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1999-12-11 03:00:00
2025-04-28 00:58:08
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A358501
Irregular triangle read by rows. Coefficients of the polynomials (-1)^n*binomial(-x - 1, -x - n - 1) * binomial(n + x, x) * (n!)^2 in ascending order of powers.
[ "1", "1", "2", "1", "4", "12", "13", "6", "1", "36", "132", "193", "144", "58", "12", "1", "576", "2400", "4180", "3980", "2273", "800", "170", "20", "1", "14400", "65760", "129076", "143700", "100805", "46710", "14523", "3000", "395", "30", "1", "518400", "2540160", "5450256", "6787872", "5482456", "3034920", "1184153", "328986", "64743", "8820", "791", "42", "1" ]
[ "nonn", "tabf" ]
7
0
3
[ "A000007", "A001044", "A358501" ]
null
Peter Luschny, Nov 26 2022
2022-11-26T09:59:35
oeisdata/seq/A358/A358501.seq
a8c6680de12a4ac4b0b75814c085a352
A358502
Triangle read by rows. The coefficients of the polynomials hypergeom([-x, -x, -n], [-x - n, -x - n], 1) * Product_{j=1..n} (j + x)^2 in ascending order of powers.
[ "1", "1", "2", "4", "12", "12", "36", "132", "180", "120", "576", "2400", "4080", "3360", "1680", "14400", "65760", "126000", "134400", "75600", "30240", "518400", "2540160", "5382720", "6350400", "4838400", "1995840", "665280", "25401600", "131725440", "299315520", "396688320", "325987200", "190935360", "60540480", "17297280" ]
[ "nonn", "tabl" ]
5
0
3
null
null
Peter Luschny, Nov 26 2022
2022-12-08T14:51:41
oeisdata/seq/A358/A358502.seq
282b9bb60646b01306a1c394f586bb35
A358503
Positions inventory sequence: for stage k >= 2 we record where all the numbers from the two previous stages have appeared, starting with a(0) = 0, a(1) = 0.
[ "0", "0", "0", "1", "1", "2", "3", "2", "3", "4", "5", "6", "4", "5", "7", "6", "8", "9", "10", "11", "7", "8", "9", "12", "10", "13", "11", "15", "14", "16", "17", "18", "19", "12", "13", "15", "14", "20", "16", "21", "17", "22", "18", "24", "19", "26", "23", "25", "28", "27", "29", "30", "31", "32", "20", "21", "22", "24", "26", "23", "33", "25", "34", "28", "36", "27", "35", "29", "38", "30", "40", "31", "42" ]
[ "nonn", "tabf" ]
35
0
6
[ "A000045", "A000071", "A001911", "A356784", "A357317", "A357443", "A358503" ]
null
Ctibor O. Zizka, Nov 21 2022
2022-11-22T22:18:09
oeisdata/seq/A358/A358503.seq
8c57e3e61a815824250f4416bd041f06
A358504
Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 3 children down to the generation of M.
[ "1", "5", "25", "137", "793", "4697", "28057", "168089", "1008025", "6047129", "36280729", "217680281", "1306073497", "7836424601", "47018514841", "282111023513", "1692666010009", "10155995797913", "60935974263193", "365615844530585", "2193695065086361", "13162170386323865", "78973022309554585" ]
[ "easy", "nonn" ]
58
0
2
[ "A076024", "A154407", "A358504", "A358598", "A358599", "A358600", "A358601" ]
null
Hans Braxmeier, Nov 19 2022
2025-03-24T04:11:10
oeisdata/seq/A358/A358504.seq
20432bc634e024552e263032bf225a75
A358505
Binary encoding of the n-th standard ordered rooted tree.
[ "0", "2", "12", "10", "56", "50", "44", "42", "52", "226", "204", "202", "184", "178", "172", "170", "240", "210", "908", "906", "824", "818", "812", "810", "180", "738", "716", "714", "696", "690", "684", "682", "228", "962", "844", "842", "3640", "3634", "3628", "3626", "820", "3298", "3276", "3274", "3256", "3250", "3244", "3242", "752", "722", "2956", "2954" ]
[ "nonn" ]
8
1
2
[ "A000108", "A001263", "A014486", "A057122", "A358371", "A358372", "A358373", "A358379", "A358453", "A358505", "A358523" ]
null
Gus Wiseman, Nov 20 2022
2022-11-21T09:38:29
oeisdata/seq/A358/A358505.seq
edb7889a092ee3e25d95472a282a8a82
A358506
Matula-Goebel number of the n-th standard ordered rooted tree.
[ "1", "2", "3", "4", "5", "6", "6", "8", "7", "10", "9", "12", "10", "12", "12", "16", "11", "14", "15", "20", "15", "18", "18", "24", "14", "20", "18", "24", "20", "24", "24", "32", "13", "22", "21", "28", "25", "30", "30", "40", "21", "30", "27", "36", "30", "36", "36", "48", "22", "28", "30", "40", "30", "36", "36", "48", "28", "40", "36", "48", "40", "48", "48", "64", "13", "26", "33", "44" ]
[ "nonn" ]
6
1
2
[ "A000081", "A000108", "A001263", "A014486", "A061775", "A127301", "A196050", "A206487", "A214577", "A358371", "A358372", "A358377", "A358378", "A358379", "A358505", "A358506", "A358507", "A358508", "A358521", "A358522" ]
null
Gus Wiseman, Nov 20 2022
2022-11-20T18:30:25
oeisdata/seq/A358/A358506.seq
fd817ab9b2f47998430e6e4f87b66c3c
A358507
Sorted list of positions of first appearances in the sequence counting permutations of Matula-Goebel trees (A206487).
[ "1", "6", "12", "24", "30", "48", "60", "72", "104", "120", "144", "148", "156", "180", "192", "222", "288", "312", "360", "390", "432", "444", "480", "576", "712", "720", "780", "832", "864", "900", "1080", "1110", "1248", "1260", "1296", "1440", "1560", "1680", "2136", "2160", "2262", "2304", "2340", "2496", "2520", "2592", "2738", "2880", "2886", "3072" ]
[ "nonn" ]
7
1
2
[ "A000081", "A000108", "A001263", "A032027", "A061775", "A127301", "A196050", "A206487", "A214577", "A358377", "A358378", "A358506", "A358507", "A358508", "A358521", "A358522" ]
null
Gus Wiseman, Nov 20 2022
2022-11-21T09:47:56
oeisdata/seq/A358/A358507.seq
23d305ae2756a05060bc19d6d82f0683
A358508
Least Matula-Goebel number of a tree with exactly n permutations.
[ "1", "6", "12", "24", "48", "30", "192", "104", "148", "72", "3072", "60", "12288", "832", "144", "712", "196608", "222", "786432", "120", "288", "13312" ]
[ "nonn", "more" ]
6
1
2
[ "A000081", "A000108", "A001263", "A032027", "A061775", "A127301", "A196050", "A206487", "A214577", "A358377", "A358378", "A358506", "A358507", "A358508", "A358521", "A358522" ]
null
Gus Wiseman, Nov 20 2022
2022-11-21T09:48:02
oeisdata/seq/A358/A358508.seq
b1ae88698ed62be683486c4e480cad0f
A358509
Sum of decimal digits of (3^n - 1)/2 (A003462).
[ "0", "1", "4", "4", "4", "4", "13", "13", "13", "22", "22", "31", "22", "31", "31", "31", "22", "31", "31", "31", "31", "31", "49", "49", "40", "40", "49", "67", "58", "58", "58", "76", "58", "76", "85", "85", "85", "85", "94", "85", "85", "94", "103", "103", "85", "94", "103", "112", "103", "112", "130", "130", "94", "121", "112", "112", "121", "103", "103", "121", "112", "121", "121", "139", "121", "148", "121", "157", "157", "157", "157", "175", "157", "157" ]
[ "nonn", "base", "easy" ]
35
0
3
[ "A003462", "A004166", "A007953", "A017209", "A358509" ]
null
Paul Curtz, Nov 20 2022
2022-11-30T00:02:01
oeisdata/seq/A358/A358509.seq
b6a907af9b3bd73c7dd81666e2627232
A358510
Positions of zeros in A342991.
[ "3", "6", "8", "9", "10", "11", "13", "20", "22", "23", "24", "25", "26", "27", "28", "29", "31", "42", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "57", "72", "74", "75", "76", "77", "78", "79", "80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "91", "110", "112", "113", "114", "115", "116", "117", "118", "119", "120", "121", "122", "123", "124" ]
[ "nonn", "easy" ]
37
1
1
[ "A342991", "A358510", "A358511" ]
null
Paolo Xausa, Nov 20 2022
2023-01-04T10:34:13
oeisdata/seq/A358/A358510.seq
d1c30df8b2e9f6909107f003d60661b9
A358511
Positions of ones in A342991.
[ "1", "2", "4", "5", "7", "12", "14", "15", "16", "17", "18", "19", "21", "30", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "43", "56", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "73", "90", "92", "93", "94", "95", "96", "97", "98", "99", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "111", "132", "134" ]
[ "nonn", "easy" ]
34
1
2
[ "A342991", "A358510", "A358511" ]
null
Paolo Xausa, Nov 20 2022
2023-01-04T10:34:08
oeisdata/seq/A358/A358511.seq
67aa902f729b16c3eeb5d8b9c098b06f
A358512
a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995).
[ "1", "2", "4", "8", "12", "30", "24", "80", "48", "72", "96", "192", "120", "180", "288", "612", "240", "624", "420", "360", "480", "900", "1632", "960", "1200", "720", "840", "1560", "2100", "1260", "1440", "3420", "2640", "3024", "1680", "2880", "8316", "4620", "3600", "3780", "4200", "2520", "3360", "6240", "9900", "6300", "7200", "8640", "6720", "13200", "7920" ]
[ "nonn", "base" ]
20
0
2
[ "A003052", "A062028", "A176995", "A230093", "A358512" ]
null
Marius A. Burtea, Dec 04 2022
2023-03-02T11:25:00
oeisdata/seq/A358/A358512.seq
92550b49cf3ef1cf9f7119cfd52c0d63
A358513
a(n) is the smallest number whose divisors include exactly n that can be written in the form m + reverse(m), for some m (A067030).
[ "1", "2", "4", "8", "12", "24", "48", "88", "220", "176", "132", "968", "264", "396", "528", "792", "1320", "1584", "2640", "3960", "5808", "5544", "8712", "14520", "11088", "24024", "21780", "36036", "40656", "39996", "53328", "87120", "60984", "72072", "205128", "132132", "121968", "144144", "293304", "199980", "266640", "439956", "264264", "360360", "733260", "396396", "660660", "799920" ]
[ "nonn", "base" ]
22
0
2
[ "A067030", "A067032", "A358513" ]
null
Marius A. Burtea, Dec 04 2022
2022-12-29T09:48:42
oeisdata/seq/A358/A358513.seq
4c7e2f6f0fb322958a47ba0df78d27c3
A358514
a(n) is the smallest number with exactly n divisors that are Achilles numbers (A052486).
[ "1", "72", "216", "432", "1296", "864", "7200", "2592", "6912", "10800", "7776", "15552", "27000", "41472", "21600", "31104", "884736", "54000", "64800", "129600", "86400", "248832", "172800", "162000", "5308416", "108000", "194400", "216000", "518400", "388800", "810000", "1323000", "1058400", "1382400", "324000", "432000", "2073600" ]
[ "nonn" ]
10
0
2
[ "A000005", "A052486", "A358514" ]
null
Marius A. Burtea, Dec 04 2022
2022-12-25T15:06:30
oeisdata/seq/A358/A358514.seq
f3911a14f1f2cc1effaf75b904209588
A358515
Number of types of generalized symmetries in diagonal Latin squares of order n in parastrophic slices.
[ "6", "0", "0", "76", "74", "199", "861" ]
[ "nonn", "more", "hard" ]
43
1
1
[ "A000041", "A274171", "A287649", "A287650", "A293777", "A357473", "A358394", "A358515", "A358891" ]
null
Eduard I. Vatutin, Nov 20 2022
2023-03-25T09:47:30
oeisdata/seq/A358/A358515.seq
0dd52e7d6a2a18fbcdd5b897b9a318d5
A358516
Decimal expansion of Sum_{k >= 1} (-1)^(k+1)*1/((k+2)*(k+3)).
[ "0", "5", "2", "9", "6", "1", "0", "2", "7", "7", "8", "6", "5", "5", "7", "2", "8", "5", "5", "0", "1", "1", "3", "0", "9", "0", "9", "5", "8", "3", "0", "1", "9", "8", "0", "2", "8", "1", "7", "6", "6", "6", "9", "3", "5", "3", "8", "7", "1", "7", "7", "1", "7", "4", "9", "0", "8", "0", "2", "6", "6", "8", "5", "6", "5", "3", "4", "5", "3", "9", "1", "0", "6", "0", "6", "0", "5", "6", "0", "9", "7", "8", "7", "8", "3", "9", "3", "3", "2", "0", "6", "5", "9", "5", "0", "4" ]
[ "nonn", "cons" ]
18
0
2
[ "A002162", "A002378", "A242023", "A242024", "A358516", "A358517", "A358519" ]
null
Claude H. R. Dequatre, Nov 20 2022
2025-02-07T05:54:20
oeisdata/seq/A358/A358516.seq
bf40c1d0b8fe88f5d98391f5e8ee6da4
A358517
Decimal expansion of 4*log(2) - 11/4.
[ "0", "2", "2", "5", "8", "8", "7", "2", "2", "2", "3", "9", "7", "8", "1", "2", "3", "7", "6", "6", "8", "9", "2", "8", "4", "8", "5", "8", "3", "2", "7", "0", "6", "2", "7", "2", "3", "0", "2", "0", "0", "0", "5", "3", "7", "4", "4", "1", "0", "2", "1", "0", "1", "6", "4", "8", "2", "7", "2", "0", "0", "3", "7", "9", "7", "3", "5", "7", "4", "4", "8", "7", "8", "7", "8", "7", "7", "8", "8", "6", "2", "4", "2", "3", "4", "5", "3", "3", "0", "7", "9", "8", "5", "6", "7" ]
[ "nonn", "cons" ]
35
0
2
[ "A002162", "A016639", "A035287", "A242023", "A242024", "A358516", "A358517", "A358519" ]
null
Claude H. R. Dequatre, Nov 20 2022
2024-11-21T08:20:49
oeisdata/seq/A358/A358517.seq
414f4e10d7ce793d9a85a1c97a3e4887
A358518
a(n) = Sum_{k=0..n} binomial(n+3*k+3,n-k) * Catalan(k).
[ "1", "5", "20", "85", "405", "2116", "11766", "68237", "407789", "2492553", "15506942", "97859544", "624880895", "4029896310", "26209648212", "171711104853", "1132143259711", "7506530891217", "50019287312324", "334784759816729", "2249720564735567", "15172573979205166", "102662981205576494" ]
[ "nonn" ]
52
0
2
[ "A000108", "A086616", "A162481", "A358518", "A360046", "A360057" ]
null
Seiichi Manyama, Jan 23 2023
2023-03-11T08:09:22
oeisdata/seq/A358/A358518.seq
5dddf2482f4eb6128db39023927702d6
A358519
Decimal expansion of Sum_{k >= 1} (-1)^(k+1)/(k^2 + 4*k - 1).
[ "1", "8", "9", "9", "5", "7", "9", "0", "7", "7", "1", "8", "0", "6", "2", "7", "2", "5", "2", "7", "1", "9", "0", "8", "4", "0", "9", "0", "6", "3", "6", "3", "6", "6", "5", "5", "2", "7", "9", "5", "6", "6", "4", "9", "1", "4", "5", "4", "0", "6", "7", "9", "5", "6", "3", "1", "3", "2", "8", "9", "3", "1", "3", "6", "2", "2", "1", "3", "1", "4", "6", "7", "1", "4", "9", "3", "6", "1", "9", "8", "5", "9", "8", "5", "3", "2", "5", "6", "4", "7", "7", "5", "6", "1", "3" ]
[ "nonn", "cons" ]
19
0
2
[ "A002162", "A028875", "A242023", "A242024", "A358516", "A358517", "A358519" ]
null
Claude H. R. Dequatre, Nov 20 2022
2024-08-05T14:21:34
oeisdata/seq/A358/A358519.seq
6ddc0383bd7dc39c0ef18572fcb41c3b
A358520
Nearest integer to n/sin(n).
[ "1", "2", "21", "-5", "-5", "-21", "11", "8", "22", "-18", "-11", "-22", "31", "14", "23", "-56", "-18", "-24", "127", "22", "25", "-2486", "-27", "-27", "-189", "34", "28", "103", "-44", "-30", "-77", "58", "33", "64", "-82", "-36", "-57", "128", "40", "54", "-258", "-46", "-52", "2486", "53", "51", "380", "-62", "-51", "-191", "76", "53", "134", "-97" ]
[ "sign", "look" ]
34
1
2
[ "A046947", "A051422", "A105666", "A272695", "A358520" ]
null
Bence Bernáth, Nov 20 2022
2022-12-12T09:14:59
oeisdata/seq/A358/A358520.seq
8a0ccc523cea5907a3825be2f57c274d
A358521
Sorted list of positions of first appearances in the sequence of Matula-Goebel numbers of standard ordered trees (A358506).
[ "1", "2", "3", "4", "5", "6", "8", "9", "10", "11", "12", "16", "17", "18", "19", "20", "22", "24", "32", "33", "34", "35", "36", "37", "38", "40", "43", "44", "48", "64", "66", "67", "68", "69", "70", "72", "74", "75", "76", "80", "86", "88", "96", "128", "129", "131", "132", "133", "134", "136", "137", "138", "139", "140", "144", "147", "148", "150", "152", "160", "171", "172" ]
[ "nonn" ]
7
1
2
[ "A000081", "A000108", "A001263", "A014486", "A061775", "A127301", "A196050", "A206487", "A214577", "A358371", "A358372", "A358377", "A358378", "A358379", "A358505", "A358506", "A358521", "A358522" ]
null
Gus Wiseman, Nov 20 2022
2022-11-20T18:30:21
oeisdata/seq/A358/A358521.seq
aaf5be790e21235f35ca43f4e85851a8
A358522
Least number k such that the k-th standard ordered tree has Matula-Goebel number n, i.e., A358506(k) = n.
[ "1", "2", "3", "4", "5", "6", "9", "8", "11", "10", "17", "12", "33", "18", "19", "16", "257", "22", "129", "20", "35", "34", "1025", "24", "37", "66", "43", "36", "513", "38", "65537", "32", "67", "514", "69", "44", "2049", "258", "131", "40" ]
[ "nonn", "more" ]
6
1
2
[ "A000081", "A000108", "A001263", "A014486", "A061775", "A127301", "A196050", "A206487", "A214577", "A358371", "A358372", "A358377", "A358378", "A358379", "A358505", "A358506", "A358521", "A358522" ]
null
Gus Wiseman, Nov 20 2022
2022-11-20T18:30:16
oeisdata/seq/A358/A358522.seq
5c3e8c610ccb24103fe1bd709289357a
A358523
Standard ordered tree numbers of ordered trees in order of their binary encodings (A014486).
[ "1", "2", "4", "3", "8", "7", "6", "9", "5", "16", "15", "14", "25", "13", "12", "11", "18", "129", "65", "10", "33", "257", "17", "32", "31", "30", "57", "29", "28", "27", "50", "385", "193", "26", "97", "769", "49", "24", "23", "22", "41", "21", "36", "35", "258", "32769", "16385", "130", "8193", "16777217", "4097", "20", "19", "66" ]
[ "nonn" ]
6
0
2
[ "A000081", "A000108", "A001263", "A014221", "A014486", "A057122", "A358371", "A358372", "A358373", "A358379", "A358505", "A358523" ]
null
Gus Wiseman, Nov 21 2022
2022-11-21T09:38:25
oeisdata/seq/A358/A358523.seq
6d09690f6a2f42978dcd1434df264a21
A358524
Binary encoding of balanced ordered rooted trees (counted by A007059).
[ "0", "2", "10", "12", "42", "52", "56", "170", "204", "212", "232", "240", "682", "820", "844", "852", "920", "936", "976", "992", "2730", "3276", "3284", "3380", "3404", "3412", "3640", "3688", "3736", "3752", "3888", "3920", "4000", "4032", "10922", "13108", "13132", "13140", "13516", "13524", "13620", "13644", "13652", "14568", "14744", "14760" ]
[ "nonn" ]
6
1
2
[ "A000081", "A000108", "A001263", "A003238", "A007059", "A014486", "A048816", "A057122", "A184155", "A244925", "A290689", "A358377", "A358379", "A358453", "A358459", "A358523", "A358524" ]
null
Gus Wiseman, Nov 21 2022
2022-11-21T22:01:53
oeisdata/seq/A358/A358524.seq
24a8e7b76ab2e3a33b307838216f43ad
A358525
Number of distinct permutations of the n-th composition in standard order.
[ "1", "1", "1", "1", "1", "2", "2", "1", "1", "2", "1", "3", "2", "3", "3", "1", "1", "2", "2", "3", "2", "3", "3", "4", "2", "3", "3", "4", "3", "4", "4", "1", "1", "2", "2", "3", "1", "6", "6", "4", "2", "6", "1", "6", "6", "6", "6", "5", "2", "3", "6", "4", "6", "6", "6", "5", "3", "4", "6", "5", "4", "5", "5", "1", "1", "2", "2", "3", "2", "6", "6", "4", "2", "3", "3", "12", "3", "12", "12", "5", "2", "6", "3", "12", "3", "4" ]
[ "nonn" ]
6
0
6
[ "A000120", "A048896", "A070939", "A272919", "A329395", "A333766", "A358371", "A358372", "A358379", "A358505", "A358507", "A358508", "A358525" ]
null
Gus Wiseman, Nov 21 2022
2022-11-21T22:01:49
oeisdata/seq/A358/A358525.seq
945684155b0092446c5ae81f1221f731
A358526
Numbers k whose prime indices have a different number of permutations than any number less than k.
[ "1", "6", "12", "24", "30", "48", "60", "72", "120", "144", "180", "192", "210", "288", "360", "384", "432", "480", "576", "720", "768", "840", "864", "900", "1080", "1152", "1260", "1296", "1440", "1680", "1728", "1920", "2160", "2304", "2520", "2592", "2880", "3072", "3360", "4320", "4608", "4620", "5040", "5400", "6300", "6912", "7200", "7560", "7680" ]
[ "nonn" ]
7
1
2
[ "A000040", "A000720", "A001221", "A001222", "A003963", "A008480", "A056239", "A061395", "A112798", "A289509", "A304938", "A316524", "A344606", "A358526" ]
null
Gus Wiseman, Nov 21 2022
2022-11-21T22:01:45
oeisdata/seq/A358/A358526.seq
82babd8c0c94e62066dfdb1118038ae5
A358527
Position of p in the factorization (without multiplicity) of 2^(p-1)-1, where p is the n-th odd prime.
[ "1", "2", "2", "2", "4", "3", "3", "2", "3", "4", "6", "6", "3", "2", "3", "2", "8", "4", "5", "8", "3", "2", "5", "6", "6", "3", "2", "8", "6", "6", "4", "4", "4", "3", "5", "7", "5", "2", "3", "2", "14", "4", "7", "7", "8", "9", "3", "2", "5", "5", "4", "12", "4", "4", "2", "3", "8", "7", "12", "3", "3", "6", "4", "10", "3", "9", "13", "2", "7", "7", "2", "3", "5", "8", "2", "3", "13", "10", "10", "4", "19", "4", "13", "3" ]
[ "nonn" ]
27
1
2
[ "A065091", "A098102", "A358527", "A358699" ]
null
G. L. Honaker, Jr., Nov 20 2022
2022-12-01T10:52:15
oeisdata/seq/A358/A358527.seq
26e4c3fd0db9d258406c6ffa295ad733
A358528
a(n) = n-th prime p(k) such that p(k) - p(k-1) > p(k-1) - p(k-2).
[ "5", "11", "17", "23", "29", "37", "47", "53", "67", "79", "89", "97", "107", "113", "127", "137", "149", "157", "173", "191", "197", "211", "233", "239", "251", "277", "293", "307", "317", "331", "347", "353", "359", "367", "389", "397", "409", "419", "431", "439", "449", "457", "467", "479", "499", "509", "521", "541", "557", "577", "587", "607", "631", "647" ]
[ "nonn", "easy" ]
7
1
1
[ "A181424", "A356347", "A358528", "A358529", "A358530", "A358531" ]
null
Clark Kimberling, Nov 21 2022
2022-11-22T22:20:24
oeisdata/seq/A358/A358528.seq
d72452f8344a896fb1266ef2462027fc
A358529
Indices of the primes in A358528.
[ "3", "5", "7", "9", "10", "12", "15", "16", "19", "22", "24", "25", "28", "30", "31", "33", "35", "37", "40", "43", "45", "47", "51", "52", "54", "59", "62", "63", "66", "67", "69", "71", "72", "73", "77", "78", "80", "81", "83", "85", "87", "88", "91", "92", "95", "97", "98", "100", "102", "106", "107", "111", "115", "118", "119", "122", "124", "125", "126", "128", "133", "136" ]
[ "nonn", "easy" ]
10
1
1
[ "A181424", "A356347", "A358528", "A358529", "A358530", "A358531" ]
null
Clark Kimberling, Nov 21 2022
2024-05-08T08:52:15
oeisdata/seq/A358/A358529.seq
69fc59a2acd051d4f99f5bee5f5ce395
A358530
a(n) = n-th prime prime(k) such that prime(k) - prime(k-1) < prime(k-1) - prime(k-2).
[ "13", "19", "31", "41", "43", "61", "71", "73", "83", "101", "103", "109", "131", "139", "151", "167", "181", "193", "199", "227", "229", "241", "257", "271", "281", "283", "311", "313", "337", "349", "373", "383", "401", "421", "433", "443", "461", "463", "487", "491", "503", "523", "547", "563", "571", "593", "601", "617", "619", "641", "643", "661", "677" ]
[ "nonn", "easy" ]
18
1
1
[ "A001223", "A051634", "A079419", "A181424", "A356347", "A358528", "A358529", "A358530", "A358531" ]
null
Clark Kimberling, Nov 21 2022
2024-09-22T02:29:48
oeisdata/seq/A358/A358530.seq
d523286106f41dcad6172153f2987100
A358531
Indices of the primes in A358530.
[ "6", "8", "11", "13", "14", "18", "20", "21", "23", "26", "27", "29", "32", "34", "36", "39", "42", "44", "46", "49", "50", "53", "55", "58", "60", "61", "64", "65", "68", "70", "74", "76", "79", "82", "84", "86", "89", "90", "93", "94", "96", "99", "101", "103", "105", "108", "110", "113", "114", "116", "117", "121", "123", "127", "129", "130", "132", "134", "135", "137" ]
[ "nonn", "easy" ]
7
1
1
[ "A001223", "A181424", "A258026", "A356347", "A358528", "A358529", "A358530", "A358531" ]
null
Clark Kimberling, Nov 21 2022
2022-11-22T22:21:01
oeisdata/seq/A358/A358531.seq
40d1a98d7cae6c5da2a00a8e3252417d
A358532
a(n) is the row position of the next open point in the structure generated by adding the largest diamond possible at the next open point on a triangular grid of side n. See Comments and Example sections for more details.
[ "1", "1", "2", "1", "2", "3", "1", "4", "1", "3", "7", "1", "3", "6", "4", "10", "1", "9", "4", "7", "9", "5", "14", "1", "11", "5", "7", "8", "11", "14", "19", "1", "6", "6", "24", "9", "14", "20", "1", "8", "8", "8", "20", "8", "19", "24", "30", "15", "19", "19", "19", "27", "1", "19", "15", "16", "20", "28", "8", "39", "11", "24", "1", "11", "16", "26", "28", "29", "30", "39", "50", "20", "31", "32", "33" ]
[ "nonn", "look", "easy" ]
27
1
3
[ "A045996", "A186434", "A194136", "A239567", "A279413", "A358532" ]
null
John Tyler Rascoe, Nov 20 2022
2023-07-22T21:06:13
oeisdata/seq/A358/A358532.seq
476847377386a37e4eb3d6f424c3c57b
A358533
Define a family of integer sequences S_0, S_1, S_2, ..., where S_0 = A000040 is the sequence of prime numbers and, for each k > 0, S_k is the result of making a "smoothing" pass through all the terms of S_(k-1) as follows: for every term other than the first, in ascending order, change its value by the minimum amount so that it will not differ from the mean of its two immediate neighbors by more than 1/2. {a(n)} is the limiting sequence S_oo.
[ "2", "3", "5", "8", "11", "14", "17", "20", "24", "28", "32", "36", "40", "44", "48", "53", "57", "62", "66", "70", "74", "79", "84", "90", "95", "99", "103", "107", "112", "118", "124", "130", "136", "142", "147", "152", "157", "162", "167", "172", "178", "184", "189", "194", "200", "206", "213", "219", "224", "229", "234", "239", "245", "251", "257", "262", "267", "272" ]
[ "nonn" ]
10
1
1
[ "A000040", "A358533" ]
null
Jon E. Schoenfield, Nov 20 2022
2022-11-20T22:35:35
oeisdata/seq/A358/A358533.seq
9afc2319ce3aad2c7dff0227064cc30b
A358534
Start with a(1)=1, a(2)=2. Thereafter, if gcd(a(n-2),a(n-1)) = 1 then a(n) is the smallest unused k such that gcd(a(n-2),k) > 1 and gcd(a(n-1),k) = 1, otherwise a(n) is the smallest unused k such that gcd(a(n-2),k) = 1 and gcd(a(n-1),k) > 1. If the latter is impossible, then a(n) = smallest missing number u. (See comments.)
[ "1", "2", "4", "3", "9", "5", "10", "6", "25", "35", "7", "15", "12", "55", "11", "20", "8", "45", "21", "40", "16", "65", "13", "30", "14", "27", "33", "17", "34", "18", "85", "95", "51", "24", "119", "49", "68", "22", "153", "39", "136", "28", "187", "99", "170", "26", "75", "57", "50", "32", "105", "63", "80", "38", "115", "23", "60", "36", "125", "145", "19", "76", "29", "87", "31", "62" ]
[ "nonn" ]
11
1
2
null
null
Michael De Vlieger and David James Sycamore, Nov 20 2022
2023-01-12T21:20:18
oeisdata/seq/A358/A358534.seq
a203a0b54b54703b5501b9e26d0dee28
A358535
a(1) = 1; let S(n) = Sum_{j=1..n-1} a(j) and let T(n) = Sum_{j=1..n-1} d(a(j)) where d(n) = A000005(n). a(n) = least novel k such that (T(n)+d(k)) | (S(n)+k).
[ "1", "2", "7", "8", "12", "27", "9", "18", "24", "64", "36", "152", "72", "128", "56", "84", "148", "80", "96", "316", "178", "88", "132", "206", "214", "104", "156", "622", "288", "344", "136", "204", "529", "228", "586", "343", "396", "484", "184", "276", "498", "384", "530", "225", "450", "469", "468", "549", "449", "511", "232", "348", "479", "545", "248", "372", "509" ]
[ "nonn" ]
9
1
2
[ "A000005", "A358535" ]
null
Michael De Vlieger and David James Sycamore, Dec 07 2022
2023-01-28T10:39:05
oeisdata/seq/A358/A358535.seq
14e45cbaf46a950c2b34d35ae9857bb3
A358536
a(n) is the least prime factor of 2^n-n-2.
[ "3", "2", "5", "2", "7", "2", "3", "2", "5", "2", "13", "2", "3", "2", "13", "2", "19", "2", "3", "2", "7", "2", "5", "2", "3", "2", "29", "2", "5", "2", "3", "2", "73", "2", "23", "2", "3", "2", "29", "2", "43", "2", "3", "2", "47", "2", "7", "2", "3", "2", "37", "2", "113", "2", "3", "2", "11", "2", "61", "2", "3", "2", "5", "2", "67", "2", "3", "2", "5", "2", "73", "2", "3", "2", "53", "2", "79", "2", "3", "2", "11", "2", "5", "2", "3", "2", "61", "2", "5", "2", "3", "2" ]
[ "nonn" ]
13
3
1
[ "A000247", "A020639", "A358536" ]
null
J. M. Bergot and Robert Israel, Nov 21 2022
2022-11-23T08:57:32
oeisdata/seq/A358/A358536.seq
37847d61f66481532a1cf896a25de6e9
A358537
For n > 0, a(n) is the total number of terms in all contiguous subsequences of the terms up to a(n-1) that sum to n; a(0) = 1.
[ "1", "1", "2", "2", "5", "4", "4", "2", "2", "5", "7", "8", "6", "11", "10", "16", "5", "22", "6", "19", "15", "22", "20", "9", "18", "5", "14", "16", "23", "9", "8", "11", "16", "12", "19", "21", "0", "21", "8", "20", "11", "17", "25", "28", "4", "18", "4", "30", "23", "40", "7", "20", "18", "18", "14", "9", "40", "9", "29", "32", "23", "6", "17", "23", "16", "8", "26", "32", "35", "27", "64", "10" ]
[ "nonn", "look" ]
71
0
3
[ "A331614", "A358537", "A359034", "A359634" ]
null
Neal Gersh Tolunsky, Dec 18 2022
2023-02-16T19:41:39
oeisdata/seq/A358/A358537.seq
6460802330712360d0001e5e7c9c5faf
A358538
Autobiographical numbers: the first digit of the term counts how many 0's the term in total has, the second how many 1's etc. up to the last digit but no more than b-1, where b is the base of the sequence. This sequence is in base b=10.
[ "1210", "2020", "21200", "3211000", "42101000", "521001000", "6210001000", "52200100019", "52200100108", "52200101007", "52200110006", "52201100004", "52210100003", "53010100019", "53010100108", "53010101007", "53010110006", "53011100004", "53110100002", "61200020006", "62200010001", "63010010001", "70200002007", "72100001000", "431110000299" ]
[ "nonn", "fini", "base" ]
72
1
1
[ "A046043", "A138480", "A358538" ]
null
Marc Morgenegg, Nov 21 2022
2023-01-28T18:24:20
oeisdata/seq/A358/A358538.seq
df2a781d9d2d4df5dd99cea054b0f1b9
A358539
a(n) is the smallest number with exactly n divisors that are n-gonal numbers.
[ "6", "36", "210", "1260", "6426", "3360", "351000", "207900", "3749460", "1153152", "15036840", "204204000", "213825150", "11737440", "91797866160", "1006485480", "2310808500", "4966241280", "22651328700", "325269404460", "14266470332400", "11203920000", "256653797400", "45843256859400", "59207908359600", "46822406400" ]
[ "nonn" ]
21
3
1
[ "A005179", "A130279", "A130317", "A356132", "A358539", "A358540", "A358541" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358539.seq
5718386367185d104328d050ed273575
A358540
a(n) is the smallest number with exactly n divisors that are n-gonal pyramidal numbers.
[ "56", "140", "1440", "11550", "351120", "41580", "742560", "29279250", "8316000", "72348396120", "3386892600", "578918340" ]
[ "nonn", "more" ]
27
3
1
[ "A005179", "A358539", "A358540", "A358541", "A358542", "A358543" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358540.seq
189da3a57ac7f00149b43ef6c84ddce7
A358541
a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers.
[ "20", "325", "912", "43771", "234784", "11025", "680680", "9143308361", "2470852896" ]
[ "nonn", "more" ]
18
3
1
[ "A005179", "A358539", "A358540", "A358541", "A358544", "A358545" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358541.seq
b922c2b16831d62b1425e26f5096cb12
A358542
a(n) is the smallest number with exactly n divisors that are tetrahedral numbers.
[ "1", "4", "56", "20", "120", "280", "560", "840", "1680", "10920", "9240", "18480", "55440", "120120", "240240", "314160", "628320", "1441440", "2282280", "7225680", "4564560", "9129120", "13693680", "27387360", "54774720", "68468400", "77597520", "136936800", "155195040", "310390080", "465585120", "775975200", "1163962800" ]
[ "nonn" ]
31
1
2
[ "A000292", "A005179", "A130317", "A279495", "A358542", "A358543", "A358544" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358542.seq
b7756dbdcf8ecc8f9f67339e4d3bbcee
A358543
a(n) is the smallest number with exactly n divisors that are square pyramidal numbers.
[ "1", "5", "30", "140", "420", "1540", "4620", "13860", "78540", "157080", "471240", "1141140", "3603600", "3423420", "13693680", "30630600", "58198140", "116396280", "214414200", "428828400", "581981400", "1163962800", "5354228880", "4073869800", "8147739600" ]
[ "nonn", "more" ]
53
1
2
[ "A000330", "A005179", "A130279", "A279496", "A358542", "A358543", "A358545" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358543.seq
a5c4d6c8234c8ff42244f79bd3e506a2
A358544
a(n) is the smallest number with exactly n divisors that are centered triangular numbers.
[ "1", "4", "20", "320", "460", "5440", "14260", "12920", "168640", "103360", "594320", "3878720", "2377280", "9211960", "18423920", "36847840", "125995840", "73695680", "865924240", "976467760", "1952935520", "3463696960", "3905871040", "31246968320", "22946992360" ]
[ "nonn", "more" ]
21
1
2
[ "A005179", "A005448", "A130317", "A300409", "A358542", "A358544", "A358545" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358544.seq
6dcf5c0cb7a1b8037067092a01d0f6b5
A358545
a(n) is the smallest number with exactly n divisors that are centered square numbers.
[ "1", "5", "25", "325", "1625", "1105", "5525", "27625", "160225", "1022125", "801125", "5928325", "8491925", "29641625", "42459625", "444215525", "314201225", "2003613625", "1571006125", "14826740825", "12882250225", "127081657625", "64411251125", "88717383625" ]
[ "nonn", "more" ]
26
1
2
[ "A001844", "A005179", "A130279", "A300410", "A358543", "A358544", "A358545" ]
null
Ilya Gutkovskiy, Nov 21 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358545.seq
35e051f2c9f5eaa5b4f75b79b807c720
A358546
Least odd number m such that m mod 3 > 0 and m*3^n is an amicable number, and -1 if no such number exists.
[ "5480828320492525", "4865", "7735", "455", "131285", "849355", "11689795", "286385", "187047685", "104255", "32851039955", "2085985", "47942199242945", "189296520259", "349700961302721360788238344333849", "580068028631", "50392682631679406080371010751466781" ]
[ "nonn", "more" ]
41
0
1
[ "A000396", "A001065", "A002025", "A090748", "A259180", "A262625", "A347770", "A358022", "A358320", "A358415", "A358546" ]
null
Jean-Marc Rebert, Nov 21 2022
2022-11-22T17:19:18
oeisdata/seq/A358/A358546.seq
3fa9fce30b6cb33edf88a3e3d167401f
A358547
a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(n-3*k)!.
[ "1", "1", "1", "3", "7", "13", "45", "151", "403", "1617", "6793", "23275", "105951", "522133", "2159077", "10964223", "61134955", "293587801", "1641566913", "10124731987", "55014334903", "335177088285", "2251814156701", "13587321392743", "89436553249347", "647267633012833", "4276528756374265", "30198747030078651" ]
[ "nonn" ]
21
0
4
[ "A122852", "A330044", "A357532", "A358547" ]
null
Seiichi Manyama, Nov 21 2022
2022-11-25T08:01:23
oeisdata/seq/A358/A358547.seq
92b350a5aafe8c7a98d2348a19adf6f1
A358548
a(n) = A003627(n+1) - A003627(n).
[ "3", "6", "6", "6", "6", "12", "6", "6", "6", "12", "12", "6", "12", "6", "6", "18", "6", "12", "18", "6", "6", "12", "6", "30", "6", "6", "12", "6", "6", "6", "12", "12", "18", "6", "30", "6", "6", "24", "6", "12", "18", "12", "12", "6", "12", "6", "12", "12", "12", "6", "12", "36", "6", "6", "18", "6", "6", "18", "24", "6", "6", "6", "18", "6", "18", "18", "24", "18", "12", "24", "12", "12", "6", "12", "18", "6", "18", "6", "24" ]
[ "nonn", "easy" ]
31
1
1
[ "A003627", "A358548", "A359257" ]
null
Jordan Gunter, Nov 19 2022
2023-01-31T12:20:04
oeisdata/seq/A358/A358548.seq
b1f1f5a06b6f44e4fbdd1affe2aff76b
A358549
Triangle read by rows where row n is reversed partial sums of row n of the Sierpinski triangle (A047999).
[ "1", "2", "1", "2", "1", "1", "4", "3", "2", "1", "2", "1", "1", "1", "1", "4", "3", "2", "2", "2", "1", "4", "3", "3", "2", "2", "1", "1", "8", "7", "6", "5", "4", "3", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "4", "3", "2", "2", "2", "2", "2", "2", "2", "1", "4", "3", "3", "2", "2", "2", "2", "2", "2", "1", "1", "8", "7", "6", "5", "4", "4", "4", "4", "4", "3", "2", "1", "4", "3", "3", "3", "3", "2", "2", "2", "2", "1", "1", "1", "1" ]
[ "nonn", "tabl", "easy" ]
28
0
2
[ "A000012", "A001316", "A047999", "A261363", "A358549" ]
null
Gary W. Adamson, Nov 21 2022
2022-12-03T23:46:23
oeisdata/seq/A358/A358549.seq
a275dd39e2eb10a658d2c5c67431f0a2
A358550
Depth of the ordered rooted tree with binary encoding A014486(n).
[ "1", "2", "2", "3", "2", "3", "3", "3", "4", "2", "3", "3", "3", "4", "3", "3", "3", "3", "4", "4", "4", "4", "5", "2", "3", "3", "3", "4", "3", "3", "3", "3", "4", "4", "4", "4", "5", "3", "3", "3", "3", "4", "3", "3", "3", "3", "4", "4", "4", "4", "5", "4", "4", "4", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "6", "2", "3", "3", "3", "4", "3", "3", "3", "3", "4", "4", "4", "4", "5", "3", "3", "3", "3", "4", "3", "3", "3" ]
[ "nonn" ]
7
1
2
[ "A000081", "A000108", "A001263", "A014137", "A014486", "A020988", "A057122", "A057514", "A057515", "A072643", "A127301", "A155587", "A358371", "A358372", "A358373", "A358379", "A358505", "A358523", "A358524", "A358550", "A358551" ]
null
Gus Wiseman, Nov 22 2022
2022-11-22T11:57:59
oeisdata/seq/A358/A358550.seq
47ee6223aacee6e289e9f5572e6a1ffa
A358551
Number of nodes in the ordered rooted tree with binary encoding A014486(n).
[ "1", "2", "3", "3", "4", "4", "4", "4", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7" ]
[ "nonn" ]
11
1
2
[ "A000081", "A000108", "A001263", "A014486", "A057122", "A057514", "A057515", "A072643", "A127301", "A358371", "A358372", "A358373", "A358379", "A358505", "A358523", "A358524", "A358550", "A358551" ]
null
Gus Wiseman, Nov 22 2022
2022-11-22T11:57:52
oeisdata/seq/A358/A358551.seq
f773b01fe350c5a8b3caac3b61d1d1e3
A358552
Node-height of the rooted tree with Matula-Goebel number n. Number of nodes in the longest path from root to leaf.
[ "1", "2", "3", "2", "4", "3", "3", "2", "3", "4", "5", "3", "4", "3", "4", "2", "4", "3", "3", "4", "3", "5", "4", "3", "4", "4", "3", "3", "5", "4", "6", "2", "5", "4", "4", "3", "4", "3", "4", "4", "5", "3", "4", "5", "4", "4", "5", "3", "3", "4", "4", "4", "3", "3", "5", "3", "3", "5", "5", "4", "4", "6", "3", "2", "4", "5", "4", "4", "4", "4", "5", "3", "4", "4", "4", "3", "5", "4", "6", "4", "3", "5", "5", "3", "4", "4", "5", "5", "4", "4", "4", "4", "6", "5", "4", "3", "5", "3", "5", "4", "5", "4", "4", "4", "4", "3", "4", "3" ]
[ "nonn" ]
19
1
2
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A080936", "A109082", "A109129", "A112798", "A196050", "A206487", "A342507", "A358379", "A358552", "A358576", "A358589", "A358592", "A358729" ]
null
Gus Wiseman, Nov 26 2022
2024-04-15T02:01:07
oeisdata/seq/A358/A358552.seq
a3a55e594457040acb7a3f34a8626af1
A358553
Number of internal (non-leaf) nodes in the n-th standard ordered rooted tree.
[ "0", "1", "2", "1", "3", "2", "2", "1", "2", "3", "3", "2", "3", "2", "2", "1", "4", "2", "4", "3", "4", "3", "3", "2", "2", "3", "3", "2", "3", "2", "2", "1", "3", "4", "3", "2", "5", "4", "4", "3", "3", "4", "4", "3", "4", "3", "3", "2", "4", "2", "4", "3", "4", "3", "3", "2", "2", "3", "3", "2", "3", "2", "2", "1", "3", "3", "5", "4", "4", "3", "3", "2", "4", "5", "5", "4", "5", "4", "4", "3", "5", "3", "5", "4", "5", "4", "4" ]
[ "nonn" ]
8
1
3
[ "A000081", "A000108", "A000891", "A001263", "A014221", "A055277", "A342507", "A358371", "A358372", "A358373", "A358379", "A358553", "A358554", "A358575", "A358585", "A358586", "A358588" ]
null
Gus Wiseman, Nov 26 2022
2022-11-27T08:56:32
oeisdata/seq/A358/A358553.seq
6d2a95d263537ab942dccce12a911c62
A358554
Least Matula-Goebel number of a rooted tree with n internal (non-leaf) nodes.
[ "1", "2", "3", "5", "11", "25", "55", "121", "275", "605", "1331", "3025", "6655", "14641", "33275", "73205" ]
[ "nonn", "more" ]
5
1
2
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A151821", "A196050", "A206487", "A342507", "A358552", "A358553", "A358554", "A358578", "A358592" ]
null
Gus Wiseman, Nov 27 2022
2022-11-27T08:56:00
oeisdata/seq/A358/A358554.seq
2dab58f48a70e0d129ca754234f93de1
A358555
Composite Fibonacci numbers that are not divisible by any Fibonacci primes.
[ "4181", "1346269", "24157817", "39088169", "165580141", "53316291173", "956722026041", "2504730781961", "4052739537881", "44945570212853", "308061521170129", "806515533049393", "1304969544928657", "14472334024676221", "61305790721611591", "1779979416004714189", "83621143489848422977" ]
[ "nonn" ]
17
1
1
[ "A000045", "A005478", "A358555" ]
null
Tanya Khovanova, Jan 04 2023
2023-01-06T17:08:54
oeisdata/seq/A358/A358555.seq
bf27aad8479152cd84a211c0ce9f0627
A358556
Triangle read by rows: T(n,k) is the number of regions formed when n points are placed along each edge of a square that divide the edges into n+1 equal parts and a line is continuously drawn from the current point to that k points, 2 <= k <= 2*n, counterclockwise around the square until the starting point is again reached.
[ "2", "5", "21", "2", "5", "5", "4", "61", "2", "5", "29", "5", "73", "25", "105", "2", "5", "25", "5", "5", "31", "141", "11", "157", "2", "5", "5", "5", "85", "5", "153", "4", "25", "61", "229", "2", "5", "25", "5", "73", "33", "5", "15", "245", "71", "297", "22", "317", "2", "5", "25", "5", "65", "29", "165", "5", "269", "81", "333", "25", "385", "109", "401", "2", "5", "5", "5", "61", "5", "153", "16", "5", "91", "377", "4", "449", "125", "61", "37", "509", "2" ]
[ "nonn", "tabf" ]
30
1
1
[ "A331452", "A345459", "A355798", "A355838", "A357058", "A358407", "A358556", "A358574", "A358627" ]
null
Scott R. Shannon, Nov 22 2022
2022-11-24T12:50:45
oeisdata/seq/A358/A358556.seq
40c67a992f33539126d19668b7f6d9a9
A358557
Numbers k for which denominator(H(k)) < LCM(1..k), where harmonic numbers H(k) = Sum_{i=1..k} 1/i = r(k)/q(k).
[ "6", "7", "8", "18", "19", "20", "21", "22", "23", "24", "25", "26", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79", "80", "81", "82", "83", "84", "85", "86", "87", "100", "101", "102" ]
[ "nonn" ]
58
1
1
[ "A001008", "A002805", "A003418", "A098464", "A110566", "A112813", "A330680", "A358557" ]
null
Yifan Xie, Nov 22 2022
2024-01-01T08:02:53
oeisdata/seq/A358/A358557.seq
a7e15ba906a094477f9692aad5ddfba6
A358558
a(n) is the number of pairs (k,m) of positive integers with 1 <= k < m <= n such that gcd(k,m) = 2^t, t > 0.
[ "0", "0", "0", "1", "1", "3", "3", "6", "6", "10", "10", "14", "14", "20", "20", "27", "27", "33", "33", "41", "41", "51", "51", "59", "59", "71", "71", "83", "83", "91", "91", "106", "106", "122", "122", "134", "134", "152", "152", "168", "168", "180", "180", "200", "200", "222", "222", "238", "238", "258", "258", "282", "282", "300", "300", "324", "324", "352", "352", "368", "368" ]
[ "nonn" ]
49
1
6
[ "A000079", "A000523", "A008805", "A049690", "A358558" ]
null
Bernard Schott, Nov 23 2022
2022-11-28T09:59:46
oeisdata/seq/A358/A358558.seq
36046170b5edc49161dc02838b39f2b5
A358559
Decimal expansion of Bi(0), where Bi is the Airy function of the second kind.
[ "6", "1", "4", "9", "2", "6", "6", "2", "7", "4", "4", "6", "0", "0", "0", "7", "3", "5", "1", "5", "0", "9", "2", "2", "3", "6", "9", "0", "9", "3", "6", "1", "3", "5", "5", "3", "5", "9", "4", "7", "2", "8", "1", "8", "8", "6", "4", "8", "5", "9", "6", "5", "0", "5", "0", "4", "0", "8", "7", "8", "7", "5", "3", "0", "1", "4", "2", "9", "6", "5", "1", "9", "3", "0", "5", "5", "2", "0", "6", "4", "0", "5", "2", "9", "3" ]
[ "cons", "nonn" ]
22
0
1
[ "A284867", "A284868", "A358559", "A358561", "A358564" ]
null
Dumitru Damian, Nov 22 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358559.seq
3dad1f4dd420a3506ac229eee056cfe6
A358560
a(n) = Sum_{k=0..floor(n/3)} (n-k)!/(k! * (n-3*k)!).
[ "1", "1", "1", "3", "7", "13", "33", "91", "223", "597", "1753", "4963", "14391", "44413", "137137", "427083", "1382383", "4534981", "14981673", "50719507", "174494983", "605276973", "2135204161", "7647369403", "27643067007", "101211363253", "375548195833", "1406858084931", "5326762882903", "20403498329437" ]
[ "nonn", "easy" ]
18
0
4
[ "A000930", "A118395", "A358547", "A358560" ]
null
Seiichi Manyama, Nov 22 2022
2022-11-25T09:46:10
oeisdata/seq/A358/A358560.seq
df81af46996be7ac229e9482742340ac
A358561
Decimal expansion of the derivative Bi'(0), where Bi is the Airy function of the second kind.
[ "4", "4", "8", "2", "8", "8", "3", "5", "7", "3", "5", "3", "8", "2", "6", "3", "5", "7", "9", "1", "4", "8", "2", "3", "7", "1", "0", "3", "9", "8", "8", "2", "8", "3", "9", "0", "8", "6", "6", "2", "2", "6", "7", "9", "9", "2", "1", "2", "2", "6", "2", "0", "6", "1", "0", "8", "2", "8", "0", "8", "7", "7", "8", "3", "7", "2", "3", "3", "0", "7", "5", "5", "0", "0", "9", "7", "8", "0", "6", "4", "7", "1", "8", "5", "0", "4" ]
[ "cons", "nonn" ]
18
0
1
[ "A284867", "A284868", "A358559", "A358561", "A358564" ]
null
Dumitru Damian, Nov 22 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358561.seq
1edd472105932389f5ad6f80614f6a25
A358562
The number of antichains in the Tamari lattice of order n.
[ "2", "3", "8", "83", "28984", "138832442543" ]
[ "nonn", "hard", "more" ]
18
1
1
[ "A000372", "A027686", "A143673", "A302250", "A358391", "A358562" ]
null
Dmitry I. Ignatov, Nov 22 2022
2023-01-12T19:24:39
oeisdata/seq/A358/A358562.seq
5fc2ace5b75430588b084360569c484f
A358563
The number of maximal antichains in the Tamari lattice of order n.
[ "1", "2", "4", "26", "1979", "161117453" ]
[ "nonn", "hard", "more" ]
12
1
2
[ "A143674", "A326358", "A358041", "A358390", "A358562", "A358563" ]
null
Dmitry I. Ignatov, Nov 22 2022
2023-01-25T09:54:46
oeisdata/seq/A358/A358563.seq
b7daa443764a476f1b115566d952e154
A358564
Decimal expansion of Gi(0), where Gi is the inhomogeneous Airy function of the first kind (also called Scorer function).
[ "2", "0", "4", "9", "7", "5", "5", "4", "2", "4", "8", "2", "0", "0", "0", "2", "4", "5", "0", "5", "0", "3", "0", "7", "4", "5", "6", "3", "6", "4", "5", "3", "7", "8", "5", "1", "1", "9", "8", "2", "4", "2", "7", "2", "9", "5", "4", "9", "5", "3", "2", "1", "6", "8", "3", "4", "6", "9", "5", "9", "5", "8", "4", "3", "3", "8", "0", "9", "8", "8", "3", "9", "7", "6", "8", "5", "0", "6", "8", "8", "0", "1", "7", "6", "4", "6", "2" ]
[ "cons", "nonn" ]
19
0
1
[ "A284867", "A284868", "A358559", "A358561", "A358564" ]
null
Dumitru Damian, Nov 22 2022
2024-11-26T14:53:08
oeisdata/seq/A358/A358564.seq
bb9fd0f0d8d406ab6dc222eefd246466
A358565
a(n) = A358548(n) / 6.
[ "1", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "2", "1", "1", "3", "1", "2", "3", "1", "1", "2", "1", "5", "1", "1", "2", "1", "1", "1", "2", "2", "3", "1", "5", "1", "1", "4", "1", "2", "3", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "6", "1", "1", "3", "1", "1", "3", "4", "1", "1", "1", "3", "1", "3", "3", "4", "3", "2", "4", "2", "2", "1", "2", "3", "1", "3", "1", "4", "3", "2", "1", "1", "3", "1", "1", "5", "1" ]
[ "nonn" ]
23
2
5
[ "A003627", "A358548", "A358565" ]
null
Jordan Gunter, Nov 22 2022
2023-01-06T02:07:56
oeisdata/seq/A358/A358565.seq
4222411f38b5b8197e6d3b98934bc7a2
A358566
Number of distinct spans of length n with no 3-term arithmetic progression, containing zero, and with maximum element smallest possible.
[ "1", "1", "2", "1", "4", "7", "6", "1", "2", "2", "2", "1", "2", "2", "20", "1", "14", "2", "2", "2", "4" ]
[ "nonn", "more" ]
21
1
3
[ "A005047", "A358566" ]
null
Joshua Zelinsky, Nov 22 2022
2022-12-20T12:02:36
oeisdata/seq/A358/A358566.seq
4bb22cd4ef4bf69b9a3f29e504fa3113
A358567
a(n) is the minimal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
[ "1", "0", "-2", "-31", "-1297", "-39837", "-2256911", "-99518694" ]
[ "sign", "hard", "more" ]
10
0
3
[ "A350930", "A358567", "A358568", "A358569", "A358570" ]
null
Stefano Spezia, Nov 22 2022
2022-12-03T09:19:04
oeisdata/seq/A358/A358567.seq
fe7fdc0aed8d21ee14f92d515284d4f5
A358568
a(n) is the maximal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
[ "1", "0", "4", "74", "1781", "58180", "2579770", "152337045" ]
[ "nonn", "hard", "more" ]
11
0
3
[ "A350931", "A358567", "A358568", "A358569", "A358570" ]
null
Stefano Spezia, Nov 22 2022
2022-12-03T09:19:17
oeisdata/seq/A358/A358568.seq
9aa14a1eebd54a7ae42ab2599e8e9066
A358569
a(n) is the minimal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
[ "1", "0", "1", "16", "451", "17376", "1022546" ]
[ "nonn", "hard", "more" ]
13
0
4
[ "A350937", "A358567", "A358568", "A358569", "A358570" ]
null
Stefano Spezia, Nov 22 2022
2023-12-28T09:23:20
oeisdata/seq/A358/A358569.seq
8e75bb8cff101a58f86f5b41149de2b9
A358570
a(n) is the maximal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
[ "1", "0", "4", "121", "6109", "494610", "58369622" ]
[ "nonn", "hard", "more" ]
12
0
3
[ "A350938", "A358567", "A358568", "A358569", "A358570" ]
null
Stefano Spezia, Nov 22 2022
2023-12-30T23:46:19
oeisdata/seq/A358/A358570.seq
a2c762bbb3a47a0892f9d27523c732a6
A358571
Lesser p of a sexy prime pair such that (p-3)/2 is also the lesser prime of a sexy prime pair.
[ "13", "17", "37", "97", "457", "557", "1117", "1217", "1297", "2237", "2377", "2897", "4937", "7237", "9277", "10457", "18797", "21317", "23557", "24077", "27817", "29437", "30757", "34757", "38917", "39157", "48157", "48817", "50497", "55897", "60617", "62297", "64997", "72617", "81157", "82457", "90017", "94597", "107837", "108877", "111857" ]
[ "nonn" ]
17
1
1
[ "A023201", "A254636", "A255361", "A256386", "A358571" ]
null
Lamine Ngom, Nov 23 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358571.seq
117e92b9cd2089bd0417a09473dbf248
A358572
Smallest prime p in a sexy prime triple such that (p-3)/2 is also the smallest prime in a sexy prime triple (A023241).
[ "17", "97", "1117", "1217", "2897", "130337", "188857", "207997", "221197", "324517", "610817", "900577", "1090877", "1452317", "1719857", "1785097", "2902477", "3069917", "3246317", "4095097", "4536517", "4977097", "5153537", "5517637", "5745557", "6399677", "7168277", "7351957", "7588697", "7661077", "8651537", "8828497", "9153337" ]
[ "nonn" ]
18
1
1
[ "A023201", "A023241", "A046118", "A254636", "A255361", "A256386", "A358571", "A358572" ]
null
Lamine Ngom, Nov 23 2022
2022-12-31T15:28:43
oeisdata/seq/A358/A358572.seq
14353251bab0d85bc445f250b43fe3de
A358573
a(n) = smallest prime p such that q, r and s are all prime, where q = p + 2*(2*n + 1), r = (p - 2*n - 1)/2, and s = (q + 2*n + 1)/2.
[ "11", "13", "19", "17", "19", "229", "47", "29", "163", "29", "31", "37", "47", "53", "1231", "41", "43", "61", "83", "61", "439", "1217", "59", "73", "59", "61", "67", "89", "83", "541", "71", "73", "103", "593", "271", "349", "83", "89", "103", "461", "239", "97", "107", "97", "211", "149", "107", "229", "263", "181", "499", "317", "139", "1453", "131", "809", "127", "137", "163" ]
[ "nonn" ]
15
0
1
[ "A001097", "A001359", "A006512", "A023201", "A077800", "A158870", "A254636", "A255361", "A256386", "A358573" ]
null
Lamine Ngom, Nov 23 2022
2022-12-31T15:29:02
oeisdata/seq/A358/A358573.seq
a364eb06a58663ee491c1ca9f1e5fca3
A358574
Triangle read by rows: T(n,k) is the number of vertices formed when n points are placed along each edge of a square that divide the edges into n+1 equal parts and a line is continuously drawn from the current point to that k points, 2 <= k <= 2*n, counterclockwise around the square until the starting point is again reached.
[ "8", "12", "20", "12", "16", "16", "16", "64", "16", "20", "36", "20", "68", "36", "100", "20", "24", "36", "24", "24", "44", "144", "29", "144", "24", "28", "28", "28", "92", "28", "140", "28", "44", "76", "208", "28", "32", "44", "32", "84", "52", "32", "39", "240", "88", "292", "46", "296", "32", "36", "48", "36", "80", "52", "164", "36", "252", "100", "316", "52", "368", "124", "364", "36", "40", "40", "40", "80", "40", "164", "47", "40", "112", "364", "40", "436", "144", "88", "67", "472", "40" ]
[ "nonn", "tabf" ]
25
1
1
[ "A331452", "A345459", "A355798", "A355838", "A357058", "A358407", "A358556", "A358574", "A358627" ]
null
Scott R. Shannon, Nov 23 2022
2022-11-24T12:51:06
oeisdata/seq/A358/A358574.seq
715f492437f1359c9742103c02f607c5
A358575
Triangle read by rows where T(n,k) is the number of unlabeled n-node rooted trees with k = 0..n-1 internal (non-leaf) nodes.
[ "1", "0", "1", "0", "1", "1", "0", "1", "2", "1", "0", "1", "3", "4", "1", "0", "1", "4", "8", "6", "1", "0", "1", "5", "14", "18", "9", "1", "0", "1", "6", "21", "39", "35", "12", "1", "0", "1", "7", "30", "72", "97", "62", "16", "1", "0", "1", "8", "40", "120", "214", "212", "103", "20", "1", "0", "1", "9", "52", "185", "416", "563", "429", "161", "25", "1" ]
[ "nonn", "tabl" ]
7
1
9
[ "A000081", "A000108", "A000891", "A001263", "A002620", "A006578", "A034781", "A055277", "A065097", "A090181", "A109129", "A185650", "A342507", "A358575", "A358578", "A358581", "A358582", "A358583", "A358584", "A358587", "A358589" ]
null
Gus Wiseman, Nov 23 2022
2022-11-25T07:22:53
oeisdata/seq/A358/A358575.seq
672d82ab07c2c6353dd124ec1e1cefe0
A358576
Matula-Goebel numbers of rooted trees whose node-height equals their number of internal (non-leaf) nodes.
[ "9", "15", "18", "21", "23", "30", "33", "35", "36", "39", "42", "46", "47", "49", "51", "57", "60", "61", "66", "70", "72", "73", "77", "78", "83", "84", "87", "91", "92", "93", "94", "95", "98", "102", "111", "113", "114", "119", "120", "122", "123", "129", "132", "133", "137", "140", "144", "146", "149", "151", "154", "156", "159", "166", "167", "168", "174", "177", "181" ]
[ "nonn" ]
13
1
1
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A209638", "A342507", "A358552", "A358576", "A358577", "A358578", "A358580", "A358581", "A358586", "A358587", "A358588", "A358589", "A358590", "A358592", "A358729" ]
null
Gus Wiseman, Nov 25 2022
2022-12-01T17:39:43
oeisdata/seq/A358/A358576.seq
dc3a224a3c077c86ed4ae82799ef82ee
A358577
Matula-Goebel numbers of "square" rooted trees, i.e., whose height equals their number of leaves.
[ "1", "4", "12", "14", "18", "19", "21", "27", "40", "52", "60", "68", "70", "74", "78", "86", "89", "90", "91", "92", "95", "100", "102", "105", "107", "111", "117", "119", "122", "129", "130", "134", "135", "138", "146", "150", "151", "153", "161", "163", "169", "170", "175", "176", "181", "183", "185", "195", "201", "206", "207", "215", "219", "221", "225", "227", "230" ]
[ "nonn" ]
10
1
2
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A342507", "A358379", "A358552", "A358576", "A358577", "A358578", "A358579", "A358580", "A358581", "A358586", "A358587", "A358588", "A358589", "A358590", "A358592" ]
null
Gus Wiseman, Nov 25 2022
2022-11-25T16:41:39
oeisdata/seq/A358/A358577.seq
2f808226c46a148d40f4c4bbfd3c1776
A358578
Matula-Goebel numbers of rooted trees whose number of leaves equals their number of internal (non-leaf) nodes.
[ "2", "6", "7", "18", "20", "21", "26", "34", "37", "43", "54", "60", "63", "67", "70", "78", "88", "91", "92", "95", "102", "111", "116", "119", "122", "129", "142", "146", "151", "162", "164", "173", "180", "181", "189", "200", "201", "202", "210", "227", "234", "236", "239", "245", "260", "264", "269", "273", "276", "278", "285", "306", "308", "314", "322", "333", "337" ]
[ "nonn" ]
9
1
1
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A342507", "A358371", "A358552", "A358576", "A358577", "A358578", "A358579", "A358580", "A358581", "A358586", "A358587", "A358588", "A358589", "A358590", "A358592" ]
null
Gus Wiseman, Nov 25 2022
2022-11-25T16:41:43
oeisdata/seq/A358/A358578.seq
5b760c5763e48ecc9c69befbca746f78
A358579
Numbers k such that the k-th standard ordered rooted tree has the same number of leaves as internal (non-leaf) nodes.
[ "2", "6", "7", "9", "20", "22", "23", "26", "27", "29", "35", "41", "66", "76", "78", "79", "84", "86", "87", "90", "91", "93", "97", "102", "103", "106", "107", "109", "115", "117", "130", "136", "138", "139", "141", "146", "153", "163", "169", "193", "196", "197", "201", "226", "241", "262", "263", "296", "300", "302", "303", "308", "310", "311", "314", "315", "317" ]
[ "nonn" ]
6
1
1
[ "A000081", "A000108", "A000891", "A001263", "A014221", "A055277", "A185650", "A206487", "A358371", "A358372", "A358373", "A358379", "A358553", "A358576", "A358577", "A358578", "A358579", "A358580", "A358587", "A358588", "A358589", "A358590" ]
null
Gus Wiseman, Nov 25 2022
2022-11-26T12:34:55
oeisdata/seq/A358/A358579.seq
fded36a3939ceb694ba4636c38d0eb4c
A358580
Difference between the number of leaves and the number of internal (non-leaf) nodes in the rooted tree with Matula-Goebel number n.
[ "1", "0", "-1", "1", "-2", "0", "0", "2", "-1", "-1", "-3", "1", "-1", "1", "-2", "3", "-1", "0", "1", "0", "0", "-2", "-2", "2", "-3", "0", "-1", "2", "-2", "-1", "-4", "4", "-3", "0", "-1", "1", "0", "2", "-1", "1", "-2", "1", "0", "-1", "-2", "-1", "-3", "3", "1", "-2", "-1", "1", "2", "0", "-4", "3", "1", "-1", "-2", "0", "-1", "-3", "0", "5", "-2", "-2", "0", "1", "-2", "0", "-1", "2", "-1", "1", "-3" ]
[ "sign" ]
4
1
5
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A342507", "A358371", "A358552", "A358576", "A358577", "A358578", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358592" ]
null
Gus Wiseman, Nov 25 2022
2022-11-26T12:35:32
oeisdata/seq/A358/A358580.seq
4dfe156dd923506baa0d9b34e173a184
A358581
Number of rooted trees with n nodes, most of which are leaves.
[ "1", "0", "1", "1", "4", "5", "20", "28", "110", "169", "663", "1078", "4217", "7169", "27979", "49191", "191440", "345771", "1341974", "2477719", "9589567", "18034670", "69612556", "132984290", "511987473", "991391707", "3807503552", "7460270591", "28585315026", "56595367747", "216381073935", "432396092153" ]
[ "nonn" ]
15
1
5
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A109129", "A185650", "A342507", "A358575", "A358577", "A358578", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358585", "A358586", "A358589", "A358590", "A358591" ]
null
Gus Wiseman, Nov 23 2022
2022-12-31T15:05:08
oeisdata/seq/A358/A358581.seq
224e6d59759854d34a862b08a50ff95d
A358582
Number of rooted trees with n nodes, most of which are not leaves.
[ "0", "0", "1", "1", "5", "7", "28", "48", "176", "336", "1179", "2420", "8269", "17855", "59832", "134289", "443407", "1025685", "3346702", "7933161", "25632265", "62000170", "198670299", "488801159", "1555187172", "3882403641", "12276230777", "31034921462", "97601239282", "249471619165", "780790439063", "2015194486878" ]
[ "nonn" ]
9
1
5
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A090181", "A109129", "A185650", "A342507", "A358575", "A358577", "A358578", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358585", "A358586", "A358589", "A358590", "A358591" ]
null
Gus Wiseman, Nov 23 2022
2022-12-30T21:38:34
oeisdata/seq/A358/A358582.seq
7ed4dc02f45cb7a1eb25893682b8d077
A358583
Number of rooted trees with n nodes, at least half of which are leaves.
[ "1", "1", "1", "3", "4", "13", "20", "67", "110", "383", "663", "2346", "4217", "15118", "27979", "101092", "191440", "695474", "1341974", "4893067", "9589567", "35055011", "69612556", "254923825", "511987473", "1877232869", "3807503552", "13972144807", "28585315026", "104955228432", "216381073935", "794739865822" ]
[ "nonn" ]
9
1
4
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A090181", "A109129", "A185650", "A342507", "A358575", "A358577", "A358578", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358585", "A358586", "A358589", "A358590" ]
null
Gus Wiseman, Nov 23 2022
2022-12-31T15:05:20
oeisdata/seq/A358/A358583.seq
ed2d960aaf0b8192f2c6eee141cf04e9
A358584
Number of rooted trees with n nodes, at most half of which are leaves.
[ "0", "1", "1", "3", "5", "15", "28", "87", "176", "550", "1179", "3688", "8269", "25804", "59832", "186190", "443407", "1375388", "3346702", "10348509", "25632265", "79020511", "198670299", "610740694", "1555187172", "4768244803", "12276230777", "37546795678", "97601239282", "297831479850", "780790439063", "2377538260547" ]
[ "nonn" ]
11
1
4
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A090181", "A109129", "A185650", "A342507", "A358575", "A358577", "A358578", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358585", "A358586", "A358589", "A358590", "A358591" ]
null
Gus Wiseman, Nov 23 2022
2022-12-30T21:38:42
oeisdata/seq/A358/A358584.seq
96395e3390bb33e22a51676f5ca327b7
A358585
Number of ordered rooted trees with n nodes, most of which are leaves.
[ "1", "0", "1", "1", "7", "11", "66", "127", "715", "1549", "8398", "19691", "104006", "258194", "1337220", "3467115", "17678835", "47440745", "238819350", "659060677", "3282060210", "9271024542", "45741281820", "131788178171", "644952073662", "1890110798926", "9183676536076", "27316119923002", "131873975875180", "397407983278484" ]
[ "nonn" ]
17
1
5
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A109129", "A185650", "A342507", "A358371", "A358575", "A358577", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358585", "A358586", "A358588", "A358589", "A358590" ]
null
Gus Wiseman, Nov 24 2022
2024-01-13T16:13:32
oeisdata/seq/A358/A358585.seq
ec573b1cbebc2765e4ee09a7c972302a
A358586
Number of ordered rooted trees with n nodes, at least half of which are leaves.
[ "1", "1", "1", "4", "7", "31", "66", "302", "715", "3313", "8398", "39095", "104006", "484706", "1337220", "6227730", "17678835", "82204045", "238819350", "1108202513", "3282060210", "15195242478", "45741281820", "211271435479", "644952073662", "2971835602526", "9183676536076", "42217430993002", "131873975875180", "604834233372884" ]
[ "nonn" ]
9
1
4
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A109129", "A185650", "A342507", "A358371", "A358575", "A358577", "A358579", "A358580", "A358581", "A358582", "A358583", "A358584", "A358585", "A358586", "A358588", "A358589", "A358590" ]
null
Gus Wiseman, Nov 24 2022
2024-01-13T16:13:28
oeisdata/seq/A358/A358586.seq
d8c88836d5bfb0808c216ba5d5e7839f
A358587
Number of n-node rooted trees of height equal to the number of internal (non-leaf) nodes.
[ "0", "0", "0", "0", "1", "4", "14", "41", "111", "282", "688", "1627", "3761", "8540", "19122", "42333", "92851", "202078", "436916", "939359", "2009781", "4281696", "9087670", "19223905", "40544951", "85284194", "178956984", "374691171", "782936761", "1632982372", "3400182458", "7068800357", "14674471611", "30422685030" ]
[ "nonn" ]
14
1
6
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A185650", "A342507", "A358552", "A358575", "A358576", "A358577", "A358578", "A358581", "A358584", "A358587", "A358588", "A358589", "A358590", "A358591" ]
null
Gus Wiseman, Nov 23 2022
2024-04-15T04:56:44
oeisdata/seq/A358/A358587.seq
fd67fae0b5f5013ec705c8ef64e34be6
A358588
Number of n-node ordered rooted trees of height equal to the number of internal (non-leaf) nodes.
[ "0", "0", "0", "0", "1", "8", "41", "171", "633", "2171", "7070", "22195", "67830", "203130", "598806", "1743258", "5023711", "14356226", "40737383", "114904941", "322432215", "900707165", "2506181060", "6948996085", "19207795836", "52944197508", "145567226556", "399314965956", "1093107693133", "2986640695436" ]
[ "nonn" ]
12
1
6
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A185650", "A342507", "A358371", "A358552", "A358575", "A358576", "A358578", "A358579", "A358586", "A358587", "A358588", "A358589", "A358590", "A358591" ]
null
Gus Wiseman, Nov 25 2022
2024-04-15T04:57:31
oeisdata/seq/A358/A358588.seq
edf4818b66f5b479face337ba5fb1046
A358589
Number of square rooted trees with n nodes.
[ "1", "0", "1", "0", "3", "2", "11", "17", "55", "107", "317", "720", "1938", "4803", "12707", "32311", "85168", "220879", "581112", "1522095", "4014186", "10568936", "27934075", "73826753", "195497427", "517927859", "1373858931", "3646158317", "9684878325", "25737819213", "68439951884", "182070121870", "484583900955", "1290213371950" ]
[ "nonn" ]
12
1
5
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A109129", "A185650", "A358552", "A358575", "A358576", "A358577", "A358578", "A358587", "A358588", "A358589", "A358590", "A358591" ]
null
Gus Wiseman, Nov 23 2022
2023-01-01T12:34:46
oeisdata/seq/A358/A358589.seq
8422e89a0d2a1f7bf4cb7ed729664d1c
A358590
Number of square ordered rooted trees with n nodes.
[ "1", "0", "1", "0", "6", "5", "36", "84", "309", "890", "3163", "9835", "32979", "108252", "360696", "1192410", "3984552", "13276769", "44371368", "148402665", "497072593", "1665557619", "5586863093", "18750662066", "62968243731", "211565969511", "711187790166", "2391640404772", "8045964959333", "27077856222546" ]
[ "nonn" ]
9
1
5
[ "A000081", "A000108", "A000891", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A109129", "A185650", "A358371", "A358552", "A358575", "A358577", "A358579", "A358586", "A358587", "A358588", "A358589", "A358590" ]
null
Gus Wiseman, Nov 25 2022
2023-01-02T00:06:12
oeisdata/seq/A358/A358590.seq
4ac08dc4c1c193e4ab988030c87d405a
A358591
Number of 2n-node rooted trees whose height, number of leaves, and number of internal (non-leaf) nodes are all equal.
[ "0", "0", "2", "17", "94", "464", "2162", "9743", "42962", "186584", "801316", "3412034", "14430740", "60700548", "254180426", "1060361147", "4409342954", "18285098288", "75645143516", "312286595342", "1286827096964", "5293833371408", "21745951533236", "89208948855542", "365523293690804", "1496048600896784" ]
[ "nonn" ]
10
1
3
[ "A000081", "A000108", "A001263", "A034781", "A055277", "A065097", "A080936", "A090181", "A109082", "A109129", "A185650", "A342507", "A358552", "A358575", "A358576", "A358577", "A358578", "A358581", "A358586", "A358587", "A358588", "A358589", "A358590", "A358591", "A358592" ]
null
Gus Wiseman, Nov 23 2022
2023-01-01T14:46:36
oeisdata/seq/A358/A358591.seq
ccd8281a7d76cacebf68ce5232b0e513
A358592
Matula-Goebel numbers of rooted trees whose height, number of leaves, and number of internal (non-leaf) nodes are all equal.
[ "18", "21", "60", "70", "78", "91", "92", "95", "102", "111", "119", "122", "129", "146", "151", "181", "201", "227", "264", "269", "308", "348", "376", "406", "418", "426", "452", "492", "497", "519", "551", "562", "574", "583", "596", "606", "659", "664", "668", "698", "707", "708", "717", "779", "794", "796", "809", "826", "834", "911", "932", "934", "942", "958" ]
[ "nonn" ]
6
1
1
[ "A000040", "A000081", "A000108", "A000720", "A001222", "A001263", "A007097", "A034781", "A055277", "A056239", "A061775", "A109082", "A109129", "A112798", "A185650", "A196050", "A206487", "A342507", "A358552", "A358576", "A358577", "A358578", "A358579", "A358580", "A358581", "A358586", "A358587", "A358588", "A358589", "A358590", "A358592" ]
null
Gus Wiseman, Nov 25 2022
2022-11-26T12:35:20
oeisdata/seq/A358/A358592.seq
a7a6a5086d8ef3598dc72679a9ebf29c
A358593
a(n) = n! * Sum_{d|n} d^(n-d) / d!^(n/d).
[ "1", "3", "7", "49", "121", "2701", "5041", "219521", "1587601", "33446701", "39916801", "17731796545", "6227020801", "2879710009177", "98069239768501", "2418218838097921", "355687428096001", "2832293713653708877", "121645100408832001", "2295597943489176040001", "71029619657111138063041" ]
[ "nonn" ]
19
1
2
[ "A038507", "A061095", "A354891", "A356668", "A358593" ]
null
Seiichi Manyama, Feb 23 2023
2023-07-31T02:25:45
oeisdata/seq/A358/A358593.seq
d076d4937224a7465c4ad3652f128ace
A358594
Expansion of e.g.f. Sum_{k>0} x^k / ((k-1)! - x^k).
[ "1", "4", "9", "52", "125", "1626", "5047", "81768", "408249", "7263910", "39916811", "990191676", "6227020813", "174356750582", "1348633786515", "41861724727696", "355687428096017", "12904788209623614", "121645100408832019", "4866124222538035620", "51490090294307945301", "2248001455555300717294" ]
[ "nonn" ]
16
1
2
[ "A061095", "A356668", "A358594" ]
null
Seiichi Manyama, Feb 23 2023
2023-07-31T02:25:48
oeisdata/seq/A358/A358594.seq
241468b6a6b125ca70fd1fa5c49081df
A358595
a(n) = n! * Sum_{d|n} d^n / d!^(n/d).
[ "1", "6", "33", "376", "3245", "67716", "828583", "22050176", "420850809", "12580687900", "285351587411", "11736333558720", "302881333613053", "13450914411140584", "463402585399165875", "22345557703564558336", "827240617573764860177", "48442529220731147887020" ]
[ "nonn" ]
17
1
2
[ "A354890", "A358593", "A358595" ]
null
Seiichi Manyama, Feb 23 2023
2023-07-31T02:25:01
oeisdata/seq/A358/A358595.seq
a26f482c8a5977b8e76cbe9b1d37f31b
A358596
a(n) is the least prime p such that the concatenation p|n has exactly n prime factors with multiplicity.
[ "3", "2", "83", "2", "67", "41", "947", "4519", "15659081", "2843", "337957", "389", "1616171", "6132829", "422116888343", "24850181", "377519743", "194486417892947", "533348873", "324403", "980825013273164555563", "25691144027", "273933405157", "1238831928746353181", "311195507789", "129917586781", "2159120477658983490299" ]
[ "nonn", "base" ]
24
1
1
[ "A001222", "A066686", "A358596" ]
null
Zak Seidov and Robert Israel, Feb 24 2023
2023-03-03T22:35:02
oeisdata/seq/A358/A358596.seq
cee1ca38b6953f92373a3236c5192cff
A358597
Number of n-tuples (p_1, p_2, ..., p_n) of Dyck paths of semilength n+1, such that each p_i is never below p_{i-1}.
[ "1", "2", "14", "330", "26026", "6852768", "6018114036", "17618122000050", "171879976152056250", "5586863607659640852000", "604960371578930672694585600", "218201797452928091289631307694720", "262138086905421645845923269465748817136", "1048861003938217198101763464819634006647101600" ]
[ "nonn" ]
16
0
2
[ "A074962", "A078920", "A123352", "A355400", "A358597" ]
null
Alois P. Heinz, Feb 24 2023
2023-09-04T19:37:31
oeisdata/seq/A358/A358597.seq
cef0439a118a7f3482975bce881cf817
A358598
Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 4 children down to the generation of M.
[ "1", "6", "40", "300", "2356", "18756", "149860", "1198500", "9587236", "76696356", "613567780", "4908536100", "39268276516", "314146187556", "2513169451300", "20105355512100", "160842843900196", "1286742750808356", "10293942005680420", "82351536043870500", "658812288347818276", "5270498306776254756" ]
[ "easy", "nonn" ]
33
0
2
[ "A000079", "A076024", "A108019", "A358504", "A358598", "A358599", "A358600", "A358601" ]
null
Hans Braxmeier, Nov 19 2022
2024-02-09T07:44:59
oeisdata/seq/A358/A358598.seq
f7f4e267f43f4d1a5632ff85a885cb15
A358599
Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 5 children down to the generation of M.
[ "1", "7", "59", "563", "5571", "55587", "555619", "5555683", "55555811", "555556067", "5555556579", "55555557603", "555555559651", "5555555563747", "55555555571939", "555555555588323", "5555555555621091", "55555555555686627", "555555555555817699", "5555555555556079843", "55555555555556604131" ]
[ "nonn", "easy" ]
24
0
2
[ "A000079", "A002279", "A076024", "A358504", "A358598", "A358599", "A358600", "A358601" ]
null
Hans Braxmeier, Nov 23 2022
2022-12-06T15:48:25
oeisdata/seq/A358/A358599.seq
ba4bf9bee4ee0e9cc65e73855590ada9
A358600
Number of genetic relatives of a person M in a genealogical tree extending back n generations and where everyone has 6 children down to the generation of M.
[ "1", "8", "82", "950", "11326", "135758", "1628782", "19544750", "234535726", "2814426158", "33773108782", "405277295150", "4863327521326", "58359930214958", "700319162497582", "8403829949807150", "100845959397358126", "1210151512767642158", "14521818153210395182", "174261817838522120750" ]
[ "nonn", "easy" ]
24
0
2
[ "A076024", "A358504", "A358598", "A358599", "A358600", "A358601" ]
null
Hans Braxmeier, Nov 23 2022
2022-12-06T03:22:45
oeisdata/seq/A358/A358600.seq
066e1de58aec8f6a5a3fb3f9aba3c69c