Eldar, Feb 26 2025
2025-02-27T06:42:46
oeisdata/seq/A381/A381547.seq
acf4d6d06668f88c1edfbab7099140e0
A381548
Numbers k such that k and k+1 both have an odd number of abundant divisors.
[ "5984", "7424", "21735", "27404", "43064", "56924", "76544", "82004", "89775", "109395", "144584", "158235", "164835", "165375", "174824", "222704", "266475", "271215", "300104", "311024", "322335", "326655", "326864", "334304", "347984", "350175", "371924", "387584", "393855", "414315", "442035", "445004", "447524", "477224" ]
[ "nonn", "changed" ]
11
1
1
[ "A096399", "A381546", "A381548", "A381549" ]
null
Amiram Eldar, Feb 26 2025
2025-04-26T05:24:52
oeisdata/seq/A381/A381548.seq
1fb5980dc368e3616de8ca966e5cbf42
A381549
Numbers k such that k, k+1 and k+2 all have an odd number of abundant divisors.
[ "96236031968", "229687160624", "274957745984", "331240852304", "363015363248", "386136575824", "407374391150", "623810538350", "734609097584", "745885389248", "1080953007848" ]
[ "nonn", "more" ]
9
1
1
[ "A096536", "A381546", "A381548", "A381549" ]
null
Amiram Eldar, Feb 26 2025
2025-03-12T13:21:14
oeisdata/seq/A381/A381549.seq
b79410ba7cad55ff5412f5ebb3a85e5f
A381550
Numbers whose sum of abundant divisors is odd.
[ "945", "1575", "1890", "2205", "3150", "3465", "3780", "4095", "4410", "4725", "5355", "5775", "5985", "6300", "6435", "6615", "6825", "6930", "7245", "7425", "7560", "8085", "8190", "8415", "8505", "8820", "8925", "9135", "9450", "9555", "9765", "10395", "10710", "11025", "11550", "11655", "11970", "12285", "12600", "12705", "12870", "12915" ]
[ "nonn", "easy" ]
9
1
1
[ "A000265", "A005101", "A006038", "A080224", "A187795", "A381547", "A381550" ]
null
Amiram Eldar, Feb 26 2025
2025-02-27T06:42:12
oeisdata/seq/A381/A381550.seq
a023d6845fd59c412d07226cb5dd7fc0
A381551
Number of 2*n X 4 binary arrays with row sums 2 and column sums n, avoiding the patterns 010 and 101 in any row and column.
[ "1", "4", "16", "64", "324", "1764", "10000", "58564", "350464", "2131600", "13133376", "81757764", "513294336", "3245580900", "20646241344", "132021769104", "848031024996", "5468890936356", "35392361925904", "229761144199876", "1495753923300484", "9762043084514704", "63858040015802256" ]
[ "nonn" ]
18
0
2
[ "A381551", "A381553", "A381554" ]
null
Christoph Koutschan, Feb 27 2025
2025-02-28T08:05:10
oeisdata/seq/A381/A381551.seq
41bacbcb9e725d426bc6f4e84131eab5
A381552
Triangle read by rows T(n,k) is the number of diamond coverings for a specific number of diamonds covering an odd length row of triangles.
[ "3", "4", "4", "5", "12", "4", "6", "25", "20", "4", "7", "44", "61", "28", "4", "8", "70", "146", "113", "36", "4", "9", "104", "301", "344", "181", "44", "4", "10", "147", "560", "876", "670", "265", "52", "4", "11", "200", "966", "1968", "2035", "1156", "365", "60", "4", "12", "264", "1572", "4026", "5368", "4082", "1834", "481", "68", "4", "13", "340", "2442", "7656", "12727", "12376", "7385", "2736", "613", "76", "4", "14", "429", "3652", "13728", "27742", "33397", "25312", "12376", "3894", "761", "84", "4" ]
[ "nonn", "tabl" ]
13
0
1
[ "A000297", "A080856", "A381552", "A381555" ]
null
Craig Knecht, Feb 27 2025
2025-03-06T10:55:01
oeisdata/seq/A381/A381552.seq
aae3005f36b67e7199b807d6dffcbd1b
A381553
Number of 2*n X 6 binary arrays with row sums 3 and column sums n, avoiding the patterns 010 and 101 in any row and column.
[ "1", "8", "64", "368", "2776", "25880", "251704", "2629080", "28964248", "331032312", "3907675376", "47392320240", "587548108400", "7421689479608", "95248568409312", "1239031994818680", "16306127772957216", "216760982171930144", "2906731043068293952", "39278080769921432856", "534346120254755625336" ]
[ "nonn" ]
10
0
2
[ "A381551", "A381553", "A381554" ]
null
Christoph Koutschan, Feb 27 2025
2025-02-28T08:04:39
oeisdata/seq/A381/A381553.seq
b7da77b65da0e125e1c48621a7274d1a
A381554
Number of 2*n X 8 binary arrays with row sums 4 and column sums n, avoiding the patterns 010 and 101 in any row and column.
[ "1", "18", "324", "2776", "34586", "575270", "10061200", "194929482", "4115573632", "91947761368", "2167131637540", "53550929019486", "1376887129235964", "36670419524921146", "1007581514656491404", "28454294028011307236", "823234343053953729538" ]
[ "nonn" ]
8
0
2
[ "A381551", "A381553", "A381554" ]
null
Christoph Koutschan, Feb 27 2025
2025-02-28T08:04:58
oeisdata/seq/A381/A381554.seq
1d9f9e880969ed4a3b55c4428f673f61
A381555
Triangle read by rows T(n,k) is the number of diamond coverings for a specific number of diamonds covering an even length row of triangles.
[ "1", "4", "1", "8", "4", "1", "13", "16", "4", "1", "19", "41", "24", "4", "1", "26", "85", "85", "32", "4", "1", "34", "155", "231", "145", "40", "4", "1", "43", "259", "532", "489", "221", "48", "4", "1", "53", "406", "1092", "1365", "891", "313", "56", "4", "1", "64", "606", "2058", "3333", "2926", "1469", "421", "64", "4", "1", "76", "870", "3630", "7359", "8294", "5551", "2255", "545", "72", "4" ]
[ "nonn", "tabf" ]
29
0
2
[ "A063496", "A081219", "A102083", "A323847", "A380346", "A380416", "A381552", "A381555" ]
null
Craig Knecht, Feb 27 2025
2025-03-06T10:55:56
oeisdata/seq/A381/A381555.seq
d2676abe5607af80c0028be298205336
A381556
Number of minimum dominating sets in the n-Lucas cube graph.
[ "1", "1", "1", "15", "35", "18", "14", "1360", "2457", "180" ]
[ "nonn", "more" ]
23
1
4
null
null
Eric W. Weisstein, Feb 27 2025
2025-03-30T09:52:11
oeisdata/seq/A381/A381556.seq
ce8a6a9228b3c17f3b77a1e277c19d5f
A381557
Number of minimum dominating sets in the n-Pell graph.
[ "2", "4", "31", "24", "86" ]
[ "nonn", "more" ]
7
1
1
null
null
Eric W. Weisstein, Feb 27 2025
2025-03-23T18:25:48
oeisdata/seq/A381/A381557.seq
0bdd81a71c950e920e7ca3e07ebf1e5d
A381558
Number of minimum dominating sets in the n-triangular honeycomb acute knight graph.
[ "1", "1", "8", "9", "1", "8", "2916", "729", "27", "1", "1728", "3442951", "9216", "1", "1" ]
[ "nonn" ]
8
1
3
null
null
Eric W. Weisstein, Feb 27 2025
2025-03-23T18:28:14
oeisdata/seq/A381/A381558.seq
983ed438962a58058b94f68138f4175c
A381559
Number of minimum dominating sets in the n-triangular honeycomb bishop graph.
[ "1", "1", "6", "2", "30", "6", "168", "24", "1080", "120", "7920", "720", "65520", "5040", "604800", "40320", "6168960", "362880", "68947200", "3628800", "838252800", "39916800", "11017036800", "479001600", "155675520000", "6227020800", "2353813862400", "87178291200", "37922556672000", "1307674368000" ]
[ "nonn", "easy" ]
6
1
3
null
null
Eric W. Weisstein, Feb 27 2025
2025-02-27T17:49:38
oeisdata/seq/A381/A381559.seq
486256191bff4ca7cf46a77fa11d702f
A381560
Number of minimum dominating sets in the n-triangular honeycomb obtuse knight graph.
[ "1", "1", "1", "1", "39", "12", "126", "6", "144", "33", "12", "1176", "810", "210" ]
[ "nonn", "more" ]
30
1
5
null
null
Eric W. Weisstein, Feb 27 2025
2025-03-27T21:31:12
oeisdata/seq/A381/A381560.seq
2f9fb263765098c6da32d368d94f6323
A381561
Number of minimum dominating sets in the n-triangular honeycomb queen graph.
[ "1", "3", "15", "15", "195", "91", "2", "702", "6", "5763", "36", "52017", "290" ]
[ "nonn" ]
13
1
2
null
null
Eric W. Weisstein, Feb 27 2025
2025-03-07T19:53:29
oeisdata/seq/A381/A381561.seq
26c204fcc9489bb2951f7850defd349a
A381562
Minimum 2-tone chromatic number of maximal planar graphs with n vertices.
[ "6", "8", "9", "9", "8", "8", "8", "8", "8", "8", "8", "7", "8", "8", "8", "7" ]
[ "nonn" ]
4
3
1
[ "A003057", "A350361", "A350362", "A350715", "A351120", "A366727", "A366728", "A381562" ]
null
Allan Bickle, Feb 27 2025
2025-02-28T12:04:30
oeisdata/seq/A381/A381562.seq
6edfc73f161fda6862ecd0eedd957a26
A381563
2-tone chromatic number of a double wheel graph with n vertices.
[ "9", "9", "8", "8", "9", "8", "8", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15" ]
[ "nonn" ]
4
5
1
[ "A003057", "A350361", "A350362", "A350715", "A351120", "A366727", "A366728", "A381562", "A381563" ]
null
Allan Bickle, Feb 27 2025
2025-02-28T12:04:37
oeisdata/seq/A381/A381563.seq
e9e50a99b2e3fad89525e77d319dec43
A381564
2-tone chromatic number of a path with n-2 vertices joined to two adjacent vertices.
[ "8", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "11", "11", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "15", "15", "15", "15", "15", "16", "16", "16" ]
[ "nonn" ]
4
4
1
[ "A003057", "A350361", "A350362", "A350715", "A351120", "A366727", "A366728", "A381562", "A381563", "A381564" ]
null
Allan Bickle, Feb 27 2025
2025-02-28T12:04:43
oeisdata/seq/A381/A381564.seq
82c694163591dca1ca6dfcd4e61f391d
A381565
2-tone chromatic number of a particular class of planar graphs with 3n+3 vertices.
[ "5", "6", "7", "7", "8", "8", "9", "9", "10", "10", "10", "11", "11", "11", "12", "12", "12", "12", "13", "13", "13", "13", "14", "14", "14", "14", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "19", "19", "19", "19", "19", "19", "20", "20", "20", "20", "20", "20", "21" ]
[ "nonn" ]
4
1
1
[ "A003057", "A350361", "A350362", "A350715", "A351120", "A366727", "A366728", "A381562", "A381565" ]
null
Allan Bickle, Feb 27 2025
2025-02-28T12:04:50
oeisdata/seq/A381/A381565.seq
d16d8c6a300a65422817b07f67c24016
A381566
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A087949.
[ "1", "1", "0", "1", "1", "0", "1", "2", "1", "0", "1", "3", "3", "2", "0", "1", "4", "6", "6", "5", "0", "1", "5", "10", "13", "15", "16", "0", "1", "6", "15", "24", "33", "46", "59", "0", "1", "7", "21", "40", "63", "99", "164", "246", "0", "1", "8", "28", "62", "110", "188", "343", "662", "1131", "0", "1", "9", "36", "91", "180", "331", "638", "1344", "2961", "5655", "0" ]
[ "nonn", "tabl" ]
12
0
8
[ "A000007", "A087949", "A379598", "A381566", "A381567", "A381569" ]
null
Seiichi Manyama, Feb 28 2025
2025-02-28T07:27:36
oeisdata/seq/A381/A381566.seq
3a9af11702539b3c236515547cd8c957
A381567
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381568.
[ "1", "1", "0", "1", "2", "0", "1", "4", "5", "0", "1", "6", "14", "22", "0", "1", "8", "27", "64", "126", "0", "1", "10", "44", "134", "365", "884", "0", "1", "12", "65", "240", "777", "2492", "7149", "0", "1", "14", "90", "390", "1438", "5238", "19578", "64688", "0", "1", "16", "119", "592", "2440", "9696", "40244", "172356", "641836", "0", "1", "18", "152", "854", "3891", "16632", "73408", "345726", "1668686", "6888740", "0" ]
[ "nonn", "tabl" ]
15
0
5
[ "A000007", "A381566", "A381567", "A381568", "A381569" ]
null
Seiichi Manyama, Feb 28 2025
2025-02-28T07:30:44
oeisdata/seq/A381/A381567.seq
c666ce1520611a1debf0351fbf655fdb
A381568
G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^2.
[ "1", "2", "5", "22", "126", "884", "7149", "64688", "641836", "6888740", "79203860", "968503090", "12525131474", "170555767116", "2436592516874", "36409825487380", "567612675812796", "9211031425896752", "155283809480528788", "2714788300934206360", "49140787009610861896", "919625415852055598804", "17768937720619971300781" ]
[ "nonn" ]
18
0
2
[ "A087949", "A120970", "A143508", "A381567", "A381568", "A381570" ]
null
Seiichi Manyama, Feb 28 2025
2025-03-01T08:35:02
oeisdata/seq/A381/A381568.seq
a10a62f3ac1ad94a4b5540c817873ff3
A381569
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381570.
[ "1", "1", "0", "1", "3", "0", "1", "6", "12", "0", "1", "9", "33", "82", "0", "1", "12", "63", "236", "732", "0", "1", "15", "102", "489", "2100", "7944", "0", "1", "18", "150", "868", "4428", "22248", "99156", "0", "1", "21", "207", "1400", "8121", "46422", "270268", "1381464", "0", "1", "24", "273", "2112", "13665", "85272", "552540", "3668568", "21065853", "0" ]
[ "nonn", "tabl" ]
12
0
5
[ "A000007", "A381566", "A381567", "A381569", "A381570" ]
null
Seiichi Manyama, Feb 28 2025
2025-02-28T07:34:05
oeisdata/seq/A381/A381569.seq
782193ac8b28f84f0acf9147d7912bb5
A381570
G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^3.
[ "1", "3", "12", "82", "732", "7944", "99156", "1381464", "21065853", "346932822", "6112226961", "114383442888", "2261347164766", "47025363829497", "1025005545866361", "23349137897005296", "554467427766694440", "13696046757037152183", "351231525904387758222", "9335221780768641038952" ]
[ "nonn" ]
14
0
2
[ "A087949", "A120972", "A212029", "A381568", "A381569", "A381570", "A381574" ]
null
Seiichi Manyama, Feb 28 2025
2025-03-01T08:34:54
oeisdata/seq/A381/A381570.seq
a8f7971845a7b9f20c06c6ffd4ec9ab0
A381571
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381572.
[ "1", "1", "0", "1", "2", "0", "1", "4", "7", "0", "1", "6", "18", "38", "0", "1", "8", "33", "104", "267", "0", "1", "10", "52", "206", "735", "2232", "0", "1", "12", "75", "352", "1488", "6064", "21200", "0", "1", "14", "102", "550", "2626", "12246", "56510", "222556", "0", "1", "16", "133", "808", "4265", "21752", "112669", "581452", "2536661", "0", "1", "18", "168", "1134", "6537", "35812", "198808", "1140150", "6501267", "31010886", "0" ]
[ "nonn", "tabl" ]
12
0
5
[ "A000007", "A379598", "A381571", "A381572", "A381573" ]
null
Seiichi Manyama, Feb 28 2025
2025-02-28T07:36:44
oeisdata/seq/A381/A381571.seq
a072820e27b1e3133e0f6db52a6ec2c5
A381572
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x*A(x)))^2.
[ "1", "2", "7", "38", "267", "2232", "21200", "222556", "2536661", "31010886", "403097573", "5535291884", "79900803514", "1207657432714", "19052200105025", "312909670649562", "5338325737985841", "94422672774323512", "1728653714036740230", "32708138881741705812", "638762549199936808759", "12859693257887577375744" ]
[ "nonn" ]
12
0
2
[ "A381029", "A381571", "A381572" ]
null
Seiichi Manyama, Feb 28 2025
2025-03-02T08:01:12
oeisdata/seq/A381/A381572.seq
c23d0dc573fa2608f9ace35d02208216
A381573
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381574.
[ "1", "1", "0", "1", "3", "0", "1", "6", "15", "0", "1", "9", "39", "118", "0", "1", "12", "72", "326", "1206", "0", "1", "15", "114", "651", "3345", "14712", "0", "1", "18", "165", "1120", "6822", "40200", "204385", "0", "1", "21", "225", "1760", "12123", "81675", "547146", "3143826", "0", "1", "24", "294", "2598", "19815", "145968", "1096080", "8239938", "52580328", "0" ]
[ "nonn", "tabl" ]
10
0
5
[ "A000007", "A379598", "A381571", "A381573", "A381574" ]
null
Seiichi Manyama, Feb 28 2025
2025-02-28T07:39:45
oeisdata/seq/A381/A381573.seq
26ccfc0d5a1a5b98a54ac9b331535379
A381574
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x*A(x)))^3.
[ "1", "3", "15", "118", "1206", "14712", "204385", "3143826", "52580328", "944416084", "18056415144", "365065244238", "7765839784508", "173123253590079", "4031536347783786", "97807655876704029", "2466489368705170539", "64527021089110890192", "1748298996924574135699", "48982266056400514509660" ]
[ "nonn" ]
12
0
2
[ "A381570", "A381573", "A381574", "A381615" ]
null
Seiichi Manyama, Feb 28 2025
2025-03-02T08:01:16
oeisdata/seq/A381/A381574.seq
c7e25cf422987207a20cc92297572b1b
A381575
Number of disjoint-union partial algebras with zero on [n].
[ "1", "2", "7", "68", "4619", "15621334" ]
[ "nonn", "more" ]
12
0
2
[ "A380571", "A381472", "A381575" ]
null
Peter J. Taylor, Feb 28 2025
2025-03-16T10:08:38
oeisdata/seq/A381/A381575.seq
924f0397440da3406bc734db94049de1
A381576
a(n) is the second element of the sorted multiset of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "2", "3", "2", "5", "1", "7", "3", "3", "1", "11", "2", "13", "1", "1", "4", "17", "2", "19", "2", "1", "1", "23", "2", "5", "1", "3", "2", "29", "1", "31", "5", "1", "1", "1", "2", "37", "1", "1", "2", "41", "1", "43", "2", "2", "1", "47", "2", "7", "2", "1", "2", "53", "2", "1", "2", "1", "1", "59", "1", "61", "1", "2", "6", "1", "1", "67", "2", "1", "1", "71", "2", "73", "1", "2", "2", "1", "1", "79", "2", "4", "1", "83", "1", "1", "1" ]
[ "nonn", "easy" ]
6
2
1
[ "A381178", "A381576" ]
null
Paolo Xausa, Feb 28 2025
2025-03-01T12:19:45
oeisdata/seq/A381/A381576.seq
0168956213b6613411245e6d203c8a7f
A381577
Unique sequence of 0's, 1's, and 2's such that for any terms x and y with x < y, the subsequence of x's and y's becomes the Thue-Morse sequence after substitution x -> 0, y -> 1.
[ "0", "1", "2", "2", "1", "0", "2", "1", "0", "0", "1", "2", "2", "1", "0", "0", "1", "2", "0", "1", "2", "2", "1", "0", "2", "1", "0", "0", "1", "2", "0", "1", "2", "2", "1", "0", "0", "1", "2", "2", "1", "0", "2", "1", "0", "0", "1", "2", "2", "1", "0", "0", "1", "2", "0", "1", "2", "2", "1", "0", "0", "1", "2", "2", "1", "0", "2", "1", "0", "0", "1", "2", "0", "1", "2", "2", "1", "0", "2", "1", "0", "0", "1", "2", "2", "1", "0" ]
[ "nonn", "easy" ]
9
0
3
[ "A010060", "A053838", "A287150", "A381577" ]
null
Andrey Zabolotskiy, Feb 28 2025
2025-02-28T13:49:23
oeisdata/seq/A381/A381577.seq
aba3293a2de9483bce552754d4b7a3da
A381578
For n > 0, for k > n, a(n) is the least k such that the pre-period and first period of the decimal expansion of n/k contains every digit of n at least as many times it is contained in n.
[ "6", "7", "8", "7", "7", "9", "8", "9", "10", "17", "17", "14", "17", "17", "17", "17", "19", "19", "21", "21", "23", "23", "29", "28", "27", "27", "28", "29", "32", "31", "34", "34", "38", "38", "38", "38", "38", "39", "46", "43", "42", "43", "46", "46", "46", "47", "49", "49", "51", "51", "53", "53", "57", "56", "57", "57", "58", "59", "61", "61", "62", "63", "65", "65", "68", "67", "68", "69" ]
[ "nonn", "base" ]
14
1
1
[ "A002371", "A007732", "A381578" ]
null
Ctibor O. Zizka, Feb 28 2025
2025-03-02T23:21:30
oeisdata/seq/A381/A381578.seq
fa3f0dcd73fa2e6b8b667f148f0ecb77
A381579
The Chung-Graham representation of n: representation of n in base of even-indexed Fibonacci numbers.
[ "0", "1", "2", "10", "11", "12", "20", "21", "100", "101", "102", "110", "111", "112", "120", "121", "200", "201", "202", "210", "211", "1000", "1001", "1002", "1010", "1011", "1012", "1020", "1021", "1100", "1101", "1102", "1110", "1111", "1112", "1120", "1121", "1200", "1201", "1202", "1210", "1211", "2000", "2001", "2002", "2010", "2011", "2012", "2020", "2021" ]
[ "nonn", "easy", "base" ]
9
0
3
[ "A000045", "A001906", "A014417", "A104326", "A291711", "A381579" ]
null
Amiram Eldar, Feb 28 2025
2025-02-28T12:08:01
oeisdata/seq/A381/A381579.seq
c391c00d4881c58eefb551dd4e8126b3
A381580
Numbers whose Chung-Graham representation (A381579) is palindromic.
[ "0", "1", "2", "4", "9", "12", "15", "18", "22", "33", "44", "56", "64", "72", "80", "88", "96", "104", "112", "120", "128", "136", "145", "174", "203", "232", "261", "290", "319", "348", "378", "399", "420", "441", "462", "483", "504", "525", "546", "567", "588", "609", "630", "651", "672", "693", "714", "735", "756", "777", "798", "819", "840", "861", "882", "903", "924", "945", "966", "988" ]
[ "nonn", "easy", "base" ]
7
1
3
[ "A000045", "A002113", "A006995", "A055588", "A094202", "A331191", "A381579", "A381580" ]
null
Amiram Eldar, Feb 28 2025
2025-02-28T12:08:12
oeisdata/seq/A381/A381580.seq
38f2f6166e5a8ef32f5cf6a3f7b784a8
A381581
Numbers divisible by the sum of the digits in their Chung-Graham representation (A381579).
[ "1", "2", "3", "4", "6", "8", "12", "16", "20", "21", "22", "24", "27", "28", "30", "40", "42", "44", "45", "48", "55", "56", "57", "58", "60", "66", "70", "72", "75", "76", "80", "84", "90", "92", "95", "96", "100", "102", "110", "111", "112", "115", "116", "120", "132", "135", "138", "140", "144", "150", "152", "153", "156", "168", "170", "175", "176", "180", "186", "190", "195", "198" ]
[ "nonn", "easy", "base" ]
7
1
2
[ "A000045", "A001651", "A001906", "A005349", "A049445", "A064150", "A291711", "A328208", "A328212", "A381581", "A381582", "A381583", "A381584", "A381585" ]
null
Amiram Eldar, Feb 28 2025
2025-02-28T12:08:25
oeisdata/seq/A381/A381581.seq
e02d6cda1aa833162bcdb26d9dda9d2a
A381582
Numbers k such that k and k+1 are both terms in A381581.
[ "1", "2", "3", "20", "21", "27", "44", "55", "56", "57", "75", "95", "110", "111", "115", "152", "175", "207", "264", "287", "291", "304", "305", "344", "364", "365", "377", "380", "395", "398", "399", "404", "425", "435", "455", "534", "584", "605", "815", "846", "847", "864", "888", "930", "987", "992", "1004", "1011", "1024", "1025", "1064", "1084", "1085", "1145", "1182" ]
[ "nonn", "easy", "base" ]
7
1
2
[ "A000045", "A001651", "A001906", "A291711", "A328209", "A330927", "A330931", "A351720", "A381581", "A381582", "A381583", "A381584", "A381585" ]
null
Amiram Eldar, Feb 28 2025
2025-02-28T12:08:32
oeisdata/seq/A381/A381582.seq
3df75578a89712af57a4876c5ffa4e57
A381583
Starts of runs of 3 consecutive integers that are all terms in A381581.
[ "1", "2", "20", "55", "56", "110", "304", "364", "398", "846", "1024", "1084", "1744", "1854", "2044", "2104", "2105", "2527", "2824", "2862", "3870", "4374", "5222", "5223", "5243", "5718", "5928", "6488", "6784", "6844", "6894", "6978", "7142", "7924", "10590", "11240", "11889", "11975", "12248", "14284", "14915", "16638", "17710", "17714", "17824" ]
[ "nonn", "easy", "base" ]
8
1
2
[ "A000045", "A001906", "A087445", "A154701", "A291711", "A328210", "A330932", "A351721", "A381581", "A381582", "A381583", "A381584", "A381585" ]
null
Amiram Eldar, Feb 28 2025
2025-02-28T12:08:38
oeisdata/seq/A381/A381583.seq
62ae4bdcce76a9d74d65d30f41964f54
A381584
Starts of runs of 4 consecutive integers that are all terms in A381581.
[ "1", "55", "2104", "5222", "24784", "63510", "64264", "69487", "95463", "121393", "184327", "327303", "374589", "463110", "468168", "561069", "572550", "596868", "671407", "740310", "759030", "819948", "902670", "956680", "1023009", "1036230", "1065030", "1259817", "1274910", "1359552", "1683154", "1714470", "1731750", "2182023" ]
[ "nonn", "base" ]
8
1
2
[ "A000045", "A001906", "A087445", "A141769", "A291711", "A328211", "A328215", "A330933", "A381581", "A381582", "A381583", "A381584", "A381585" ]
null
Amiram Eldar, Feb 28 2025
2025-02-28T12:08:47
oeisdata/seq/A381/A381584.seq
b43a8057dd0c4f28faca97bfa61e7e6a
A381585
Starts of runs of 5 consecutive integers that are all terms in A381581.
[ "57744971", "159104411", "203738652", "212548572", "260463851", "361823291", "413644572", "431577521", "440353328", "520800012", "717222337", "726300972", "779825648", "843559091", "913313321", "945016812", "986681527", "1091786528", "1116032201", "1185786431", "1318751081", "1347208812", "1360423692", "1418212627" ]
[ "nonn", "base" ]
18
1
1
[ "A291711", "A330928", "A334373", "A364220", "A364383", "A381581", "A381582", "A381583", "A381584", "A381585" ]
null
Amiram Eldar, Feb 28 2025
2025-03-03T13:27:39
oeisdata/seq/A381/A381585.seq
81ee91b05bd91e3745d974b35d704149
A381586
Number of simple graphs on n unlabeled vertices whose degree sequence is consecutive.
[ "1", "1", "2", "4", "9", "24", "98", "622", "7293", "162052", "6997100", "578605618", "90558592724", "26673271109299", "14758661765740616" ]
[ "nonn", "more" ]
19
0
3
[ "A000088", "A005176", "A381586" ]
null
John P. McSorley, Feb 28 2025
2025-03-07T08:16:32
oeisdata/seq/A381/A381586.seq
5ddd5f8acdd8266d5141369c9755d798
A381587
a(1) = 1; thereafter the sequence is extended by iteratively appending the run length transform of the reverse of the sequence thus far.
[ "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "3", "1", "1", "1", "2", "1", "3", "1", "1", "1", "3", "1", "1", "1", "2", "1", "3", "1", "3", "1", "1", "1", "3", "1", "1", "1", "3", "1", "1", "1", "2", "1", "3", "1", "3", "1", "3", "1", "1", "1", "1", "1", "3", "1", "3", "1", "1", "1", "3", "1", "1", "1", "3", "1", "1", "1", "2", "1", "3", "1", "3", "1", "3", "1", "1", "1", "5", "1", "1", "1", "1", "1", "1", "1", "3", "1", "3" ]
[ "tabf", "nonn" ]
31
1
3
[ "A306211", "A306346", "A381356", "A381357", "A381358", "A381587" ]
null
Neal Gersh Tolunsky, Feb 27 2025
2025-03-04T07:35:18
oeisdata/seq/A381/A381587.seq
90fbbfdb18ae093e77186f03444f9e99
A381588
If n = Product (p_j^k_j) then a(n) = Product (lcm(p_j, k_j)), with a(1) = 1.
[ "1", "2", "3", "2", "5", "6", "7", "6", "6", "10", "11", "6", "13", "14", "15", "4", "17", "12", "19", "10", "21", "22", "23", "18", "10", "26", "3", "14", "29", "30", "31", "10", "33", "34", "35", "12", "37", "38", "39", "30", "41", "42", "43", "22", "30", "46", "47", "12", "14", "20", "51", "26", "53", "6", "55", "42", "57", "58", "59", "30", "61", "62", "42", "6", "65", "66", "67", "34", "69", "70", "71" ]
[ "nonn", "mult", "easy" ]
20
1
2
[ "A008473", "A008477", "A035306", "A144338", "A369008", "A381588" ]
null
Paolo Xausa, Feb 28 2025
2025-03-02T22:50:08
oeisdata/seq/A381/A381588.seq
15c0d6c10fd857bcbab4116afd008f9d
A381589
The number of face-magic cubes with magic sum n and distinct positive integers at the vertices including 1.
[ "3", "2", "6", "6", "16", "13", "21", "28", "38", "40", "57", "58", "81", "92", "108", "118", "150", "158", "188", "213", "242", "257", "309", "324", "373", "408", "448", "483", "551", "578", "643", "695", "759", "804", "894", "935", "1023", "1097", "1177", "1243", "1360", "1416", "1528", "1625", "1731", "1816", "1959", "2041", "2181", "2300", "2430", "2541", "2721", "2822", "2992", "3141", "3300", "3441", "3650", "3781", "3985", "4163", "4358", "4526", "4777", "4934" ]
[ "nonn" ]
41
18
1
[ "A115264", "A203286", "A381589" ]
null
R. J. Mathar, Mar 12 2025
2025-03-12T11:02:36
oeisdata/seq/A381/A381589.seq
fa412064811d166b77de01ff17d9414a
A381590
Primes with primitive root -100.
[ "3", "7", "19", "23", "31", "43", "47", "59", "67", "71", "83", "107", "131", "151", "163", "167", "179", "191", "199", "223", "227", "263", "283", "307", "311", "347", "359", "367", "379", "383", "419", "431", "439", "443", "467", "479", "487", "491", "499", "503", "523", "563", "571", "587", "599", "619", "631", "647", "659", "683", "719", "727", "743", "787", "811" ]
[ "nonn", "easy" ]
11
1
1
[ "A006883", "A097443", "A381590" ]
null
Davide Rotondo, Feb 28 2025
2025-03-10T22:56:14
oeisdata/seq/A381/A381590.seq
3b1ac5c86385084b48f0906c15355ed0
A381591
Elimination order of the first person in a variation of the Josephus problem, where there are n people total and two people are skipped each time.
[ "1", "1", "2", "4", "2", "6", "6", "3", "9", "6", "4", "7", "11", "5", "11", "15", "6", "13", "11", "7", "12", "16", "8", "23", "18", "9", "22", "16", "10", "17", "31", "11", "27", "30", "12", "35", "21", "13", "22", "37", "14", "30", "35", "15", "32", "26", "16", "27", "35", "17", "47", "37", "18", "53", "31", "19", "32", "47", "20", "57", "56", "21", "51", "36", "22", "37", "65", "23", "49", "70" ]
[ "nonn" ]
20
1
3
[ "A006257", "A008585", "A054995", "A225381", "A321298", "A378635", "A380195", "A381591", "A381667" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 02 2025
2025-03-26T22:02:08
oeisdata/seq/A381/A381591.seq
6f6831d4dc869cff7afc036f18cc6f9c
A381592
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381600.
[ "1", "1", "0", "1", "1", "0", "1", "2", "5", "0", "1", "3", "11", "39", "0", "1", "4", "18", "88", "383", "0", "1", "5", "26", "148", "869", "4360", "0", "1", "6", "35", "220", "1473", "9876", "55201", "0", "1", "7", "45", "305", "2211", "16740", "124473", "758877", "0", "1", "8", "56", "404", "3100", "25164", "210260", "1701630", "11157081", "0", "1", "9", "68", "518", "4158", "35381", "315312", "2860317", "24870695", "173623407", "0" ]
[ "nonn", "tabl" ]
23
0
8
[ "A000007", "A379599", "A381571", "A381592", "A381593", "A381594", "A381600", "A381602" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-03T10:42:12
oeisdata/seq/A381/A381592.seq
1b2f1bd105ec91dcd73a42ed1a89608c
A381593
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x) * A(x*A(x)))^2.
[ "1", "2", "11", "88", "869", "9876", "124473", "1701630", "24870695", "384795184", "6257294780", "106377162620", "1882982975521", "34593496243070", "657935674477431", "12927331575084846", "261951066040220637", "5466177185459699916", "117315664923801661485", "2586804284853871362408" ]
[ "nonn" ]
13
0
2
[ "A088714", "A107096", "A381572", "A381592", "A381593", "A381595", "A381600" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:37:29
oeisdata/seq/A381/A381593.seq
cf1942c677fde179d7264b0d1c948047
A381594
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381601.
[ "1", "1", "0", "1", "1", "0", "1", "2", "7", "0", "1", "3", "15", "79", "0", "1", "4", "24", "172", "1134", "0", "1", "5", "34", "280", "2475", "18953", "0", "1", "6", "45", "404", "4044", "41280", "353134", "0", "1", "7", "57", "545", "5863", "67365", "766291", "7154751", "0", "1", "8", "70", "704", "7955", "97620", "1246534", "15460284", "155181240", "0", "1", "9", "84", "882", "10344", "132486", "1801536", "25051422", "333896388", "3565276582", "0" ]
[ "nonn", "tabl" ]
16
0
8
[ "A000007", "A379599", "A381573", "A381592", "A381594", "A381601" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:36:21
oeisdata/seq/A381/A381594.seq
141fdcc3c1b634397dbcb26dc1e13a16
A381595
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x) * A(x*A(x)))^3.
[ "1", "3", "24", "280", "4044", "67365", "1246534", "25051422", "538836147", "12279937669", "294374405652", "7382843258466", "192917842671564", "5235276617405133", "147163222059602313", "4275948043251399950", "128196303568520249238", "3959890522003241945409", "125863828745364900374059" ]
[ "nonn" ]
10
0
2
[ "A088714", "A145160", "A381574", "A381593", "A381594", "A381595", "A381601" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:36:12
oeisdata/seq/A381/A381595.seq
2256a2de71cf00de303eacfcdb8f7e2b
A381596
a(n) = number of real zeros (counted with multiplicity) of the polynomial P(n,z) = Sum_{i=1..n} A001223(i)*z^(i-1) where A001223(i) = differences between consecutive primes.
[ "0", "1", "0", "1", "2", "1", "2", "1", "2", "3", "2", "3", "2", "1", "2", "1", "4", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "3", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "3", "2", "3", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1" ]
[ "nonn" ]
16
1
5
[ "A000040", "A001223", "A381596", "A381604" ]
null
Michel Lagneau, Mar 01 2025
2025-03-12T08:38:32
oeisdata/seq/A381/A381596.seq
1ab7332ca681d826d2bb8f5d1d2f0c54
A381597
Lexicographically earliest sequence of positive integers such that for any t and k, with k>=1, where t = a(n) = a(n+k) = a(n+2*k), only one occurrence of k, for a given t, appears anywhere in the sequence.
[ "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "2", "1", "1", "2", "1", "1", "3", "2", "3", "2", "1", "3", "1", "2", "3", "2", "2", "1", "3", "3", "2", "1", "2", "3", "3", "3", "1", "1", "4", "1", "2", "3", "4", "3", "1", "3", "1", "4", "4", "2", "3", "2", "2", "4", "3", "4", "2", "4", "4", "2", "1", "4", "1", "3", "2", "2", "4", "5", "3", "1", "3", "3", "1", "4", "4", "2", "4", "4", "3", "1", "1", "2", "3", "3", "2", "5", "5", "3", "5", "2", "1", "3", "4", "5", "4", "1", "5", "4", "3", "1", "2", "4", "1", "4", "1", "5", "2", "2", "3", "3", "5", "5", "5", "4", "5", "1", "4", "3", "2", "5" ]
[ "nonn" ]
7
1
4
[ "A229037", "A281511", "A370708", "A381597", "A381598", "A381599" ]
null
Scott R. Shannon, Mar 01 2025
2025-03-01T22:48:58
oeisdata/seq/A381/A381597.seq
c31c291e57f3d4c452621bfdcb8a37c6
A381598
Index of first term of three consecutive n's in A381597.
[ "1", "9", "34", "147", "111", "359", "437", "389", "594", "826", "1102", "83317", "1789", "5142", "2931", "12671" ]
[ "nonn", "more" ]
7
1
2
[ "A229037", "A281511", "A370708", "A381597", "A381598", "A381599" ]
null
Scott R. Shannon, Mar 01 2025
2025-03-01T22:48:39
oeisdata/seq/A381/A381598.seq
c8168483e7f1e9ddca843fc3690cea06
A381599
Index where n first appears in A381597.
[ "1", "4", "17", "39", "68", "124", "191", "286", "441", "577", "776", "1043", "1192", "1556", "1736", "2214", "2744", "3221", "3519", "4248", "5028", "5542", "6574", "7013", "8093", "8945", "10110", "11043", "12413", "13223", "14476", "15923", "17430", "18617", "20027", "21991", "24016", "25364", "27414", "29356", "31392", "32614", "35743", "37888", "40301", "42620", "45696", "47776", "51109", "53264", "56429", "58471", "61676", "64468", "69437", "72011", "75626" ]
[ "nonn" ]
6
1
2
[ "A229037", "A281511", "A370708", "A381597", "A381598", "A381599" ]
null
Scott R. Shannon, Mar 01 2025
2025-03-01T22:48:30
oeisdata/seq/A381/A381599.seq
a6feb8502dbdc697ef2312ee69af08a5
A381600
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x)^2 * A(x*A(x)^2)^2).
[ "1", "1", "5", "39", "383", "4360", "55201", "758877", "11157081", "173623407", "2838995592", "48515016273", "862904739711", "15923514065053", "304089551295359", "5997295071211547", "121944040723497105", "2552667957311169834", "54944459391676448365", "1214747696691087352576", "27559533140410855702244" ]
[ "nonn" ]
7
0
3
[ "A120971", "A381592", "A381600" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:37:37
oeisdata/seq/A381/A381600.seq
38466e24aca152af83d2d7680b0784dc
A381601
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x)^3 * A(x*A(x)^3)^3).
[ "1", "1", "7", "79", "1134", "18953", "353134", "7154751", "155181240", "3565276582", "86122663681", "2175366732971", "57218428637862", "1562164759518688", "44156180231275177", "1289514761824080659", "38840440076269957435", "1204858168452465020445", "38445264045516464373511" ]
[ "nonn" ]
7
0
3
[ "A381594", "A381601" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:36:16
oeisdata/seq/A381/A381601.seq
5e112595e65f5f9f2dab702a09d56f84
A381602
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A120971.
[ "1", "1", "0", "1", "1", "0", "1", "2", "4", "0", "1", "3", "9", "26", "0", "1", "4", "15", "60", "218", "0", "1", "5", "22", "103", "504", "2151", "0", "1", "6", "30", "156", "870", "4946", "23854", "0", "1", "7", "39", "220", "1329", "8511", "54430", "289555", "0", "1", "8", "49", "296", "1895", "12988", "93070", "655362", "3783568", "0", "1", "9", "60", "385", "2583", "18536", "141316", "1112382", "8496454", "52624689", "0" ]
[ "nonn", "tabl" ]
10
0
8
[ "A000007", "A120971", "A379598", "A381602", "A381603" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:36:08
oeisdata/seq/A381/A381602.seq
3a60ab8af3ec72fa28f1c2253d6a4a14
A381603
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A120973.
[ "1", "1", "0", "1", "1", "0", "1", "2", "6", "0", "1", "3", "13", "60", "0", "1", "4", "21", "132", "776", "0", "1", "5", "30", "217", "1708", "11802", "0", "1", "6", "40", "316", "2814", "25876", "201465", "0", "1", "7", "51", "430", "4113", "42510", "439446", "3759100", "0", "1", "8", "63", "560", "5625", "62016", "718647", "8155874", "75404151", "0", "1", "9", "76", "707", "7371", "84731", "1044228", "13270944", "162762498", "1608036861", "0" ]
[ "nonn", "tabl" ]
10
0
8
[ "A000007", "A120973", "A379598", "A381602", "A381603" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T08:35:59
oeisdata/seq/A381/A381603.seq
6eac66e266b9925fea882322a86936bc
A381604
Least number k such that A381596(k) = n.
[ "1", "2", "5", "10", "17", "116", "501", "512" ]
[ "nonn", "hard", "more" ]
9
0
2
[ "A001223", "A381596", "A381604" ]
null
Michel Lagneau, Mar 01 2025
2025-03-12T08:39:26
oeisdata/seq/A381/A381604.seq
6c289818023d6b6d75b14501f0a454c6
A381605
Number of distinct prime divisors of n^3+1.
[ "1", "1", "2", "2", "3", "2", "2", "2", "3", "3", "3", "3", "3", "3", "2", "2", "4", "2", "3", "3", "3", "2", "3", "3", "3", "3", "4", "2", "4", "3", "3", "3", "4", "3", "3", "3", "4", "4", "3", "3", "4", "2", "4", "3", "4", "3", "4", "3", "4", "4", "3", "3", "3", "4", "3", "4", "4", "2", "5", "2", "4", "4", "2", "4", "5", "3", "3", "4", "5", "2", "3", "2", "4", "3", "5", "3", "4", "2", "3", "3", "3", "4", "4", "4", "4", "3", "4", "4", "5", "3", "3", "3", "4", "4", "4", "3", "4", "3", "4", "2" ]
[ "nonn" ]
37
1
3
[ "A001093", "A001221", "A128428", "A366580", "A381605" ]
null
Joost de Winter, Mar 01 2025
2025-04-03T14:03:15
oeisdata/seq/A381/A381605.seq
7a1fe8d0ed01d893e409c7fa66384e18
A381606
a(n) is the smallest prime number greater than n that contains n as a substring of its digits.
[ "101", "11", "23", "13", "41", "53", "61", "17", "83", "19", "101", "113", "127", "113", "149", "151", "163", "173", "181", "191", "1201", "211", "223", "223", "241", "251", "263", "127", "281", "229", "307", "131", "1321", "233", "347", "353", "367", "137", "383", "139", "401", "241", "421", "431", "443", "457", "461", "347", "487", "149", "503", "151", "521", "353", "541" ]
[ "nonn", "base" ]
65
0
1
[ "A062584", "A064735", "A354114", "A381099", "A381606" ]
null
Joost de Winter, Mar 01 2025
2025-03-18T16:15:07
oeisdata/seq/A381/A381606.seq
2a65c5c3c8a2e30b9759b5f637be700c
A381607
For any nonnegative integer n with ternary expansion Sum_{k >= 0} t_k * 3^k, a(n) = Sum_{k >= 0} t_k * A000045(2*k + 2).
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "8", "9", "10", "11", "12", "13", "14", "15", "16", "16", "17", "18", "19", "20", "21", "22", "23", "24", "21", "22", "23", "24", "25", "26", "27", "28", "29", "29", "30", "31", "32", "33", "34", "35", "36", "37", "37", "38", "39", "40", "41", "42", "43", "44", "45", "42", "43", "44", "45", "46", "47", "48", "49", "50", "50", "51", "52", "53", "54" ]
[ "nonn", "base", "easy" ]
8
0
3
[ "A000045", "A022290", "A028898", "A381579", "A381607" ]
null
Rémy Sigrist, Mar 01 2025
2025-03-03T09:33:02
oeisdata/seq/A381/A381607.seq
6cc01db89560c71b868981f3e431a090
A381608
Nonnegative integers whose ternary expansion does not contain pairs of 2's only separated by (zero or more) 1's, with offset 0.
[ "0", "1", "2", "3", "4", "5", "6", "7", "9", "10", "11", "12", "13", "14", "15", "16", "18", "19", "20", "21", "22", "27", "28", "29", "30", "31", "32", "33", "34", "36", "37", "38", "39", "40", "41", "42", "43", "45", "46", "47", "48", "49", "54", "55", "56", "57", "58", "59", "60", "61", "63", "64", "65", "66", "67", "81", "82", "83", "84", "85", "86", "87", "88", "90", "91", "92", "93" ]
[ "nonn", "base" ]
6
0
3
[ "A028898", "A381579", "A381607", "A381608" ]
null
Rémy Sigrist, Mar 01 2025
2025-03-03T09:33:07
oeisdata/seq/A381/A381608.seq
1996a8d3918813b39c286c920201bc81
A381609
a(n) is the number of occurrences of n in A381607.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "3", "2", "2", "2", "2", "3", "2", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "2", "1", "1" ]
[ "nonn", "base" ]
8
0
9
[ "A381579", "A381607", "A381609" ]
null
Rémy Sigrist, Mar 01 2025
2025-03-03T09:33:12
oeisdata/seq/A381/A381609.seq
52d17ae77a10bb9bfdd89610b9eab3d4
A381610
Irregular table T(n, k), n >= 0, k = 1..A381609(n), read by rows: the n-th row lists the numbers m such that A381607(m) = n.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "27", "24", "28", "25", "29", "26", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "54", "51", "55", "52", "56", "53", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67" ]
[ "nonn", "base", "tabf" ]
10
0
3
[ "A381607", "A381609", "A381610", "A381611" ]
null
Rémy Sigrist, Mar 01 2025
2025-03-03T09:33:16
oeisdata/seq/A381/A381610.seq
70f29f2a3f12f3ae76c0df40d5d676cf
A381611
Inverse permutation to A381610.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "25", "27", "29", "24", "26", "28", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "52", "54", "56", "51", "53", "55", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67" ]
[ "nonn", "base" ]
8
0
3
[ "A381610", "A381611" ]
null
Rémy Sigrist, Mar 01 2025
2025-03-03T09:33:19
oeisdata/seq/A381/A381611.seq
8789cae2ae92677cf0a81450157c9c18
A381612
Irregular triangle read by rows: T(n,k) for n-1 <= k <= A328378(n) is the number of permutations of length n having a sum of differences equal to k.
[ "2", "2", "4", "2", "4", "12", "4", "2", "2", "4", "14", "32", "18", "28", "14", "8", "2", "4", "16", "36", "92", "68", "128", "92", "122", "72", "64", "16", "8", "2", "4", "18", "40", "112", "240", "256", "448", "438", "668", "502", "696", "480", "496", "264", "240", "88", "48", "2", "4", "20", "44", "134", "288", "696", "776", "1566", "1620", "2788", "2524", "3914", "3192", "4544", "3376", "4056", "2720", "2960", "1776", "1712", "816", "576", "144", "72" ]
[ "nonn", "tabf" ]
22
2
1
[ "A000982", "A328378", "A381612" ]
null
Norman Whitehead, Mar 01 2025
2025-03-25T19:55:03
oeisdata/seq/A381/A381612.seq
145d95a5e96994d0df6c0a1ce0f91a0c
A381613
If n = Product (p_j^k_j) then a(n) = Product (min(p_j, k_j)), with a(1) = 1.
[ "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "2", "1", "3", "2", "1", "1", "1", "2", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "2", "2", "1", "2", "1", "3", "1", "2", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "1", "1", "4", "1", "1", "2", "2", "1", "1", "1", "2", "3", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1" ]
[ "nonn", "mult", "easy" ]
20
1
4
[ "A008473", "A008477", "A035306", "A323308", "A369008", "A381588", "A381613", "A381614" ]
null
Paolo Xausa, Mar 01 2025
2025-03-07T02:55:43
oeisdata/seq/A381/A381613.seq
597f2bf5cdad78e8b1f9f82c5e6302d5
A381614
If n = Product (p_j^k_j) then a(n) = Product (max(p_j, k_j)), with a(1) = 1.
[ "1", "2", "3", "2", "5", "6", "7", "3", "3", "10", "11", "6", "13", "14", "15", "4", "17", "6", "19", "10", "21", "22", "23", "9", "5", "26", "3", "14", "29", "30", "31", "5", "33", "34", "35", "6", "37", "38", "39", "15", "41", "42", "43", "22", "15", "46", "47", "12", "7", "10", "51", "26", "53", "6", "55", "21", "57", "58", "59", "30", "61", "62", "21", "6", "65", "66", "67", "34", "69", "70", "71", "9", "73" ]
[ "nonn", "mult", "easy" ]
19
1
2
[ "A008473", "A008477", "A035306", "A065463", "A369008", "A381588", "A381613", "A381614" ]
null
Paolo Xausa, Mar 01 2025
2025-03-07T02:55:40
oeisdata/seq/A381/A381614.seq
92ffaaf6a773a0503c1e479d3f3cb712
A381615
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^3)^3).
[ "1", "1", "4", "31", "320", "3969", "56080", "876204", "14860614", "270231265", "5223002719", "106613106181", "2287120272173", "51367948203527", "1204141944566399", "29385603693050274", "744943334951904519", "19580887642660810193", "532781828387893449124", "14984377196395037979472" ]
[ "nonn" ]
12
0
3
[ "A088714", "A120973", "A212029", "A381029", "A381574", "A381601", "A381615" ]
null
Seiichi Manyama, Mar 01 2025
2025-03-01T22:48:10
oeisdata/seq/A381/A381615.seq
2b207b39f38c6d0af07d77346b4f5b14
A381616
a(n) is the smallest prime that starts the first occurrence of exactly n consecutive primes in A381019.
[ "7643", "31", "3517", "1049", "2", "41", "173", "401", "523", "113", "337", "449", "6599", "251", "1993", "2543", "743", "593", "1481", "1301", "1069", "2357", "17657", "4079", "2797", "8219", "64123", "81299", "19289", "40129", "6709", "13999", "4271", "1669", "37579", "28793", "38039", "12413", "125711", "24907", "3181", "41597", "27253" ]
[ "nonn" ]
10
1
1
[ "A381019", "A381117", "A381616" ]
null
Gonzalo Martínez, Mar 01 2025
2025-03-03T13:28:48
oeisdata/seq/A381/A381616.seq
23e6a9fe3a27dc52045c8ec41815309e
A381617
A sequence constructed so that the probability of occurrence of integer i > 0 matches the zeta distribution for parameter value 2, 1/(zeta(2)*i^2).
[ "1", "2", "1", "1", "3", "1", "4", "1", "1", "2", "1", "1", "5", "1", "2", "1", "1", "6", "1", "3", "1", "1", "2", "1", "7", "1", "1", "8", "1", "2", "1", "1", "4", "1", "3", "1", "2", "1", "1", "1", "9", "1", "2", "1", "1", "10", "1", "2", "1", "1", "3", "1", "5", "1", "1", "2", "1", "11", "1", "1", "4", "1", "2", "1", "1", "3", "1", "1", "2", "1", "12", "1", "1", "13", "1", "2", "1", "1", "3", "1", "6", "1", "2", "1", "1", "1", "4", "1", "2", "1", "1", "14" ]
[ "nonn" ]
25
1
2
[ "A241773", "A381522", "A381617" ]
null
Jwalin Bhatt, Mar 10 2025
2025-03-25T22:36:22
oeisdata/seq/A381/A381617.seq
997c0ee04dc1b0bd78bad83ab0a6160f
A381618
Reverse the Chung-Graham representation of n while preserving its trailing zeros: a(n) = A381607(A263273(A381608(n))).
[ "0", "1", "2", "3", "4", "7", "6", "5", "8", "9", "17", "11", "12", "20", "19", "15", "16", "10", "18", "14", "13", "21", "22", "43", "24", "30", "51", "45", "38", "29", "25", "46", "32", "33", "54", "53", "41", "50", "28", "49", "40", "36", "42", "23", "44", "27", "31", "52", "48", "39", "37", "26", "47", "35", "34", "55", "56", "111", "58", "77", "132", "113", "98", "63", "64", "119", "79" ]
[ "nonn", "base" ]
8
0
3
[ "A000045", "A263273", "A345201", "A381579", "A381607", "A381608", "A381618" ]
null
Rémy Sigrist, Mar 02 2025
2025-03-03T09:33:24
oeisdata/seq/A381/A381618.seq
9ddb9520d8bd6dac07d0d28ed735f125
A381619
Sorted list of sums of 3 prices in minor currency units for a currency that has a 2-decimal minor unit, such that the riddle "sum of prices equals product of prices" has a solution, with prices expressed as floating point numbers with 2 decimals.
[ "525", "540", "546", "549", "555", "561", "567", "570", "585", "588", "600", "612", "630", "642", "660", "660", "663", "675", "726", "735", "744", "750", "759", "765", "783", "792", "798", "810", "819", "825", "840", "840", "891", "897", "900", "930", "945", "957", "966", "966", "975", "981", "996", "1050", "1050", "1071", "1080", "1092", "1125", "1134", "1155", "1155", "1170" ]
[ "nonn", "base", "fini", "full" ]
12
1
1
[ "A380887", "A381187", "A381619" ]
null
Hugo Pfoertner and Markus Sigg, Mar 02 2025
2025-03-04T07:33:30
oeisdata/seq/A381/A381619.seq
484109753791535c22daef9ab2942ba0
A381620
a(n) is the number of solutions to the problem described in A381619 with smallest price equal to n.
[ "50", "50", "12", "30", "25", "26", "8", "30", "9", "25", "5", "15", "2", "4", "13", "5", "2", "8", "3", "30", "3", "3", "1", "8", "25", "4", "1", "4", "2", "12", "0", "10", "2", "1", "5", "5", "0", "1", "0", "15", "2", "4", "1", "3", "8", "2", "1", "2", "0", "15", "1", "2", "0", "1", "2", "2", "0", "1", "1", "15", "1", "0", "2", "0", "3", "3", "1", "2", "2", "5", "1", "6", "1", "2", "9", "3", "1", "0", "0", "5", "1", "4" ]
[ "nonn", "fini", "full" ]
6
1
1
[ "A380887", "A381187", "A381619", "A381620" ]
null
Hugo Pfoertner, Mar 12 2025
2025-03-12T11:02:30
oeisdata/seq/A381/A381620.seq
613f316af9cf3b5d42b76cbe1e316d71
A381621
Sorted list of sums of 4 prices in minor currency units for a currency that has a 2-decimal minor unit, such that the riddle "sum of prices equals product of prices" has a solution, with prices expressed as floating point numbers with 2 decimals.
[ "644", "651", "660", "663", "665", "672", "675", "675", "678", "680", "684", "684", "686", "689", "693", "693", "702", "705", "707", "707", "708", "711", "713", "714", "714", "720", "720", "720", "725", "726", "728", "728", "729", "735", "735", "735", "737", "747", "750", "752", "756", "756", "756", "756", "762", "765", "765", "765", "765", "767", "770", "770", "774", "774", "774", "777" ]
[ "nonn", "base", "fini" ]
17
1
1
[ "A380887", "A381187", "A381619", "A381621", "A382508" ]
null
Hugo Pfoertner, Mar 04 2025
2025-03-31T15:38:17
oeisdata/seq/A381/A381621.seq
c66e95df2031a2d8ab4f072e95c20832
A381622
Triangle T(n,k) read by rows, where row n is a permutation of the numbers 1 through n, such that if a deck of n cards is prepared in this order, and down-under-under dealing is used, then the resulting cards will be dealt in increasing order.
[ "1", "1", "2", "1", "2", "3", "1", "3", "4", "2", "1", "5", "3", "2", "4", "1", "3", "5", "2", "6", "4", "1", "7", "5", "2", "4", "6", "3", "1", "7", "4", "2", "8", "6", "3", "5", "1", "4", "6", "2", "8", "5", "3", "9", "7", "1", "10", "8", "2", "5", "7", "3", "9", "6", "4", "1", "7", "5", "2", "11", "9", "3", "6", "8", "4", "10", "1", "5", "11", "2", "8", "6", "3", "12", "10", "4", "7", "9", "1", "8", "10", "2", "6", "12", "3", "9", "7", "4", "13", "11", "5" ]
[ "nonn", "tabl" ]
10
1
3
[ "A006257", "A016777", "A054995", "A225381", "A321298", "A378635", "A381622", "A381623" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025
2025-04-05T23:25:07
oeisdata/seq/A381/A381622.seq
7847559d2cb87b042f810f06ed7e227a
A381623
Triangle read by rows: T(n,k) is the number of the k-th eliminated person in the variation of the Josephus elimination process for n people, where the first person is eliminated, then two people are skipped, and then the process repeats.
[ "1", "1", "2", "1", "2", "3", "1", "4", "2", "3", "1", "4", "3", "5", "2", "1", "4", "2", "6", "3", "5", "1", "4", "7", "5", "3", "6", "2", "1", "4", "7", "3", "8", "6", "2", "5", "1", "4", "7", "2", "6", "3", "9", "5", "8", "1", "4", "7", "10", "5", "9", "6", "3", "8", "2", "1", "4", "7", "10", "3", "8", "2", "9", "6", "11", "5", "1", "4", "7", "10", "2", "6", "11", "5", "12", "9", "3", "8", "1", "4", "7", "10", "13", "5", "9", "2", "8", "3", "12", "6", "11" ]
[ "nonn", "tabl" ]
15
1
3
[ "A006257", "A016777", "A054995", "A225381", "A321298", "A378635", "A381622", "A381623" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025
2025-04-05T23:40:31
oeisdata/seq/A381/A381623.seq
8c159445399f81574c6584f3991fd2ec
A381624
For any nonnegative integer n with ternary expansion Sum_{k >= 0} t_k * 3^k, a(n) = Sum_{k >= 0} t_k * (2^(k+1) - 1).
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "7", "8", "9", "10", "11", "12", "13", "14", "15", "14", "15", "16", "17", "18", "19", "20", "21", "22", "15", "16", "17", "18", "19", "20", "21", "22", "23", "22", "23", "24", "25", "26", "27", "28", "29", "30", "29", "30", "31", "32", "33", "34", "35", "36", "37", "30", "31", "32", "33", "34", "35", "36", "37", "38", "37", "38", "39", "40", "41" ]
[ "nonn", "base", "easy" ]
7
0
3
[ "A354047", "A381624", "A381625" ]
null
Rémy Sigrist, Mar 02 2025
2025-03-03T09:33:27
oeisdata/seq/A381/A381624.seq
f8db877be5e81586f2f87f9f5920f77e
A381625
a(n) is the number of occurrences of n in A381624.
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "3", "2", "2", "2", "2", "2", "2", "3", "2", "1", "1", "1", "1", "1", "2", "3", "3", "3", "3", "3", "3", "3", "4", "4", "3", "2", "2", "2", "2", "3", "4", "4", "3", "3", "3", "3", "3", "3", "3", "2", "1", "1", "1", "1", "1", "2", "3", "3", "4", "4", "4", "4", "4", "5", "5", "5", "4", "3", "3", "3", "4", "5", "6", "6", "5", "5", "5", "5", "5", "5", "5", "3" ]
[ "nonn", "base" ]
6
0
8
[ "A169683", "A381624", "A381625" ]
null
Rémy Sigrist, Mar 02 2025
2025-03-03T09:33:31
oeisdata/seq/A381/A381625.seq
3833d4eb15a08626bd3b504dade75ec6
A381626
Number of horizontal plane Brown's diagonal Latin squares of order 2n.
[ "0", "48", "92160", "1981808640", "1735113100492800" ]
[ "nonn", "more", "hard" ]
10
1
2
[ "A292516", "A339641", "A340186", "A379145", "A381626" ]
null
Eduard I. Vatutin, Mar 02 2025
2025-04-09T07:45:57
oeisdata/seq/A381/A381626.seq
9e8df533d150709614af64bcf21413db
A381627
Irregular table T(n, k), n >= 0, k = 1..A381625(n): the n-th row lists the numbers m such that A381624(m) = n.
[ "0", "1", "2", "3", "4", "5", "6", "7", "9", "8", "10", "11", "12", "13", "14", "15", "16", "18", "17", "19", "27", "20", "28", "21", "29", "22", "30", "23", "31", "24", "32", "25", "33", "26", "34", "36", "35", "37", "38", "39", "40", "41", "42", "43", "45", "44", "46", "54", "47", "55", "81", "48", "56", "82", "49", "57", "83", "50", "58", "84", "51", "59", "85", "52", "60", "86", "53", "61", "63", "87" ]
[ "nonn", "base", "tabf" ]
8
0
3
[ "A381624", "A381625", "A381627", "A381628" ]
null
Rémy Sigrist, Mar 02 2025
2025-03-03T09:33:35
oeisdata/seq/A381/A381627.seq
78e4d0147f127bd7b8ea354d2115c62e
A381628
Inverse permutation to A381627.
[ "0", "1", "2", "3", "4", "5", "6", "7", "9", "8", "10", "11", "12", "13", "14", "15", "16", "18", "17", "19", "21", "23", "25", "27", "29", "31", "33", "20", "22", "24", "26", "28", "30", "32", "34", "36", "35", "37", "38", "39", "40", "41", "42", "43", "45", "44", "46", "48", "51", "54", "57", "60", "63", "66", "47", "49", "52", "55", "58", "61", "64", "67", "70", "68", "71", "74", "77", "79" ]
[ "nonn", "base" ]
7
0
3
[ "A381627", "A381628" ]
null
Rémy Sigrist, Mar 02 2025
2025-03-03T09:33:39
oeisdata/seq/A381/A381628.seq
c1b400d90d2b398ce3d9ab5653f0beae
A381629
Lexicographically earliest sequence of positive integers such that no subsequence of terms at indices in arithmetic progression form an arithmetic progression in any order.
[ "1", "1", "2", "1", "1", "2", "2", "4", "4", "1", "1", "2", "1", "1", "2", "2", "4", "4", "2", "4", "4", "5", "5", "8", "5", "5", "9", "9", "4", "2", "5", "11", "2", "2", "4", "1", "1", "5", "1", "1", "10", "2", "2", "4", "1", "1", "4", "4", "10", "10", "4", "10", "10", "12", "2", "4", "1", "2", "5", "4", "5", "10", "4", "2", "8", "2", "10", "5", "5", "10", "5", "13", "12", "13", "2", "5", "10", "5", "10", "10", "13", "5" ]
[ "nonn" ]
34
1
3
[ "A361933", "A381629" ]
null
Neal Gersh Tolunsky, Mar 29 2025
2025-03-31T11:56:54
oeisdata/seq/A381/A381629.seq
4b4b35b70a79244a74750df8ff38e136