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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
A379602
a(n) is the least n-digit number whose square contains only digits greater than 5.
[ "3", "26", "264", "3114", "25824", "260167", "2639867", "25845676", "260147437", "2582245083", "25843178924", "258241744863", "2582010592114", "25825761924437", "258218875510676", "2581990857627114", "25820083014911063", "258199298347206526", "2581988959445543367", "25819892911624938937", "258198891881411585714" ]
[ "nonn", "base" ]
18
1
1
[ "A053972", "A053974", "A058471", "A164772", "A164773", "A164778", "A164841", "A291631", "A379602", "A379603" ]
null
Zhining Yang, Dec 27 2024
2025-01-11T19:14:43
oeisdata/seq/A379/A379602.seq
14ad68363470d7c4a1c6c0378111f2d9
A379603
a(n) is the largest n-digit number whose square contains only digits greater than 5.
[ "3", "83", "937", "9833", "98336", "998333", "9994833", "99983333", "999939437", "9999833333", "99998333336", "999998333333", "9999983333336", "99999983333333", "999999833333336", "9999999833333333", "99999998333333336", "999999998333333333", "9999999983333333336", "99999999983333333333", "999999999833333333336" ]
[ "nonn", "base" ]
29
1
1
[ "A053972", "A053974", "A058471", "A164772", "A164773", "A164778", "A164841", "A291631", "A379602", "A379603" ]
null
Zhining Yang, Dec 27 2024
2025-01-11T19:18:37
oeisdata/seq/A379/A379603.seq
3c94b650227b0e2cb73aead50b48f162
A379604
a(n) is the maximum number of items in a bucket for the bucket sort algorithm with input {0, 1, ..., n-1} and B = floor(sqrt(n)) buckets.
[ "1", "2", "3", "2", "3", "3", "4", "4", "3", "4", "4", "4", "5", "5", "5", "4", "5", "5", "5", "5", "6", "6", "6", "6", "5", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "6", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "7", "8", "8", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "9", "9", "8", "9", "9", "9", "9", "9", "9", "9", "9", "10", "10", "10", "10", "10", "10", "10", "10", "9", "10", "10", "10" ]
[ "nonn", "easy" ]
31
1
2
[ "A000196", "A006446", "A379604" ]
null
Darío Clavijo, Dec 28 2024
2025-02-03T21:26:55
oeisdata/seq/A379/A379604.seq
9c8dd03fcac5c0292c379ab6756a0fe1
A379605
Decimal expansion of sigma_sup = sup{real(s): Psi(s) = 0}, where Psi(s) = Sum_{n>=1} 1/n!^s.
[ "7", "2", "6", "3", "4", "7", "5", "0", "8", "5", "7", "6", "2", "0", "1", "1", "4", "5", "9", "4", "1", "6", "4", "0", "2", "6", "2", "2", "6", "9", "5", "2", "3", "2", "5", "0", "8", "5", "0", "1", "3", "4", "3", "3", "4", "3", "0", "0", "6", "4", "1", "2", "7", "8", "1", "8", "4", "6", "8", "3", "6", "3", "4", "1", "2", "6", "5", "6", "2", "9", "9", "1", "7", "8", "3", "2", "3", "2", "9", "9", "1", "1", "9", "3", "4", "0", "8", "9", "2", "3", "5", "9", "0", "6", "4", "4", "6", "9", "8", "3" ]
[ "nonn", "cons" ]
10
0
1
[ "A373204", "A379605" ]
null
Roberto Trocchi, Dec 27 2024
2024-12-30T09:18:02
oeisdata/seq/A379/A379605.seq
33f0839bf4107f6333ddc0ac9c83f1d7
A379606
S = (A-sin(A))/2 gives the area of a segment of the unit circle in terms of the arc length A (<= Pi). Expressing A in terms of S we get A = Sum_{n>=0} b^(2n+1)*c(n) where b = (12*S)^(1/3). Sequence gives numerators of c(n).
[ "1", "1", "1", "1", "43", "1213", "151439", "33227", "16542537833", "887278009", "15233801224559", "9597171184603", "1374085664813273149", "1593410154419351", "53299328587804322691259", "1065024810026227256263721", "11374760871959174491194191", "70563256104582737796094772987", "657272463951301325116190773432261" ]
[ "nonn", "frac" ]
25
0
5
[ "A379606", "A379607" ]
null
Robert B Fowler, Dec 27 2024
2025-01-15T10:10:19
oeisdata/seq/A379/A379606.seq
c326f430865492d5c67b4c1c40989102
A379607
Denominators corresponding to A379606.
[ "1", "60", "1400", "25200", "17248000", "7207200000", "12713500800000", "38118080000000", "252957982717440000000", "177399104762880000000", "39217856135377920000000000", "314173814535060480000000000", "566078379029271972864000000000000", "8188688361066909696000000000000", "3391339339748110516021960704000000000000" ]
[ "nonn", "frac" ]
17
0
2
[ "A379606", "A379607" ]
null
Robert B Fowler, Dec 27 2024
2025-01-14T16:33:44
oeisdata/seq/A379/A379607.seq
0ea406a06120157f866a2e7381cb1c5d
A379608
Number of unlabeled Riordan posets with n elements.
[ "1", "2", "5", "11", "33", "74", "144", "232" ]
[ "nonn", "more" ]
6
1
2
[ "A000112", "A000608", "A349401", "A379608" ]
null
Salah Uddin Mohammad, Dec 27 2024
2025-01-11T19:13:34
oeisdata/seq/A379/A379608.seq
cfca657ba73a053ea14da239bc572e35
A379609
Triples (x,y,z) such that T(x)*T(y) = T(z) with 2 <= x <= y, where T(n) is the n-th triangular number, sorted first by values of z, then by values of x.
[ "3", "3", "8", "2", "5", "9", "4", "6", "20", "2", "20", "35", "3", "14", "35", "4", "12", "39", "5", "11", "44", "7", "10", "55", "5", "19", "75", "3", "34", "84", "9", "13", "90", "6", "21", "98", "2", "76", "132", "6", "33", "153", "4", "55", "175", "14", "18", "189", "13", "20", "195", "12", "23", "207", "15", "20", "224", "14", "22", "230", "11", "28", "231", "12", "29", "260", "7", "51", "272", "10", "38", "285", "11", "36", "296", "5", "90", "350", "3", "143", "351", "10", "50", "374", "7", "75", "399", "9", "68", "459", "19", "34", "475" ]
[ "nonn", "tabf" ]
32
1
1
[ "A000217", "A188630", "A198453", "A225390", "A379609" ]
null
Kelvin Voskuijl, Dec 27 2024
2025-01-17T19:37:07
oeisdata/seq/A379/A379609.seq
66848cee2b0c06f85fc6853b658506c5
A379610
a(n) = Sum_{j=0..n} binomial(2*j,j)^4 * binomial(n,j)^2 * Sum_{k=0..n} binomial(k+j,k-j)^2 * binomial(2*j,n-k) * binomial(2*j,k-j).
[ "1", "16", "2576", "1383568", "873960976", "615833930816", "526152430612496", "502263183380000576", "507670642053018634768", "542989589742114444434176", "609997002301177503142835776", "710665335270156912049219940096", "853208134042451055649274133396496", "1051685299255545900736463773134099328" ]
[ "nonn" ]
7
0
2
[ "A092815", "A094424", "A379610" ]
null
Seiichi Manyama, Dec 27 2024
2025-02-16T08:34:07
oeisdata/seq/A379/A379610.seq
c35becfd0d56fd71c32f223b553f2667
A379611
Table read by rows: T(n, k) = (n + 1)^(n - 1) - (k - 1)*(n + 1)^(n - 2), by convention T(1, 0) = 1.
[ "2", "1", "1", "4", "3", "2", "20", "16", "12", "8", "150", "125", "100", "75", "50", "1512", "1296", "1080", "864", "648", "432", "19208", "16807", "14406", "12005", "9604", "7203", "4802", "294912", "262144", "229376", "196608", "163840", "131072", "98304", "65536", "5314410", "4782969", "4251528", "3720087", "3188646", "2657205", "2125764", "1594323", "1062882" ]
[ "nonn", "tabl" ]
13
0
1
[ "A007334", "A374756", "A375616", "A379611", "A379612", "A379613" ]
null
Peter Luschny, Dec 27 2024
2024-12-28T10:21:49
oeisdata/seq/A379/A379611.seq
6e670e174e369be356e80ecace12d8ff
A379612
a(n) = (n + 1)^(n - 1) + (n + 1)^(n - 2), by convention a(1) = 1.
[ "2", "1", "4", "20", "150", "1512", "19208", "294912", "5314410", "110000000", "2572306572", "67077144576", "1930018885886", "60743477544960", "2075941406250000", "76561193665298432", "3030800878069216722", "128186171713071710208", "5768828271352423353620", "275251200000000000000000", "13879377432727741655370342" ]
[ "nonn" ]
12
0
1
[ "A379611", "A379612" ]
null
Peter Luschny, Dec 27 2024
2025-03-19T09:03:21
oeisdata/seq/A379/A379612.seq
fa5d944f85301dd5e70befff2c7bf41d
A379613
a(n) = n^(n - 1) - 2*(n + 1)^(n - 2), by convention a(0) = 0.
[ "0", "0", "0", "1", "14", "193", "2974", "52113", "1034270", "23046721", "571282238", "15617863897", "467291386990", "15198954783153", "534222097472894", "20185726770649633", "816165851488045118", "35167910642711951617", "1609028732603454196606", "77912950297911241532841", "3981118415206568940420878" ]
[ "nonn" ]
18
0
5
[ "A000169", "A007334", "A374756", "A379611", "A379613" ]
null
Peter Luschny, Dec 27 2024
2025-03-19T09:03:27
oeisdata/seq/A379/A379613.seq
4cd14d6970102f28b570c91357c2cb22
A379614
a(n) = Sum_{k=0..n} 2^((n + k - 1)*(n - k)/2) * n! / (n - k)!. Row sums of A365638.
[ "1", "2", "8", "62", "920", "26104", "1420496", "148881328", "30184791424", "11884978702720", "9119462417850112", "13676896785924429056", "40193177909606893812736", "231954028321633491248270336", "2633539132301114752459257620480", "58919202504421532088999537276311552", "2601059501207939343360641860628003520512" ]
[ "nonn" ]
17
0
2
[ "A365638", "A379614", "A382240" ]
null
Peter Luschny, Dec 31 2024
2025-03-19T13:57:58
oeisdata/seq/A379/A379614.seq
47f3c30ab14cfa27a92f6a131a0ef7fa
A379615
Numerators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
[ "1", "4", "19", "107", "39", "61", "259", "89", "93", "857", "887", "181", "1303", "331", "1345", "4091", "4175", "21127", "4301", "21757", "87973", "88813", "90073", "90577", "1192621", "1201981", "1211809", "1221637", "1234741", "1240201", "626243", "89909", "45247", "15169", "30533", "153601", "2941819", "2956639", "20807623", "20876783" ]
[ "nonn", "easy", "frac" ]
8
1
2
[ "A188999", "A307159", "A370904", "A379615", "A379616", "A379617" ]
null
Amiram Eldar, Dec 27 2024
2024-12-28T09:11:16
oeisdata/seq/A379/A379615.seq
54eea456a412b0cd36b725901ef73743
A379616
Denominators of the partial sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
[ "1", "3", "12", "60", "20", "30", "120", "40", "40", "360", "360", "72", "504", "126", "504", "1512", "1512", "7560", "1512", "7560", "30240", "30240", "30240", "30240", "393120", "393120", "393120", "393120", "393120", "393120", "196560", "28080", "14040", "4680", "9360", "46800", "889200", "889200", "6224400", "6224400", "889200", "1778400" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A188999", "A307159", "A370904", "A379615", "A379616", "A379618" ]
null
Amiram Eldar, Dec 27 2024
2024-12-28T09:11:30
oeisdata/seq/A379/A379616.seq
2fde852c3df971902f7f15a018a44a10
A379617
Numerators of the partial alternating sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
[ "1", "2", "11", "43", "53", "4", "37", "103", "23", "65", "71", "337", "2539", "1217", "2539", "7337", "7757", "1501", "7883", "7631", "31469", "30629", "31889", "6277", "84625", "82753", "423593", "82753", "426869", "421409", "216847", "213727", "108911", "11899", "24253", "119081", "2317139", "760853", "773203", "6889667", "7037867", "13946059" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A188999", "A307159", "A370904", "A379615", "A379617", "A379618" ]
null
Amiram Eldar, Dec 27 2024
2024-12-28T09:10:55
oeisdata/seq/A379/A379617.seq
53b4b309b478f1c7dd442701be88e1e1
A379618
Denominators of the partial alternating sums of the reciprocals of the sum of bi-unitary divisors function (A188999).
[ "1", "3", "12", "60", "60", "5", "40", "120", "24", "72", "72", "360", "2520", "1260", "2520", "7560", "7560", "1512", "7560", "7560", "30240", "30240", "30240", "6048", "78624", "78624", "393120", "78624", "393120", "393120", "196560", "196560", "98280", "10920", "21840", "109200", "2074800", "691600", "691600", "6224400", "6224400", "12448800" ]
[ "nonn", "easy", "frac" ]
7
1
2
[ "A188999", "A307159", "A370904", "A379616", "A379617", "A379618" ]
null
Amiram Eldar, Dec 27 2024
2024-12-28T09:10:39
oeisdata/seq/A379/A379618.seq
3ee6ea8e1f5d0ec2178f55844a362eb3
A379619
Numerators of the partial sums of the reciprocals of the alternating sum of divisors function (A206369).
[ "1", "2", "5", "17", "37", "43", "15", "79", "573", "152", "311", "484", "657", "2041", "4187", "46897", "94949", "97589", "295847", "300467", "305087", "310631", "313151", "63739", "9181", "9313", "46961", "47401", "333787", "340717", "68513", "9863", "49711", "25103", "6317", "44549", "89483", "90253", "181661", "183047", "9187", "18605", "18671" ]
[ "nonn", "easy", "frac" ]
11
1
2
[ "A206369", "A370905", "A370906", "A379619", "A379620", "A379621" ]
null
Amiram Eldar, Dec 27 2024
2025-01-08T11:41:45
oeisdata/seq/A379/A379619.seq
c3a4a0c6b63dc85aba54229e8385fba0
A379620
Denominators of the partial sums of the reciprocals of the alternating sum of divisors function (A206369).
[ "1", "1", "2", "6", "12", "12", "4", "20", "140", "35", "70", "105", "140", "420", "840", "9240", "18480", "18480", "55440", "55440", "55440", "55440", "55440", "11088", "1584", "1584", "7920", "7920", "55440", "55440", "11088", "1584", "7920", "3960", "990", "6930", "13860", "13860", "27720", "27720", "1386", "2772", "2772", "13860", "3465", "6930", "79695" ]
[ "nonn", "easy", "frac" ]
9
1
3
[ "A206369", "A370905", "A370906", "A379619", "A379620", "A379622" ]
null
Amiram Eldar, Dec 27 2024
2025-01-08T11:41:53
oeisdata/seq/A379/A379620.seq
b8ba9d0678c21ae3c27740b2a833e39f
A379621
Numerators of the partial alternating sums of the reciprocals of the alternating sum of divisors function (A206369).
[ "1", "0", "1", "1", "5", "-1", "1", "-7", "11", "-47", "-13", "-61", "-29", "-157", "-209", "-3139", "-5123", "-1109", "-2887", "-3547", "-2887", "-3679", "-3319", "-4111", "-26137", "-30757", "-5597", "-2071", "-277", "-343", "-1627", "-12269", "-2269", "-625", "-391", "-1261", "-3629", "-3937", "-1853", "-4979", "-19223", "-21533", "-20873", "-21797" ]
[ "sign", "easy", "frac" ]
9
1
5
[ "A206369", "A370905", "A370906", "A379619", "A379621", "A379622" ]
null
Amiram Eldar, Dec 27 2024
2024-12-28T09:08:59
oeisdata/seq/A379/A379621.seq
6d7258a7260fa391ad86f2d487d591f3
A379622
Denominators of the partial alternating sums of the reciprocals of the alternating sum of divisors function (A206369).
[ "1", "1", "2", "6", "12", "12", "12", "60", "420", "210", "105", "210", "140", "420", "840", "9240", "18480", "2640", "7920", "7920", "7920", "7920", "7920", "7920", "55440", "55440", "11088", "3696", "528", "528", "2640", "18480", "3696", "924", "616", "1848", "5544", "5544", "2772", "6930", "27720", "27720", "27720", "27720", "27720", "27720", "637560" ]
[ "nonn", "easy", "frac" ]
8
1
3
[ "A206369", "A370905", "A370906", "A379620", "A379621", "A379622" ]
null
Amiram Eldar, Dec 27 2024
2024-12-28T09:09:19
oeisdata/seq/A379/A379622.seq
c23a8e2bb8686e1f0c87d6509941c4dc
A379623
Irregular triangle read by rows: T(n,k) is the number of free polyominoes with n cells and width k, n >= 1, 1 <= k <= ceiling(n/2).
[ "1", "1", "1", "1", "1", "4", "1", "5", "6", "1", "12", "22", "1", "18", "71", "18", "1", "37", "193", "138", "1", "60", "490", "661", "73", "1", "117", "1221", "2547", "769", "1", "200", "3011", "8417", "5189", "255", "1", "379", "7393", "26164", "25920", "3743", "1", "669", "18025", "78074", "108834", "32038", "950", "1", "1250", "43847", "229881", "408217", "201956", "16819" ]
[ "nonn", "tabf" ]
47
1
6
[ "A000105", "A057051", "A110654", "A352720", "A379623", "A379624", "A379627", "A379628" ]
null
Omar E. Pol, Jan 07 2025
2025-02-17T22:37:09
oeisdata/seq/A379/A379623.seq
6f876eeca85632c7daf526cacb563b44
A379624
Triangle read by rows: T(n,k) is the number of free polyominoes with n cells and length k, n >= 1, k = 1..n.
[ "1", "0", "1", "0", "1", "1", "0", "1", "3", "1", "0", "0", "8", "3", "1", "0", "0", "8", "21", "5", "1", "0", "0", "7", "59", "36", "5", "1", "0", "0", "3", "137", "167", "54", "7", "1", "0", "0", "1", "223", "669", "307", "77", "7", "1", "0", "0", "0", "287", "2089", "1627", "539", "103", "9", "1", "0", "0", "0", "255", "5472", "7126", "3237", "839", "134", "9", "1", "0", "0", "0", "169", "11919", "27504", "16706", "5851", "1271", "168", "11", "1" ]
[ "nonn", "tabl" ]
53
1
9
[ "A000007", "A000012", "A000105", "A109613", "A379623", "A379624", "A379627", "A379628" ]
null
Omar E. Pol, Jan 07 2025
2025-02-17T22:37:18
oeisdata/seq/A379/A379624.seq
fc3002cf28de2d882864874b28256662
A379625
Triangle read by rows: T(n,k) is the number of free polyominoes with n cells whose difference between length and width is k, n >= 1, k >= 0.
[ "1", "0", "1", "1", "0", "1", "1", "3", "0", "1", "6", "2", "3", "0", "1", "7", "16", "6", "5", "0", "1", "25", "39", "27", "11", "5", "0", "1", "80", "120", "97", "45", "19", "7", "0", "1", "255", "425", "307", "191", "71", "28", "7", "0", "1", "795", "1565", "1077", "706", "347", "115", "40", "9", "0", "1", "2919", "5217", "4170", "2505", "1454", "574", "171", "53", "9", "0", "1", "10378", "18511", "15164", "10069", "5481", "2740", "919", "257", "69", "11", "0", "1" ]
[ "nonn", "tabl" ]
53
1
8
[ "A000004", "A000012", "A000105", "A109613", "A259087", "A259088", "A379623", "A379624", "A379625", "A379626", "A379627", "A379628", "A379629", "A379637", "A379638", "A380283", "A380284" ]
null
Omar E. Pol, Jan 12 2025
2025-02-17T22:37:14
oeisdata/seq/A379/A379625.seq
e630f51078fa7016d7c38238a375861d
A379626
Sum of the widths of the free polyominoes with n cells.
[ "1", "1", "3", "9", "29", "91", "322", "1206", "4600", "17931", "70577", "279652", "1110758", "4424120", "17647314", "70484576", "281750598", "1127181327" ]
[ "nonn", "more" ]
22
1
3
[ "A000105", "A379623", "A379625", "A379626", "A379627", "A379629", "A379637" ]
null
Omar E. Pol, Jan 16 2025
2025-02-16T13:54:19
oeisdata/seq/A379/A379626.seq
85f9484806e2f5f065a5df3bd7465f5d
A379627
Total area of the bounding boxes of the free polyominoes with n cells.
[ "1", "2", "7", "26", "95", "353", "1387", "5699", "23592", "99020", "415796", "1748722", "7336978", "30741661", "128510698", "536268877", "2233642396", "9288889882" ]
[ "nonn", "more" ]
39
1
2
[ "A000105", "A057766", "A379623", "A379624", "A379627", "A379628" ]
null
Omar E. Pol, Jan 07 2025
2025-02-16T17:19:31
oeisdata/seq/A379/A379627.seq
35f6bfab5102eed2d842667df3f2b03a
A379628
Total area between the free polyominoes with n cells and their bounding boxes.
[ "0", "0", "1", "6", "35", "143", "631", "2747", "12027", "52470", "227993", "985522", "4235295", "18114067", "77112058", "327000797", "1381807943", "5821692946" ]
[ "nonn", "more" ]
43
1
4
[ "A000105", "A057766", "A379623", "A379624", "A379627", "A379628" ]
null
Omar E. Pol, Jan 07 2025
2025-02-16T13:55:05
oeisdata/seq/A379/A379628.seq
55e6a95e8da16ed1117e8d5251ade1e2
A379629
Sum of the lengths of the free polyominoes with n cells.
[ "1", "2", "5", "15", "41", "139", "474", "1773", "6686", "26043", "101814", "402297", "1593124", "6332329", "25200575", "100462874", "400908688", "1601541747" ]
[ "nonn", "more" ]
27
1
2
[ "A000105", "A379624", "A379625", "A379626", "A379627", "A379629", "A379638" ]
null
Omar E. Pol, Jan 16 2025
2025-02-21T11:45:16
oeisdata/seq/A379/A379629.seq
287f68e8f79e49f7d66d761a061d825f
A379630
Irregular triangle read by rows in which row n lists the smallest parts of the partitions of n into consecutive parts followed by the conjugate corresponding odd divisors of n in accordance with the theorem of correspondence described in the Comments lines.
[ "1", "1", "2", "1", "3", "1", "3", "1", "4", "1", "5", "2", "5", "1", "6", "1", "3", "1", "7", "3", "7", "1", "8", "1", "9", "4", "2", "3", "9", "1", "10", "1", "5", "1", "11", "5", "11", "1", "12", "3", "3", "1", "13", "6", "13", "1", "14", "2", "7", "1", "15", "7", "4", "1", "5", "3", "15", "1", "16", "1", "17", "8", "17", "1", "18", "5", "3", "9", "3", "1", "19", "9", "19", "1", "20", "2", "5", "1", "21", "10", "6", "1", "7", "3", "21", "1", "22", "4", "11", "1", "23", "11", "23", "1", "24", "7", "3", "1" ]
[ "nonn", "tabf" ]
76
1
3
[ "A000012", "A000027", "A000593", "A001227", "A054844", "A182469", "A196020", "A204217", "A235791", "A236104", "A237048", "A237270", "A237271", "A237591", "A237593", "A245092", "A261697", "A261699", "A262626", "A286000", "A286001", "A286014", "A299765", "A341971", "A379630" ]
null
Omar E. Pol, Dec 28 2024
2024-12-30T17:02:30
oeisdata/seq/A379/A379630.seq
371d9e3ea461846584fddf8c4fd265fd
A379631
Irregular triangle read by rows: T(n,m), n >= 1, m >= 1, in which row n lists the largest parts of the partitions of n into consecutive parts followed by the conjugate corresponding odd divisors of n in accordance with the theorem described in A379630.
[ "1", "1", "2", "1", "3", "2", "3", "1", "4", "1", "5", "3", "5", "1", "6", "3", "3", "1", "7", "4", "7", "1", "8", "1", "9", "5", "4", "3", "9", "1", "10", "4", "5", "1", "11", "6", "11", "1", "12", "5", "3", "1", "13", "7", "13", "1", "14", "5", "7", "1", "15", "8", "6", "5", "5", "3", "15", "1", "16", "1", "17", "9", "17", "1", "18", "7", "6", "9", "3", "1", "19", "10", "19", "1", "20", "6", "5", "1", "21", "11", "8", "6", "7", "3", "21", "1", "22", "7", "11", "1", "23", "12", "23", "1", "24", "9", "3", "1" ]
[ "nonn", "tabf" ]
33
1
3
[ "A000012", "A000027", "A000593", "A001227", "A054844", "A182469", "A196020", "A204217", "A235791", "A236104", "A237048", "A237270", "A237271", "A237591", "A237593", "A245092", "A261697", "A261699", "A262626", "A286000", "A286015", "A299765", "A379630", "A379631", "A379632", "A379633", "A379634" ]
null
Omar E. Pol, Dec 30 2024
2025-01-07T10:51:53
oeisdata/seq/A379/A379631.seq
909578850536af467af09065e57b96d6
A379632
Irregular triangle read by rows in which row n lists the smallest parts of the partitions of n into consecutive parts (with the partitions ordered by increasing number of parts).
[ "1", "2", "3", "1", "4", "5", "2", "6", "1", "7", "3", "8", "9", "4", "2", "10", "1", "11", "5", "12", "3", "13", "6", "14", "2", "15", "7", "4", "1", "16", "17", "8", "18", "5", "3", "19", "9", "20", "2", "21", "10", "6", "1", "22", "4", "23", "11", "24", "7", "25", "12", "3", "26", "5", "27", "13", "8", "2", "28", "1", "29", "14", "30", "9", "6", "4", "31", "15", "32", "33", "16", "10", "3", "34", "7", "35", "17", "5", "2", "36", "11", "1", "37", "18", "38", "8", "39", "19", "12", "4", "40", "6", "41", "20" ]
[ "nonn", "tabf" ]
28
1
2
[ "A000027", "A001227", "A118235", "A196020", "A211343", "A235791", "A236104", "A237048", "A237591", "A237593", "A245092", "A262626", "A286001", "A286014", "A299765", "A341971", "A379630", "A379631", "A379632", "A379633", "A379634" ]
null
Omar E. Pol, Dec 31 2024
2025-01-07T10:12:31
oeisdata/seq/A379/A379632.seq
6e4cc23c15f633997722a95d579716b7
A379633
Irregular triangle read by rows in which row n lists the largest parts of the partitions of n into consecutive parts (with the partitions ordered by increasing number of parts).
[ "1", "2", "3", "2", "4", "5", "3", "6", "3", "7", "4", "8", "9", "5", "4", "10", "4", "11", "6", "12", "5", "13", "7", "14", "5", "15", "8", "6", "5", "16", "17", "9", "18", "7", "6", "19", "10", "20", "6", "21", "11", "8", "6", "22", "7", "23", "12", "24", "9", "25", "13", "7", "26", "8", "27", "14", "10", "7", "28", "7", "29", "15", "30", "11", "9", "8", "31", "16", "32", "33", "17", "12", "8", "34", "10", "35", "18", "9", "8", "36", "13", "8", "37", "19", "38", "11", "39", "20", "14", "9", "40", "10", "41", "21" ]
[ "nonn", "tabf" ]
23
1
2
[ "A000027", "A001227", "A196020", "A212652", "A235791", "A236104", "A237048", "A237591", "A237593", "A245092", "A262626", "A286000", "A286013", "A286015", "A299765", "A379630", "A379631", "A379632", "A379633", "A379634" ]
null
Omar E. Pol, Dec 31 2024
2025-01-07T10:13:40
oeisdata/seq/A379/A379633.seq
ba433c4fffb6e697c41a7853503c5b69
A379634
Irregular triangle read by rows in which row n lists the odd divisors of n ordered as the mirror of A261697.
[ "1", "1", "3", "1", "1", "5", "1", "3", "1", "7", "1", "1", "3", "9", "1", "5", "1", "11", "1", "3", "1", "13", "1", "7", "1", "5", "3", "15", "1", "1", "17", "1", "9", "3", "1", "19", "1", "5", "1", "7", "3", "21", "1", "11", "1", "23", "1", "3", "1", "5", "25", "1", "13", "1", "9", "3", "27", "1", "7", "1", "29", "1", "5", "15", "3", "1", "31", "1", "1", "11", "3", "33", "1", "17", "1", "7", "5", "35", "1", "9", "3", "1", "37", "1", "19", "1", "13", "3", "39", "1", "5", "1", "41", "1", "7", "21", "3", "1", "43", "1", "11", "1" ]
[ "nonn", "tabf" ]
34
1
3
[ "A000012", "A000593", "A001227", "A182469", "A196020", "A235791", "A236104", "A237048", "A237591", "A237593", "A261350", "A261697", "A261698", "A261699", "A379630", "A379631", "A379632", "A379633", "A379634" ]
null
Omar E. Pol, Dec 31 2024
2025-01-07T10:13:54
oeisdata/seq/A379/A379634.seq
435794d55d7ff97decd530e4cb6ee4ea
A379635
Triangle read by rows: T(n,k) = A000203(k)*A000203(n-k+1), n >= 1, k >= 1.
[ "1", "3", "3", "4", "9", "4", "7", "12", "12", "7", "6", "21", "16", "21", "6", "12", "18", "28", "28", "18", "12", "8", "36", "24", "49", "24", "36", "8", "15", "24", "48", "42", "42", "48", "24", "15", "13", "45", "32", "84", "36", "84", "32", "45", "13", "18", "39", "60", "56", "72", "72", "56", "60", "39", "18", "12", "54", "52", "105", "48", "144", "48", "105", "52", "54", "12", "28", "36", "72", "91", "90", "96", "96", "90", "91", "72", "36", "28" ]
[ "nonn", "tabl" ]
21
1
2
[ "A000203", "A000385", "A072861", "A221529", "A379635" ]
null
Omar E. Pol, Jan 14 2025
2025-01-15T22:44:30
oeisdata/seq/A379/A379635.seq
b3d1c3da1de043d8ddbebe5b1147001b
A379636
Triangle read by rows: T(n,k) (n >= k) is the maximum number of black cells in a n X k grid such that no black cell is edge-adjacent to more than one black cell.
[ "1", "2", "2", "2", "4", "5", "3", "4", "7", "8", "4", "6", "9", "11", "14", "4", "6", "10", "12", "16", "18", "5", "8", "12", "15", "19", "22", "26", "6", "8", "14", "16", "22", "24", "30", "32", "6", "10", "15", "19", "24", "28", "33", "38", "42", "7", "10", "17", "20", "27", "30", "37", "40", "47", "50", "8", "12", "19", "23", "30", "34", "41", "46", "52", "57", "63", "8", "12", "20", "24", "32" ]
[ "nonn", "tabl", "easy" ]
49
1
2
[ "A260090", "A379636" ]
null
Yifan Xie, Mar 12 2025
2025-03-15T12:28:53
oeisdata/seq/A379/A379636.seq
663adbba3e78a43ad1dc65bd506fae7d
A379637
Irregular triangle read by rows: T(n,k) is the sum of the widths of the free polyominoes with n cells and width k, n >= 1, 1 <= k <= ceiling(n/2).
[ "1", "1", "1", "2", "1", "8", "1", "10", "18", "1", "24", "66", "1", "36", "213", "72", "1", "74", "579", "552", "1", "120", "1470", "2644", "365", "1", "234", "3663", "10188", "3845", "1", "400", "9033", "33668", "25945", "1530", "1", "758", "22179", "104656", "129600", "22458", "1", "1338", "54075", "312296", "544170", "192228", "6650", "1", "2500", "131541", "919524", "2041085", "1211736", "117733" ]
[ "nonn", "tabf" ]
15
1
4
[ "A000105", "A110654", "A379623", "A379625", "A379626", "A379627", "A379637", "A379638" ]
null
Omar E. Pol, Jan 16 2025
2025-01-16T21:24:59
oeisdata/seq/A379/A379637.seq
69bbb8fbda9d2d8612f7708c796bad7f
A379638
Triangle read by rows: T(n,k) is the sum of the lengths of the free polyominoes with n cells and length k, n >= 1, k >= 1.
[ "1", "0", "2", "0", "2", "3", "0", "2", "9", "4", "0", "0", "24", "12", "5", "0", "0", "24", "84", "25", "6", "0", "0", "21", "236", "180", "30", "7", "0", "0", "9", "548", "835", "324", "49", "8", "0", "0", "3", "892", "3345", "1842", "539", "56", "9", "0", "0", "0", "1148", "10445", "9762", "3773", "824", "81", "10", "0", "0", "0", "1020", "27360", "42756", "22659", "6712", "1206", "90", "11", "0", "0", "0", "676", "59595", "165024", "116942", "46808", "11439", "1680", "121", "12" ]
[ "nonn", "tabl" ]
17
1
3
[ "A000105", "A379624", "A379625", "A379627", "A379629", "A379637", "A379638" ]
null
Omar E. Pol, Jan 16 2025
2025-01-16T21:25:07
oeisdata/seq/A379/A379638.seq
f32af632e5b4c721576c4da52853ec21
A379639
Smallest primitive prime factor of 6^n-1.
[ "5", "7", "43", "37", "311", "31", "55987", "1297", "19", "11", "23", "13", "3433", "29", "1171", "17", "239", "46441", "191", "241", "1822428931", "51828151", "47", "1678321", "18198701", "53", "163", "421", "7369130657357778596659", "1950271", "5333", "353", "67", "190537", "71", "73", "149", "1787", "3143401", "41", "8648131", "2527867231" ]
[ "nonn" ]
13
1
1
[ "A007138", "A112092", "A112927", "A143663", "A143665", "A252170", "A274907", "A379639", "A379640", "A379641", "A379642", "A379644" ]
null
Sean A. Irvine, Dec 28 2024
2025-02-27T11:05:45
oeisdata/seq/A379/A379639.seq
8f97271dce169a7200895dedc9b8a70d
A379640
Smallest primitive prime factor of 7^n-1.
[ "2", "1", "19", "5", "2801", "43", "29", "1201", "37", "11", "1123", "13", "16148168401", "113", "31", "17", "14009", "117307", "419", "281", "11898664849", "23", "47", "73", "2551", "53", "109", "13564461457", "59", "6568801", "311", "353", "3631", "29078814248401", "2127431041", "13841169553", "223", "351121", "486643", "41", "83", "51031" ]
[ "nonn" ]
11
1
1
[ "A007138", "A074249", "A112092", "A112927", "A143663", "A143665", "A252170", "A379639", "A379640", "A379641", "A379642", "A379644" ]
null
Sean A. Irvine, Dec 28 2024
2025-02-27T11:04:34
oeisdata/seq/A379/A379640.seq
e1949df7ec1bce047427c4de017d34b4
A379641
Smallest primitive prime factor of 8^n-1.
[ "7", "3", "73", "5", "31", "19", "127", "17", "262657", "11", "23", "37", "79", "43", "631", "97", "103", "87211", "32377", "41", "92737", "67", "47", "433", "601", "2731", "2593", "29", "233", "18837001", "2147483647", "193", "199", "307", "71", "246241", "223", "571", "937", "61681", "13367", "77158673929", "431", "397", "271", "139", "2351", "577" ]
[ "nonn" ]
11
1
1
[ "A007138", "A112092", "A112927", "A143663", "A143665", "A252170", "A274908", "A379639", "A379640", "A379641", "A379642", "A379644" ]
null
Sean A. Irvine, Dec 28 2024
2025-02-27T11:06:45
oeisdata/seq/A379/A379641.seq
49278fecf26a8a748ccd56c69c4d4073
A379642
Smallest primitive prime factor of 9^n-1.
[ "2", "5", "7", "41", "11", "73", "547", "17", "19", "1181", "23", "6481", "398581", "29", "31", "21523361", "103", "530713", "1597", "42521761", "43", "5501", "47", "97", "151", "53", "109", "430697", "59", "47763361", "683", "926510094425921", "25411", "956353", "71", "282429005041", "18427", "5301533", "79", "14401", "83", "2857", "431", "89" ]
[ "nonn" ]
11
1
1
[ "A007138", "A112092", "A112927", "A143663", "A143665", "A252170", "A274909", "A379639", "A379640", "A379641", "A379642", "A379644" ]
null
Sean A. Irvine, Dec 28 2024
2025-02-27T11:16:18
oeisdata/seq/A379/A379642.seq
93b965242704778911c15524995cbe27
A379643
List of x coordinates of prime numbers in a Cartesian grid, where the first prime 2 is placed at the origin (0,0) and the second prime 3 at (1,0). For the n-th prime prime(n), n >= 3, take a unit step in the direction (prime(n)-3)*45 degrees counterclockwise from the positive x-axis.
[ "0", "1", "1", "0", "1", "1", "1", "2", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "2", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "2", "2", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "0", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "-1", "-1", "-1", "0", "0", "1", "0", "0", "0", "1", "1", "2", "2", "2", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "-1", "0" ]
[ "sign" ]
26
1
8
[ "A277730", "A297447", "A297448", "A345293", "A379643", "A379731" ]
null
Ya-Ping Lu, Dec 28 2024
2025-01-07T08:37:05
oeisdata/seq/A379/A379643.seq
6ed8eb2226300e090a2409c9a440a790
A379644
Smallest primitive prime factor of 11^n-1.
[ "2", "3", "7", "61", "3221", "37", "43", "7321", "1772893", "13421", "15797", "13", "1093", "1623931", "195019441", "17", "50544702849929377", "590077", "6115909044841454629", "212601841", "1723", "23", "829", "10657", "3001", "53", "5559917315850179173", "29", "523", "31", "50159", "51329", "661", "71707", "211", "3138426605161" ]
[ "nonn" ]
11
1
1
[ "A007138", "A112092", "A112927", "A143663", "A143665", "A252170", "A274910", "A379639", "A379640", "A379641", "A379642", "A379644" ]
null
Sean A. Irvine, Dec 28 2024
2025-02-27T11:16:21
oeisdata/seq/A379/A379644.seq
82edcdce5f5019cf0a0a33721220681f
A379645
Let D(k) = {d(k,i)}, i = 1,2,...,q be the set of q divisors of an integer k. a(n) is the smallest number k such that there exist exactly n distinct integers M, 1 < M < k, where each set D(k) mod M is a multiplicative group.
[ "1", "3", "12", "5", "7", "45", "63", "11", "17", "23", "119", "19", "128", "31", "73", "29", "533", "289", "125", "41", "97", "377", "121", "79", "1691", "529", "127", "223", "625", "71", "2209", "109", "15049", "961", "2593", "197", "26533", "343", "2048", "281", "2809", "841", "66221", "1331", "199", "10609", "65699", "181", "1369", "647", "11449", "6143", "69931" ]
[ "nonn" ]
12
0
2
[ "A027750", "A379645", "A379647" ]
null
Michel Lagneau, Dec 28 2024
2025-01-23T12:45:52
oeisdata/seq/A379/A379645.seq
3817222197ba1f99a450afea73d061bb
A379646
Irregular triangle T(n,k) where row n contains the trajectory of recursive mappings of A001175(x) starting with x = n and ending at fixed point A235249(n).
[ "1", "2", "3", "8", "12", "24", "3", "8", "12", "24", "4", "6", "24", "5", "20", "60", "120", "6", "24", "7", "16", "24", "8", "12", "24", "9", "24", "10", "60", "120", "11", "10", "60", "120", "12", "24", "13", "28", "48", "24", "14", "48", "24", "15", "40", "60", "120", "16", "24", "17", "36", "24", "18", "24", "19", "18", "24", "20", "60", "120", "21", "16", "24", "22", "30", "120", "23", "48", "24" ]
[ "nonn", "tabf" ]
8
1
2
[ "A001175", "A001179", "A235249", "A235702", "A379646" ]
null
Michael De Vlieger, Dec 30 2024
2025-01-03T02:20:59
oeisdata/seq/A379/A379646.seq
e87a379bc9c58a69766893e6c279aec9
A379647
Let D(k) = {d(k,i)}, i = 1,2,...,q be the set of q divisors of an integer k. a(n) is the smallest number k such that there exist exactly n distinct integers M, 1 < M <= k, where each set D(k) mod M = {0,1,2,...,M-1}.
[ "1", "2", "6", "12", "84", "60", "120", "420", "2280", "840", "3360", "2520", "5040", "10080", "13860", "21840", "32760", "55440", "65520", "98280", "163800", "196560", "491400", "556920", "360360", "720720", "1670760", "1801800", "1081080", "2162160", "4324320", "5266800", "6126120", "12612600", "10450440", "12252240", "17907120" ]
[ "nonn" ]
12
0
2
[ "A027750", "A379645", "A379647" ]
null
Michel Lagneau, Dec 28 2024
2025-01-23T12:46:13
oeisdata/seq/A379/A379647.seq
c2f18a8d58c9f49c62ec36253abb3049
A379648
a(n) = position of prime(n) in A379652, or a(n) = -1 if prime(n) is not in A379652.
[ "1", "7", "2", "8", "3", "13", "11", "6", "4", "17", "9", "14", "26", "49", "5", "47", "18", "154", "29", "12", "44", "46", "27", "120", "33", "16", "102", "48", "43", "36", "10", "87", "21", "52", "41", "15", "71", "86", "28", "58", "121", "31", "114", "172", "45", "190", "89", "189", "37", "108", "150", "19", "230", "83", "247", "88", "146", "30", "103", "74", "149", "59", "55", "119" ]
[ "nonn", "easy" ]
6
1
2
[ "A379648", "A379652" ]
null
Michael De Vlieger, Jan 01 2025
2025-01-01T01:48:38
oeisdata/seq/A379/A379648.seq
146fff557d49b4b8b75f60bf0eb44c93
A379649
a(0) = 1, a(n) = position of prime(n) in A379727, or a(n) = -1 if prime(n) is not in A379727.
[ "1", "-1", "2", "4", "3", "5", "9", "15", "8", "6", "13", "44", "10", "17", "40", "7", "38", "14", "134", "20", "16", "35", "37", "18", "46", "24", "12", "153", "39", "34", "27", "45", "71", "104", "43", "32", "11", "95", "70", "19", "82", "47", "22", "165", "98", "36", "179", "73", "178", "28", "159", "130", "554", "365", "67", "220", "72", "124", "21", "154", "58", "127", "83", "79" ]
[ "sign", "easy" ]
5
0
3
[ "A379649", "A379727" ]
null
Michael De Vlieger, Jan 01 2025
2025-01-01T01:49:07
oeisdata/seq/A379/A379649.seq
84c4eebeb06fbbbebfcd798f512837c8
A379650
a(n) is the least number whose fifth power is an n-digit fifth power which has the maximum sum of digits (A374025(n)).
[ "1", "2", "3", "6", "9", "15", "18", "37", "58", "93", "156", "179", "368", "549", "756", "1379", "2139", "3965", "4956", "9746", "11156", "25046", "38779", "60006", "98746", "151446", "231755", "389658", "585516", "819199", "1584779", "1776339", "3803469", "5400759", "9744998", "11463799", "23936959", "28737498", "62943519", "95635199", "156373159", "225142779", "351816939", "595519999" ]
[ "nonn", "base" ]
40
1
2
[ "A000584", "A370522", "A373914", "A374025", "A379650", "A379869", "A380111" ]
null
Zhining Yang, Jan 12 2025
2025-03-31T07:00:48
oeisdata/seq/A379/A379650.seq
f97316ed879f2c2418b7ace3d0f600de
A379651
Decimal expansion of the smallest number greater than 1 whose decimal and binary expansions have the same succession of digits.
[ "1", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "0", "1", "1", "0", "1", "0", "1", "1", "1", "1", "0", "1", "0" ]
[ "nonn", "cons", "base", "nice" ]
64
2
null
[ "A181929", "A379079", "A379651", "A380293", "A381088", "A382714" ]
null
Dominic McCarty, Jan 11 2025
2025-04-08T21:39:15
oeisdata/seq/A379/A379651.seq
99f44b5d53ed3217e309e0816757a462
A379652
a(1) = 2. For n > 1, a(n) = smallest prime factor of c=2*a(n-1)+1 that is not in {a(1), ..., a(n-1)}; if all prime factors of c are in {a(1), ..., a(n-1)}, then we try the next value of c, which is 2*c+1; and so on.
[ "2", "5", "11", "23", "47", "19", "3", "7", "31", "127", "17", "71", "13", "37", "151", "101", "29", "59", "239", "479", "137", "1103", "2207", "883", "2357", "41", "83", "167", "67", "271", "181", "727", "97", "1567", "6271", "113", "227", "911", "1823", "521", "149", "599", "109", "73", "197", "79", "53", "107", "43", "563", "347", "139", "373", "997", "307", "1231" ]
[ "nonn" ]
35
1
1
[ "A031439", "A072268", "A131200", "A174162", "A379648", "A379652" ]
null
Robert C. Lyons, Dec 28 2024
2025-01-02T14:23:28
oeisdata/seq/A379/A379652.seq
98692aae18d31067addfb17c5b379efb
A379653
Primes p such that p == 1 (mod 4) and the Paley graph of order p is not alpha-critical.
[ "41", "113", "229", "337", "349", "433", "457", "461", "557", "593", "617", "653", "677", "853", "857", "877", "929", "977", "997", "1021", "1129", "1153" ]
[ "nonn", "more" ]
15
1
1
null
null
Craig Eric Larson, Dec 28 2024
2025-01-18T09:34:47
oeisdata/seq/A379/A379653.seq
84a93e21ec567cefad0a96e9a9f35538
A379654
Least positive integer k <= n such that |tau(k)|*n + 1 is prime, or 0 if such k does not exist, where the tau function is given by A000594.
[ "1", "1", "2", "1", "5", "1", "5", "2", "3", "1", "4", "1", "2", "2", "11", "1", "2", "1", "2", "5", "13", "1", "4", "2", "2", "3", "5", "1", "3", "1", "5", "2", "3", "6", "3", "1", "21", "15", "2", "1", "3", "1", "2", "11", "5", "1", "2", "2", "6", "2", "3", "1", "4", "2", "2", "11", "7", "1", "3", "1", "3", "2", "3", "5", "3", "1", "2", "3", "2", "1", "4", "1", "2", "2", "2", "6", "10", "1", "15", "3", "4", "1", "2", "2", "5", "3", "2", "1", "2", "2", "6", "12", "4", "3", "2", "1", "7", "3", "2", "1" ]
[ "nonn" ]
15
1
3
[ "A000040", "A000594", "A034693", "A379654" ]
null
Zhi-Wei Sun, Dec 28 2024
2024-12-30T21:52:48
oeisdata/seq/A379/A379654.seq
cd69925ee96f27ac86923af347e18d00
A379655
Numbers k such that k and k+1 are both possible values of the sum of divisors function (A000203).
[ "3", "6", "7", "12", "13", "14", "30", "31", "38", "39", "56", "62", "90", "120", "126", "127", "132", "182", "194", "216", "255", "306", "307", "363", "380", "398", "399", "402", "464", "510", "511", "548", "552", "740", "780", "846", "847", "854", "920", "930", "960", "961", "992", "1022", "1023", "1092", "1093", "1280", "1407", "1650", "1658", "1722", "1723", "1728" ]
[ "nonn", "easy" ]
58
1
1
[ "A000203", "A002191", "A342555", "A342560", "A379655" ]
null
Amiram Eldar, Jan 03 2025
2025-01-03T21:46:37
oeisdata/seq/A379/A379655.seq
a5090d4d02b19b60d3e98eed7dfbd850
A379656
Carmichael numbers that are the sum of 2 positive cubes.
[ "1729", "15841", "46657", "126217", "188461", "1082809", "1773289", "2628073", "3146221", "5049001", "6868261", "14469841", "19683001", "31146661", "40917241", "78091201", "92625121", "144218341", "252141121", "1836304561", "2616662881", "3035837161", "4354716961", "4828075561", "10779325921", "13200275881", "14235803713" ]
[ "nonn" ]
16
1
1
[ "A001235", "A002997", "A003325", "A033502", "A046025", "A265628", "A379656" ]
null
Amiram Eldar, Dec 29 2024
2024-12-29T08:50:12
oeisdata/seq/A379/A379656.seq
49b5101d6f1dceefe4babd165511b000
A379657
The nonadjacent form of a(n) is obtained by inserting a digit 0 before each nonzero digit in the balanced ternary expansion of n.
[ "0", "1", "3", "2", "5", "11", "6", "13", "7", "4", "9", "19", "10", "21", "43", "22", "45", "23", "12", "25", "51", "26", "53", "27", "14", "29", "15", "8", "17", "35", "18", "37", "75", "38", "77", "39", "20", "41", "83", "42", "85", "171", "86", "173", "87", "44", "89", "179", "90", "181", "91", "46", "93", "47", "24", "49", "99", "50", "101", "203", "102", "205", "103", "52", "105" ]
[ "nonn", "base" ]
10
0
3
[ "A048680", "A065363", "A334913", "A379657", "A379658" ]
null
Rémy Sigrist, Dec 29 2024
2024-12-30T16:07:38
oeisdata/seq/A379/A379657.seq
eeeef562abb5a01b15b47ef5b4afa513
A379658
The balanced ternary expansion of a(n) is obtained by removing a digit 0 before each nonzero digit in the nonadjacent form of n.
[ "0", "1", "3", "2", "9", "4", "6", "8", "27", "10", "12", "5", "18", "7", "24", "26", "81", "28", "30", "11", "36", "13", "15", "17", "54", "19", "21", "23", "72", "25", "78", "80", "243", "82", "84", "29", "90", "31", "33", "35", "108", "37", "39", "14", "45", "16", "51", "53", "162", "55", "57", "20", "63", "22", "69", "71", "216", "73", "75", "77", "234", "79", "240", "242", "729" ]
[ "nonn", "base" ]
9
0
3
[ "A048679", "A065363", "A334913", "A379657", "A379658" ]
null
Rémy Sigrist, Dec 29 2024
2024-12-30T16:07:33
oeisdata/seq/A379/A379658.seq
34c56b75fa3d5967bb35a83998cd5e7f
A379659
Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-x) - 2*x) ).
[ "1", "3", "35", "766", "25037", "1096026", "60318343", "4004850718", "311682426329", "27835056557650", "2806352022690971", "315328008662299062", "39076741980040016293", "5294976627701723411866", "778852468463039787264911", "123599090729382829502733646", "21049364262909179898132228017", "3829309039543060842371185060770" ]
[ "nonn" ]
8
0
2
[ "A000272", "A377890", "A379659", "A379660" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-29T08:49:10
oeisdata/seq/A379/A379659.seq
bd9fb132150fe7c34b2fb69514a7aba4
A379660
Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-x) - 3*x) ).
[ "1", "4", "63", "1861", "82097", "4850511", "360275791", "32284172215", "3391036374849", "408722465393947", "55615320933323831", "8433939560030789091", "1410592999486776429841", "257966146919938099737511", "51211682886276933924579999", "10968423456294584033965364191", "2521058533839507726700577317889" ]
[ "nonn" ]
7
0
2
[ "A000272", "A377890", "A379659", "A379660" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-29T08:49:06
oeisdata/seq/A379/A379660.seq
78abc7a067380b0dffe8006ef2a30aa9
A379661
Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-2*x) - x) ).
[ "1", "3", "32", "638", "18992", "757152", "37946944", "2294428880", "162614380544", "13224995258624", "1214230905887744", "124244350629669888", "14021254268885487616", "1730161184870597414912", "231756218205467830255616", "33492293939832097344370688", "5194237715163522538324557824", "860510764365813120075516739584" ]
[ "nonn" ]
7
0
2
[ "A377890", "A379661", "A379662" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-29T08:49:03
oeisdata/seq/A379/A379661.seq
a54f2f9edae2e38ef6480c05081ca81b
A379662
Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-3*x) - x) ).
[ "1", "4", "55", "1407", "53697", "2743893", "176247927", "13657260501", "1240444335969", "129281173193385", "15210977483374479", "1994549350608453609", "288445997202717914433", "45611213861740547292093", "7829287622920723803498279", "1449907335654700964735333997", "288151338120152032299063196737" ]
[ "nonn" ]
8
0
2
[ "A377890", "A379661", "A379662" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-29T08:48:58
oeisdata/seq/A379/A379662.seq
2747ccd4c69176b53f1f9af8eefb6ed2
A379663
a(n) is the number of integer-sided triangles whose sides are in geometric progression with smallest side n.
[ "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "2", "1", "1", "1", "2", "4", "1", "2", "2", "1", "1", "1", "3", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "3", "5", "4", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "2", "5", "1", "1", "1", "2", "1", "1", "1", "4", "1", "1", "4", "2", "1", "1", "1", "3", "6", "1", "1", "2", "1", "1", "1", "2" ]
[ "nonn" ]
6
1
4
[ "A000188", "A000201", "A008833", "A027750", "A046951", "A057918", "A060143", "A366398", "A370599", "A376900", "A379033", "A379340", "A379341", "A379663", "A379705" ]
null
Felix Huber, Jan 07 2025
2025-01-17T19:38:25
oeisdata/seq/A379/A379663.seq
cd1b3055b902b911c52bc7f50bcf518c
A379664
Decimal expansion of hypergeom([1/2, 1/2], [1], -2).
[ "7", "4", "5", "7", "4", "9", "1", "8", "7", "3", "1", "6", "3", "2", "9", "6", "0", "9", "9", "6", "2", "4", "8", "2", "0", "6", "5", "3", "5", "3", "4", "5", "1", "1", "0", "4", "3", "0", "2", "6", "7", "5", "1", "9", "7", "9", "8", "3", "2", "2", "1", "8", "6", "7", "2", "3", "3", "7", "4", "1", "3", "3", "7", "1", "0", "7", "0", "1", "0", "2", "5", "2", "0", "7", "5", "3", "5", "9", "1", "5", "2", "3", "2", "8", "6", "2", "9", "8", "9", "8", "4", "8", "2", "2", "2", "8", "2", "5", "4", "1" ]
[ "nonn", "cons" ]
11
0
1
[ "A000796", "A002194", "A304656", "A379664" ]
null
Stefano Spezia, Dec 29 2024
2025-02-05T00:18:19
oeisdata/seq/A379/A379664.seq
543916de25e66d522d4c24ebcae1ceac
A379665
Minimum number of intercalates in a Brown's diagonal Latin square of order 2n.
[ "0", "0", "12", "9", "16", "25" ]
[ "nonn", "more", "hard" ]
23
0
3
[ "A307163", "A339641", "A379665" ]
null
Eduard I. Vatutin, Dec 29 2024
2025-04-08T13:09:19
oeisdata/seq/A379/A379665.seq
869c9d0355a4f9950d6aa488725ad45e
A379666
Array read by antidiagonals downward where A(n,k) is the number of integer partitions of n with product k.
[ "1", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "2", "1", "1", "1", "0", "0", "0", "0", "0", "2", "1", "1", "1", "0", "0", "0", "0", "0", "1", "2", "1", "1", "1", "0", "0", "0", "0", "0", "1", "1", "2", "1", "1", "1", "0", "0", "0", "0", "0", "0", "2", "1", "2", "1", "1", "1" ]
[ "nonn", "tabl" ]
7
1
33
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A008284", "A025147", "A028422", "A045778", "A057567", "A057568", "A069016", "A096276", "A096765", "A111133", "A114324", "A301987", "A316439", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325036", "A325037", "A325038", "A325041", "A325042", "A325044", "A326149", "A326152", "A326155", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Jan 01 2025
2025-01-02T21:27:58
oeisdata/seq/A379/A379666.seq
65d6a6eba3669e5d0ec567165095ca52
A379667
Number of finite multisets of positive integers with sum + product = n.
[ "0", "1", "1", "1", "2", "2", "3", "3", "5", "5", "6", "7", "8", "8", "11", "12", "13", "14", "15", "17", "19", "19", "20", "22", "26", "26", "29", "30", "31", "34", "35", "36", "38", "40", "43", "46", "48", "48", "50", "53", "55", "57", "61", "62", "66", "66", "69", "73", "75", "77", "79", "82", "83", "85", "89", "91", "94", "94", "95", "103", "106", "107", "111", "113", "116", "119", "121" ]
[ "nonn" ]
5
0
5
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A008284", "A025147", "A028422", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A316439", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325036", "A325037", "A325038", "A325041", "A325044", "A326149", "A326152", "A326155", "A326156", "A326172", "A326178", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Jan 03 2025
2025-01-03T23:29:39
oeisdata/seq/A379/A379667.seq
907bfcedf78e8ddfe6735960e2241627
A379668
Array read by antidiagonals downward where A(n,k) is the number of integer partitions of n into parts > 1 with product k.
[ "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ]
[ "nonn", "tabl" ]
17
1
33
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A008284", "A025147", "A028422", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A316439", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325036", "A325037", "A325038", "A325041", "A325042", "A325044", "A326149", "A326152", "A326155", "A326178", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Dec 31 2024
2025-01-02T10:49:57
oeisdata/seq/A379/A379668.seq
6bff1bd7767a0b28b62e84d7586ecf1c
A379669
Number of finite multisets of positive integers > 1 with sum + product = n.
[ "0", "1", "0", "0", "1", "0", "1", "0", "2", "0", "1", "1", "1", "0", "3", "1", "1", "1", "1", "2", "2", "0", "1", "2", "4", "0", "3", "1", "1", "3", "1", "1", "2", "2", "3", "3", "2", "0", "2", "3", "2", "2", "4", "1", "4", "0", "3", "4", "2", "2", "2", "3", "1", "2", "4", "2", "3", "0", "1", "8", "3", "1", "4", "2", "3", "3", "2", "1", "3", "5", "1", "4", "3", "1", "4", "2", "7", "2", "3", "4", "3", "0", "2", "4", "6", "2", "4", "4" ]
[ "nonn" ]
6
0
9
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A025147", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325036", "A325037", "A325038", "A325044", "A326149", "A326152", "A326155", "A326156", "A326172", "A326178", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Jan 03 2025
2025-01-03T23:28:40
oeisdata/seq/A379/A379669.seq
bee54fc4bae1b7b4af5c5cce9b36fd3f
A379670
Numbers that are not the sum + product of any multiset of positive integers > 1. Zeros of A379669.
[ "2", "3", "5", "7", "9", "13", "21", "25", "37", "45", "57", "81", "133", "157", "193", "225", "253", "273", "325", "477", "613", "1821" ]
[ "nonn", "more" ]
9
1
1
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A025147", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A318029", "A318950", "A319000", "A319005", "A319057", "A325036", "A325037", "A325038", "A325044", "A326149", "A326152", "A326155", "A326156", "A326172", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736", "A379839", "A379840" ]
null
Gus Wiseman, Jan 04 2025
2025-01-05T22:36:29
oeisdata/seq/A379/A379670.seq
e3a347eaf0adce801a83121eb5662e9a
A379671
Array read by antidiagonals downward where A(n,k) is the number of finite sets of positive integers with sum n and product k.
[ "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0" ]
[ "nonn", "tabl" ]
7
1
73
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A008284", "A025147", "A028422", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A316439", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325036", "A325037", "A325038", "A325041", "A325042", "A325044", "A326149", "A326152", "A326155", "A326622", "A328966", "A379666", "A379667", "A379668", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Jan 01 2025
2025-01-02T21:27:51
oeisdata/seq/A379/A379671.seq
edbfc6bab5fb62272bb1f280b7048dac
A379672
Number of finite sets of positive integers with sum + product = n.
[ "0", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "2", "2", "1", "2", "2", "2", "3", "2", "1", "3", "3", "1", "2", "3", "2", "3", "3", "2", "3", "3", "3", "4", "3", "1", "2", "4", "4", "4", "3", "2", "4", "3", "1", "5", "5", "2", "3", "4", "3", "3", "5", "5", "4", "2", "1", "5", "6", "3", "4", "4", "3", "4", "3", "2", "4", "6", "4", "5", "6", "3", "4", "5", "4", "4", "4", "5", "5", "2", "2", "6", "7", "4", "3", "5" ]
[ "nonn" ]
17
0
12
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A025147", "A028422", "A045778", "A057567", "A057568", "A096276", "A096765", "A111133", "A114324", "A301987", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325036", "A325037", "A325038", "A325044", "A326149", "A326152", "A326155", "A326156", "A326172", "A326178", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Jan 03 2025
2025-01-11T10:26:25
oeisdata/seq/A379/A379672.seq
f2a6b229fd7066b68deec82c83d3063c
A379673
Records in A378865.
[ "2", "3", "4", "12", "22", "33", "38", "65", "112", "127", "222", "333", "625", "1112", "1247", "2222", "3333", "3612", "3685", "3979", "4028", "6162", "15618", "43125", "65625", "78125", "81875", "84375" ]
[ "nonn", "base", "more" ]
14
1
1
[ "A074157", "A378865", "A379673" ]
null
Gonzalo Martínez, Jan 02 2025
2025-01-13T22:59:05
oeisdata/seq/A379/A379673.seq
45d325cd3153d708cf45b8656b9bd626
A379674
Expansion of e.g.f. -log( 1 - log(1 - x)^4 / 24 ).
[ "0", "0", "0", "0", "1", "10", "85", "735", "6804", "68544", "754130", "9044750", "117779431", "1657347978", "25083122701", "406495546275", "7025691638029", "129034238530984", "2510053743368448", "51563288466007704", "1115617292385725186", "25359995212317017700", "604332959567317283050", "15066452630930326289950" ]
[ "nonn" ]
30
0
6
[ "A346966", "A377376", "A379674", "A380370" ]
null
Seiichi Manyama, Jan 23 2025
2025-01-23T08:31:44
oeisdata/seq/A379/A379674.seq
347e772f769a761259609ccfd824ecac
A379675
a(0) = 0, and for any n > 0, a(n) is the least integer (in absolute value) not yet in the sequence such that the absolute difference of a(n-1) and a(n) is a square and a(n) is positive iff n is odd.
[ "0", "1", "-3", "6", "-10", "15", "-1", "3", "-6", "10", "-15", "21", "-4", "5", "-11", "14", "-2", "2", "-7", "9", "-16", "20", "-5", "4", "-12", "13", "-23", "26", "-38", "11", "-14", "22", "-27", "37", "-44", "56", "-8", "8", "-17", "19", "-30", "34", "-47", "17", "-19", "30", "-34", "47", "-53", "28", "-21", "43", "-57", "7", "-9", "16", "-20", "29", "-35", "46", "-18", "18" ]
[ "sign" ]
10
0
3
[ "A277616", "A377091", "A379675" ]
null
Rémy Sigrist, Dec 29 2024
2024-12-30T16:07:59
oeisdata/seq/A379/A379675.seq
65d2e50394e9d9ea093ab023753d56a8
A379676
For n >= 0, a(n) is the least k >= 2 such that (n + 1)*(2*k + n) / 2 is a triangular number (A000217).
[ "3", "7", "4", "15", "7", "5", "10", "31", "13", "6", "16", "12", "19", "10", "7", "63", "25", "11", "28", "22", "8", "15", "34", "21", "37", "16", "40", "9", "43", "20", "46", "127", "14", "21", "18", "10", "55", "25", "15", "19", "61", "26", "64", "45", "11", "30", "70", "44", "73", "31", "21", "55", "79", "35", "12", "70", "22", "36", "88", "18", "91", "40", "34", "255", "31", "13", "100", "19", "28", "24", "106", "92", "109", "46", "29", "78", "25", "14", "118", "91", "121", "51", "124", "63", "42", "55", "35", "39", "133", "43", "15" ]
[ "nonn" ]
9
0
1
[ "A000217", "A076114", "A076116", "A083390", "A379676" ]
null
Ctibor O. Zizka, Dec 29 2024
2024-12-30T02:13:11
oeisdata/seq/A379/A379676.seq
aed31796d5bcda1d0a6a7b36fcd9ff1d
A379677
Numbers k for which 10k+1, 10k+3, 10k+7, 10k+9, 10k+31, 10k+33, 10k+37, and 10k+39 are primes.
[ "100630", "259495", "391921", "960055", "1053106", "10881631", "13144570", "15237073", "15713164", "17902876", "21195025", "25535221", "26758786", "55745863", "68512435", "72449137", "82135765", "87141136", "103026208", "110310436", "128216002", "138120127", "142769863", "143237995", "144399400", "159672133", "194876008" ]
[ "nonn" ]
11
1
1
[ "A007811", "A059925", "A379677" ]
null
Mike Speciner, Dec 29 2024
2024-12-31T15:40:37
oeisdata/seq/A379/A379677.seq
6e59ca88b8d4be800df191d58a01f51d
A379678
Array read by antidiagonals downward where A(n,k) is the number of finite sets of positive integers > 1 with sum n and product k.
[ "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ]
[ "nonn", "tabl" ]
13
1
null
[ "A000009", "A000041", "A001055", "A002865", "A008284", "A025147", "A028422", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A316439", "A318029", "A318950", "A319005", "A319057", "A325036", "A325037", "A325038", "A325041", "A325042", "A325044", "A326149", "A326152", "A326155", "A326156", "A326172", "A326178", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736", "A379737" ]
null
Gus Wiseman, Jan 01 2025
2025-01-06T03:56:08
oeisdata/seq/A379/A379678.seq
817d8024daed5b3c1ac0f2ac1211b77e
A379679
Number of finite sets of positive integers > 1 with sum + product = n.
[ "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "2", "0", "1", "1", "1", "1", "2", "0", "1", "2", "1", "0", "2", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "0", "2", "2", "2", "2", "1", "1", "3", "0", "1", "4", "1", "1", "2", "2", "1", "2", "3", "2", "2", "0", "1", "4", "2", "1", "3", "1", "2", "2", "1", "1", "3", "3", "1", "4", "2", "1", "3", "2", "2", "2", "2", "3", "2", "0", "2", "4", "3", "1", "2", "3" ]
[ "nonn" ]
9
1
14
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A008284", "A025147", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A316439", "A318029", "A318950", "A319000", "A319005", "A319057", "A319916", "A325037", "A325038", "A325044", "A326149", "A326152", "A326155", "A326156", "A326172", "A326178", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736" ]
null
Gus Wiseman, Jan 03 2025
2025-01-09T08:01:40
oeisdata/seq/A379/A379679.seq
3d253dc52afb988f6f7e49dd477cd523
A379680
Numbers that are not the sum + product of any set of positive integers > 1. Zeros of A379679.
[ "2", "3", "5", "7", "9", "13", "15", "21", "25", "37", "45", "57", "81", "93", "121", "133", "157", "165", "193", "217", "225", "253", "273", "297", "325", "477", "525", "613", "981", "1201", "1213", "1317", "1813", "1821", "2401", "4273", "5113", "5905", "7477" ]
[ "nonn", "look", "more" ]
9
1
1
[ "A000009", "A000041", "A001055", "A002865", "A003963", "A025147", "A045778", "A057567", "A057568", "A069016", "A096276", "A111133", "A114324", "A301987", "A318029", "A318950", "A319000", "A319005", "A319057", "A325036", "A325037", "A325038", "A325044", "A326149", "A326155", "A326156", "A326172", "A326178", "A326622", "A328966", "A379666", "A379667", "A379668", "A379669", "A379670", "A379671", "A379672", "A379678", "A379679", "A379680", "A379720", "A379721", "A379722", "A379733", "A379736", "A379841", "A379842" ]
null
Gus Wiseman, Jan 04 2025
2025-01-06T09:00:28
oeisdata/seq/A379/A379680.seq
f012d48cd080ef02813b0fb3f21ca8b0
A379681
Sum plus product of the multiset of prime indices of n.
[ "1", "2", "4", "3", "6", "5", "8", "4", "8", "7", "10", "6", "12", "9", "11", "5", "14", "9", "16", "8", "14", "11", "18", "7", "15", "13", "14", "10", "20", "12", "22", "6", "17", "15", "19", "10", "24", "17", "20", "9", "26", "15", "28", "12", "19", "19", "30", "8", "24", "16", "23", "14", "32", "15", "23", "11", "26", "21", "34", "13", "36", "23", "24", "7", "27", "18", "38", "16", "29", "20" ]
[ "nonn" ]
6
1
2
[ "A000040", "A000720", "A001055", "A001222", "A001223", "A003963", "A028422", "A055396", "A056239", "A061395", "A075254", "A075255", "A096276", "A112798", "A114324", "A175508", "A178503", "A301987", "A319000", "A319005", "A325032", "A325033", "A325034", "A325035", "A325036", "A325037", "A325038", "A325040", "A325041", "A325042", "A325044", "A379681", "A379682", "A379721" ]
null
Gus Wiseman, Jan 05 2025
2025-01-05T22:35:07
oeisdata/seq/A379/A379681.seq
defcd6114daeff9e92cd4a1fbc155a3f
A379682
Least number whose prime indices have sum + product = n.
[ "1", "2", "4", "3", "6", "5", "10", "7", "14", "11", "15", "13", "26", "17", "25", "19", "33", "23", "35", "29", "58", "31", "51", "37", "74", "41", "65", "43", "69", "47", "85", "53", "105", "59", "93", "61", "122", "67", "115", "71", "123", "73", "145", "79", "158", "83", "141", "89", "161", "97", "185", "101", "177", "103", "205", "107", "214", "109", "201", "113", "226", "127" ]
[ "nonn" ]
5
1
2
[ "A000040", "A000720", "A001055", "A001222", "A001223", "A003963", "A028422", "A055396", "A056239", "A061395", "A075254", "A096276", "A112798", "A114324", "A175508", "A178503", "A301987", "A319000", "A319005", "A325032", "A325033", "A325034", "A325035", "A325036", "A325037", "A325038", "A325040", "A325041", "A325042", "A325044", "A379681", "A379682", "A379721" ]
null
Gus Wiseman, Jan 05 2025
2025-01-05T22:34:58
oeisdata/seq/A379/A379682.seq
b4f4ab678dc95506b5c7955a1d134d0f
A379683
a(n) is the least number k that has exactly n divisors <= sqrt(k) of the form 4*j+3.
[ "1", "9", "63", "231", "945", "1890", "3465", "5775", "12285", "10395", "20790", "60060", "45045", "75075", "98175", "103950", "176715", "135135", "225225", "270270", "405405", "900900", "1060290", "810810", "765765", "675675", "1354815", "1351350", "1711710", "2702700", "2027025", "4542615", "2297295", "3378375", "5360355", "6216210", "3828825", "6774075", "10270260" ]
[ "nonn" ]
6
0
2
[ "A364387", "A379683" ]
null
Robert Israel, Dec 29 2024
2024-12-30T02:17:46
oeisdata/seq/A379/A379683.seq
400e2c2b61080311bcc391ddb2d00377
A379684
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) * (1 - x*exp(x)) ).
[ "1", "0", "3", "11", "193", "2389", "50191", "1088205", "29836353", "902845673", "31428924631", "1207426391137", "51394833121105", "2386048646491197", "120379283952129567", "6547887322803355589", "382306453347573490177", "23839225109022069540817", "1581540933047988924532135" ]
[ "nonn" ]
8
0
3
[ "A213644", "A377890", "A379684", "A379685" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-30T02:17:00
oeisdata/seq/A379/A379684.seq
13800d0cb70d20a84b1d05ab52515ada
A379685
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x) * (1 - x*exp(x)) ).
[ "1", "3", "30", "551", "15028", "547717", "25068058", "1383323517", "89443699176", "6634682537993", "555501170856934", "51828125728865257", "5332620999430989244", "599894268098223894525", "73253745510185331985842", "9650159930850877102454693", "1364228585624978795929566928", "206008264557747708717576118417" ]
[ "nonn" ]
8
0
2
[ "A213644", "A377890", "A379684", "A379685" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-30T04:28:25
oeisdata/seq/A379/A379685.seq
6e3877b5c1daffeb6c4252f76b4117aa
A379686
a(n) = (a(n-1)+1)*(a(n-2)+1)*(a(n-3)+1)*(a(n-4)+1)/a(n-5), with a(1)=1, a(2)=2, a(3)=6, a(4)=42, a(5)=1806.
[ "1", "2", "6", "42", "1806", "1631721", "443752508927", "9376966151402427009536", "292117920945338351144537464770855449375232", "1098221126335915194898500730834145753769059346709551018699709189743396297017856" ]
[ "nonn" ]
29
1
2
[ "A007018", "A072713", "A276453", "A379686" ]
null
Antoine de Saint Germain, Dec 29 2024
2025-01-12T07:31:58
oeisdata/seq/A379/A379686.seq
06df78f6051211b3d6ab3d7f3c000a72
A379687
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) * (1 - 2*x*exp(x)) ).
[ "1", "1", "11", "158", "3597", "107994", "4082695", "186003166", "9930511577", "608225910290", "42049314628251", "3239451955702038", "275220868466701861", "25565354021529630970", "2577774089234276245391", "280406846696018760511694", "32732658189778781519050161", "4081497882738710247779141922" ]
[ "nonn" ]
8
0
3
[ "A379659", "A379687", "A379688" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-30T04:28:19
oeisdata/seq/A379/A379687.seq
4e4ae5175a8b983ac6510a957fa584c5
A379688
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - 2*x*exp(x)) ).
[ "1", "2", "20", "366", "9992", "365130", "16769292", "929022206", "60323670416", "4494465562770", "378025706776340", "35434198578761862", "3663111561838580568", "414057463231218044186", "50805545997014472821276", "6725525908390393438264590", "955435863749903677193184032", "144987884255349864723586105122" ]
[ "nonn" ]
16
0
2
[ "A213644", "A379659", "A379687", "A379688", "A380095", "A380097" ]
null
Seiichi Manyama, Dec 29 2024
2025-01-12T10:17:28
oeisdata/seq/A379/A379688.seq
d9e187ba33d635e7f2efce1c9bca983c
A379689
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) * (1 - x*exp(2*x)) ).
[ "1", "0", "5", "26", "557", "9504", "254737", "7405712", "264468185", "10599167744", "484155176381", "24530813822976", "1373346539948869", "83980088153710592", "5576376312266516681", "399370804845913339904", "30695207044654060184753", "2519882221014204064727040", "220076205166821624927515893" ]
[ "nonn" ]
9
0
3
[ "A379661", "A379689", "A379690", "A379691" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-30T04:28:08
oeisdata/seq/A379/A379689.seq
19757113fb535754d05a8aaa76e6aa63
A379690
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*exp(2*x)) ).
[ "1", "1", "8", "102", "1952", "49920", "1603392", "62100304", "2818386944", "146748098304", "8624885719040", "564885716972544", "40800979548180480", "3222148806557544448", "276214603877715378176", "25544721442331112192000", "2535168741071076287971328", "268757182971129822376624128", "30311086789573678207758237696" ]
[ "nonn" ]
9
0
3
[ "A379661", "A379689", "A379690", "A379691" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-30T04:28:01
oeisdata/seq/A379/A379690.seq
6f476c0d693389e6b3502607a139bb78
A379691
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) * (1 - x*exp(2*x)) ).
[ "1", "2", "17", "274", "6597", "212736", "8624581", "421843472", "24185705417", "1591194859264", "118184516071641", "9782950785024000", "893132377427288653", "89156432069922504704", "9661304014254414999821", "1129505503357457643206656", "141711496280128816909982097", "18992404410135723679211716608" ]
[ "nonn" ]
9
0
2
[ "A379661", "A379689", "A379690", "A379691" ]
null
Seiichi Manyama, Dec 29 2024
2024-12-30T04:27:55
oeisdata/seq/A379/A379691.seq
ebe29e25cc4a4cf2603f413f859a6b9e
A379692
a(1) = 1; a(n) is the most recently occurring value not among the last k terms where k is the number of times a(n-1) has occurred; if no such value exists, a(n) is the smallest unused positive integer.
[ "1", "2", "1", "3", "1", "2", "3", "1", "4", "1", "5", "1", "2", "4", "1", "3", "2", "5", "3", "1", "6", "1", "7", "1", "4", "6", "1", "8", "1", "2", "4", "6", "1", "3", "8", "1", "5", "3", "6", "8", "5", "1", "7", "5", "6", "8", "1", "4", "7", "8", "6", "5", "3", "2", "4", "7", "5", "8", "6", "1", "9", "1", "10", "1", "11", "1", "12", "1", "13", "1", "14", "1", "15", "1", "16", "1", "17", "1", "18", "1", "3", "15", "1", "4" ]
[ "nonn" ]
12
1
2
[ "A358921", "A379692" ]
null
Neal Gersh Tolunsky, Dec 29 2024
2025-01-02T11:55:18
oeisdata/seq/A379/A379692.seq
d8a1cadecd42fb7fc9523c34929341d3
A379693
a(n) is the least number k that has exactly n divisors <= sqrt(k) of the form 4*j+1.
[ "1", "25", "90", "585", "1575", "2475", "5850", "9945", "16380", "20475", "36855", "45045", "69615", "122850", "135135", "176715", "218295", "225225", "495495", "405405", "348075", "696150", "675675", "765765", "1461915", "1351350", "2304225", "1576575", "4037670", "2027025", "2837835", "2297295", "4542615", "4594590", "5135130", "3828825", "6912675", "5360355", "8558550" ]
[ "nonn" ]
5
1
2
[ "A364358", "A379683", "A379693" ]
null
Robert Israel, Dec 29 2024
2024-12-30T02:17:55
oeisdata/seq/A379/A379693.seq
27422e0872dd32692cc47e1b2fed187f
A379694
Numbers k such that 4^k - prime(k) is prime.
[ "1", "2", "3", "5", "9", "24", "49", "1466", "4588", "27804", "60126" ]
[ "nonn", "more" ]
19
1
2
[ "A078583", "A110066", "A379694" ]
null
Vincenzo Librandi, Dec 30 2024
2025-01-03T18:45:12
oeisdata/seq/A379/A379694.seq
f04453c6ab56e07597e3108a61472cd8
A379695
Number of equivalence classes of regular vines in dimension n.
[ "1", "1", "1", "2", "6", "40", "560", "17024" ]
[ "nonn", "more" ]
25
1
4
null
null
Thomas Zaslavsky, Jan 03 2025
2025-01-11T19:24:45
oeisdata/seq/A379/A379695.seq
a17899cfda61f7584b15be493a6951f9
A379696
Number of n-node combinatorial game trees in normal form.
[ "0", "1", "2", "3", "6", "9", "20", "33", "68", "131", "264", "523", "1094", "2214", "4670", "9747" ]
[ "nonn", "more" ]
41
0
3
null
null
Jelmer S. Firet, Jan 05 2025
2025-02-03T10:58:16
oeisdata/seq/A379/A379696.seq
6079700e05e9322a7b52ff04646c436f
A379697
For n >= 3, a(n) is the least k >= 0 such that (k + 1)*(2*n + k) / 2 is a triangular number (A000217).
[ "0", "2", "5", "0", "1", "20", "4", "0", "2", "6", "8", "2", "0", "10", "119", "3", "4", "20", "0", "1", "5", "14", "2", "5", "1", "0", "32", "6", "7", "464", "20", "2", "8", "0", "24", "8", "2", "4", "65", "9", "10", "47", "0", "3", "11", "30", "17", "2", "3", "1", "59", "12", "0", "2", "21", "4", "14", "38", "40", "14", "4", "42", "101", "0", "16", "74", "2", "5", "17", "46", "48", "17", "5", "1", "11", "0", "19", "125", "10", "6", "20", "54", "1", "20", "6", "44", "272", "21", "0" ]
[ "nonn", "look" ]
15
3
2
[ "A000217", "A074377", "A379676", "A379697" ]
null
Ctibor O. Zizka, Dec 30 2024
2025-01-31T04:28:03
oeisdata/seq/A379/A379697.seq
63c4cd1d12cb018f1622121f673236ad
A379698
Exponent of highest power of 2 that divides the n-th practical number A005153(n).
[ "0", "1", "2", "1", "3", "2", "4", "1", "2", "3", "2", "1", "5", "2", "3", "1", "4", "1", "3", "2", "6", "1", "3", "1", "4", "2", "3", "1", "5", "2", "3", "2", "4", "3", "1", "7", "2", "2", "4", "1", "2", "5", "1", "3", "4", "2", "6", "2", "1", "3", "2", "4", "1", "3", "2", "5", "2", "1", "4", "2", "8", "2", "3", "1", "4", "2", "3", "5", "1", "2", "4", "1", "2", "3", "6", "2", "1", "4", "2", "1", "2", "5", "3", "2", "4", "1", "2", "7", "1", "3", "2", "4", "3", "1", "5", "2", "4", "3", "6", "1", "3", "2", "1", "4", "2", "2", "5", "1", "4", "2", "3", "1", "9", "3", "1", "4", "2", "2", "5", "1" ]
[ "nonn" ]
15
1
3
[ "A005153", "A007814", "A379325", "A379698" ]
null
Frank M Jackson, Dec 30 2024
2025-01-04T22:27:36
oeisdata/seq/A379/A379698.seq
d57e77c87028bc04c47f28540d4cdc8c
A379699
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + 2*x*exp(x)) ).
[ "1", "3", "27", "430", "10013", "309146", "11932303", "553740958", "30053978361", "1868855561938", "131048808861491", "10232894227577462", "880688476587319573", "82836081054992159194", "8454536286883278469431", "930656450818831650930766", "109910217042754940709650417", "13862746369348872200671305890" ]
[ "nonn" ]
10
0
2
[ "A201470", "A377373", "A379456", "A379699", "A379700" ]
null
Seiichi Manyama, Dec 30 2024
2024-12-30T10:50:22
oeisdata/seq/A379/A379699.seq
577e12570af555a57953b9911f6271d9
A379700
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + 3*x*exp(x)) ).
[ "1", "4", "45", "889", "25613", "977271", "46586281", "2669066695", "178800270009", "13720918482235", "1187217400278941", "114379273346497611", "12144899525595998821", "1409261040317551952935", "177436990866294436727409", "24094164269339964351367231", "3510079015962779901366174449", "546103202348225740056486964467" ]
[ "nonn" ]
8
0
2
[ "A377374", "A379456", "A379699", "A379700" ]
null
Seiichi Manyama, Dec 30 2024
2024-12-30T10:50:18
oeisdata/seq/A379/A379700.seq
c51a56d2bbcb46f76eac9b31750ab989
A379701
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) / (1 + x*exp(2*x)) ).
[ "1", "0", "3", "2", "113", "304", "13747", "83600", "3590337", "38193920", "1650383171", "26535997696", "1186785903217", "26244849422336", "1234578346302771", "35176362803984384", "1757110507998276353", "61533880908307038208", "3281634015502670522371", "136392534106346468999168" ]
[ "nonn" ]
9
0
3
[ "A108919", "A366232", "A379701", "A379702" ]
null
Seiichi Manyama, Dec 30 2024
2024-12-30T11:24:07
oeisdata/seq/A379/A379701.seq
4074532cccc10a79716824ff2273d1c0