Datasets:
christopher
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oeis

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2
sequence_id
stringlengths
7
7
sequence_name
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4
573
sequence
listlengths
1
348
keywords
listlengths
1
8
score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
listlengths
1
128
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listlengths
1
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author
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7
231
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-19 00:40:46
filename
stringlengths
29
29
hash
stringlengths
32
32
A383421
a(1)=1; thereafter if a(n-1) is a first occurrence, then a(n) is the number of values that occur exactly once in the sequence thus far. Otherwise; a(n) is the number of terms that are the same distance away from an earlier equal value as a(n-1) is from its previous last occurrence.
[ "1", "1", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "2", "3", "4", "5", "1", "3", "6", "2", "5", "4", "6", "7", "1", "2", "2", "3", "2", "4", "3", "6", "5", "2", "5", "5", "4", "9", "2", "6", "5", "7", "3", "4", "10", "2", "11", "3", "8", "4", "4", "5", "5", "6", "9", "10", "6", "8", "6", "6", "7", "7", "8", "10", "7", "10", "7", "8", "12", "2", "3", "5", "10", "13", "3", "9", "8", "8", "9", "11", "5", "9", "12", "12" ]
[ "nonn" ]
13
1
4
[ "A383339", "A383340", "A383421" ]
null
Neal Gersh Tolunsky, Apr 26 2025
2025-05-09T22:33:49
oeisdata/seq/A383/A383421.seq
f497f13463844ef03e2826ea4aef26e8
A383422
The infinite Lucas word; the limiting word generated by s(0) = 0, s(1) = 011, and s(n) = s(n-1)s(n-2).
[ "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1" ]
[ "nonn" ]
21
0
null
[ "A000032", "A000045", "A050140", "A287775", "A383422", "A383423", "A383424", "A383425", "A383426", "A383427" ]
null
Clark Kimberling, Apr 27 2025
2025-06-06T00:09:53
oeisdata/seq/A383/A383422.seq
6b99c810d1a741425558be54e0608c24
A383423
Indices k such that A003849(k) = 0 and A383422(k) = 0.
[ "0", "3", "7", "10", "11", "15", "18", "21", "28", "29", "32", "36", "39", "44", "47", "50", "54", "57", "58", "62", "65", "68", "75", "76", "79", "83", "86", "87", "91", "94", "97", "104", "105", "109", "112", "115", "120", "123", "126", "130", "133", "134", "138", "141", "144", "151", "152", "155", "159", "162", "167", "170", "173", "180", "181", "185", "188", "191" ]
[ "nonn" ]
17
1
2
[ "A003849", "A383422", "A383423", "A383424", "A383425", "A383426", "A383427" ]
null
Clark Kimberling, Apr 27 2025
2025-05-22T17:50:38
oeisdata/seq/A383/A383423.seq
ccb139d23b7cefea1f27f7d9bbeaabd9
A383424
Indices k such that A003849(k) = 1 and A383422(k) = 1.
[ "1", "6", "9", "12", "17", "19", "27", "30", "35", "38", "46", "48", "53", "56", "59", "64", "67", "74", "77", "82", "85", "88", "93", "95", "103", "106", "111", "114", "122", "124", "129", "132", "135", "140", "142", "150", "153", "158", "161", "169", "171", "179", "182", "187", "190", "197", "200", "205", "208", "211", "216", "218", "226", "229", "234", "237", "245" ]
[ "nonn" ]
11
1
2
[ "A003849", "A383422", "A383423", "A383424", "A383425", "A383426", "A383427" ]
null
Clark Kimberling, Apr 27 2025
2025-05-07T01:01:47
oeisdata/seq/A383/A383424.seq
7eebb4e63665d80b5ac0d4ff6fcb55cd
A383425
Indices k such that A003849(k) = 0 and A383422(k) = 1.
[ "2", "5", "8", "13", "16", "20", "23", "24", "26", "31", "34", "37", "41", "42", "45", "49", "52", "55", "60", "63", "66", "70", "71", "73", "78", "81", "84", "89", "92", "96", "99", "100", "102", "107", "110", "113", "117", "118", "121", "125", "128", "131", "136", "139", "143", "146", "147", "149", "154", "157", "160", "164", "165", "168", "172", "175", "176", "178" ]
[ "nonn" ]
11
1
1
[ "A003849", "A383422", "A383423", "A383424", "A383425", "A383426", "A383427" ]
null
Clark Kimberling, Apr 27 2025
2025-05-07T01:01:15
oeisdata/seq/A383/A383425.seq
26a9f33336cedac0d6183ecaf2aa31f1
A383426
Indices k such that A003849(k) = 1 and A383422(k) = 0.
[ "4", "14", "22", "25", "33", "40", "43", "51", "61", "69", "72", "80", "90", "98", "101", "108", "116", "119", "127", "137", "145", "148", "156", "163", "166", "174", "177", "184", "192", "195", "203", "213", "221", "224", "232", "239", "242", "250", "260", "268", "271", "279", "286", "289", "297" ]
[ "nonn" ]
16
1
1
[ "A003849", "A383422", "A383423", "A383424", "A383425", "A383426", "A383427" ]
null
Clark Kimberling, Apr 27 2025
2025-05-22T17:50:19
oeisdata/seq/A383/A383426.seq
4a55951d25e349d68199c996e3a4acc5
A383427
Indices k such that A003849(k) = A383422(k).
[ "0", "1", "3", "6", "7", "9", "10", "11", "12", "15", "17", "18", "19", "21", "27", "28", "29", "30", "32", "35", "36", "38", "39", "44", "46", "47", "48", "50", "53", "54", "56", "57", "58", "59", "62", "64", "65", "67", "68", "74", "75", "76", "77", "79", "82", "83", "85", "86", "87", "88", "91", "93", "94", "95", "97", "103", "104", "105", "106", "109", "111", "112", "114", "115" ]
[ "nonn" ]
11
1
3
[ "A003849", "A383422", "A383423", "A383424", "A383425", "A383426", "A383427" ]
null
Clark Kimberling, Apr 27 2025
2025-05-07T00:59:49
oeisdata/seq/A383/A383427.seq
945bff7f2a5ae30ffaaf600421c57012
A383428
Primitive terms in A066192: number k such that k is a term of A066192 and k/2 is not.
[ "4", "12", "56", "120", "528", "672", "992", "1456", "2160", "2208", "6720", "9024", "9120", "11904", "13104", "16256", "17472", "24800", "29568", "55104", "55552", "73440", "90816", "95040", "119040", "120960", "121024", "123648", "131040", "146688", "151680", "174720", "195072", "223104", "297600", "397440", "399616", "445536", "505344" ]
[ "nonn" ]
10
1
1
[ "A000396", "A066191", "A066192", "A069519", "A091570", "A383428" ]
null
Amiram Eldar, Apr 27 2025
2025-04-27T09:08:37
oeisdata/seq/A383/A383428.seq
d9d13f746b2a1f7972f956dddefa76ba
A383429
a(1)=1, and for n>1, a(n) = a(n-1) concatenated with the length of the decimal representation of a(n-1).
[ "1", "11", "112", "1123", "11234", "112345", "1123456", "11234567", "112345678", "1123456789", "112345678910", "11234567891012", "1123456789101214", "112345678910121416", "11234567891012141618", "1123456789101214161820", "112345678910121416182022", "11234567891012141618202224" ]
[ "nonn", "base", "easy" ]
12
1
2
[ "A007908", "A055642", "A117804", "A383429" ]
null
Jason Bard, Apr 27 2025
2025-05-05T00:26:02
oeisdata/seq/A383/A383429.seq
53fdfef8740da71376b71a18c33989f7
A383430
a(n) is the size of the largest subset of {1,...,n} such that no two elements differ by 5 or 8.
[ "1", "2", "3", "4", "5", "5", "5", "5", "5", "5", "6", "6", "6", "7", "8", "8", "9", "10", "10", "10", "11", "11", "11", "12", "12", "12", "13", "14", "14", "15", "16", "16", "16", "17", "17", "17", "18", "18", "18", "19", "20", "20", "21", "22", "22", "22", "23", "23", "23", "24", "24", "24", "25", "26", "26", "27", "28", "28", "28", "29", "29", "29", "30", "30", "30", "31", "32", "32", "33", "34", "34", "34", "35", "35", "35", "36" ]
[ "nonn", "easy" ]
37
1
2
[ "A369149", "A383430" ]
null
Andrej Jakobcic, May 05 2025
2025-05-13T17:07:45
oeisdata/seq/A383/A383430.seq
97e4896fb798994ba414c34d238ff8e1
A383431
a(n) is the denominator of tanh(Sum_{k=1..n-1} artanh(k/n)), where artanh is the inverse hyperbolic tangent function.
[ "1", "2", "11", "18", "127", "463", "1717", "3218", "24311", "92379", "352717", "1352079", "5200301", "20058301", "77558761", "150270098", "1166803111", "4537567651", "17672631901", "68923264411", "269128937221", "1052049481861", "4116715363801", "16123801841551", "63205303218877", "247959266474053", "973469712824057", "3824345300380221", "15033633249770521" ]
[ "nonn", "frac" ]
12
1
2
[ "A001700", "A382257", "A383431" ]
null
Thomas Ordowski, Apr 27 2025
2025-04-29T12:52:10
oeisdata/seq/A383/A383431.seq
f07e828b1ac28d5bc80a4b4050f94eb4
A383432
Decimal expansion of the multiple prime zeta value p[2, 1, 1].
[ "0", "3", "7", "1", "6", "7", "3", "4", "3", "5", "4" ]
[ "nonn", "cons", "more" ]
17
0
2
[ "A085541", "A085548", "A085965", "A382234", "A382235", "A382236", "A382634", "A382635", "A382636", "A382637", "A383432" ]
null
Artur Jasinski, Apr 27 2025
2025-05-20T10:41:39
oeisdata/seq/A383/A383432.seq
6addd14ef8ecb3c535feca15d4fa05a4
A383433
Number of king permutations on n elements avoiding the mesh pattern (12, {(0,0),(0,2),(1,0),(1,2),(2,1)}).
[ "1", "1", "0", "0", "2", "12", "76", "556", "4592", "42328", "431184", "4812936", "58440200", "767098296", "10826066776", "163496360680", "2631146363384", "44953977477160", "812713132751832", "15501004918724712", "311078390317974872", "6552553451281418472", "144550752700158416920", "3332886257051337065128", "80168754370190239256408" ]
[ "nonn", "easy" ]
6
0
5
[ "A002464", "A382644", "A382645", "A382651", "A383040", "A383107", "A383312", "A383406", "A383407", "A383408", "A383433" ]
null
Dan Li, Apr 27 2025
2025-05-03T21:42:52
oeisdata/seq/A383/A383433.seq
18292d166f4826ccfa79e4a9a762f164
A383434
Number of king permutations on n elements avoiding the mesh pattern (12, {(0,2),(1,0),(1,1),(2,0),(2,1)}).
[ "1", "1", "0", "0", "2", "10", "68", "500", "4170", "38730", "397172", "4459116", "54421082", "717571442", "10167743668", "154104395348", "2487968793386", "42630767594522", "772730550801940", "14773475294401180", "297121458577213850", "6270996358146824738", "138591948457411817684", "3200867594024256790020", "77112844928711640695594" ]
[ "nonn", "easy" ]
6
0
5
[ "A002464", "A382644", "A382645", "A382651", "A383040", "A383107", "A383312", "A383406", "A383407", "A383408", "A383433", "A383434" ]
null
Dan Li, Apr 27 2025
2025-05-03T21:42:32
oeisdata/seq/A383/A383434.seq
5ec6c3e671783a12dd3aa85706c5d942
A383435
Number of minimum dominating sets in the n X n X n grid graph.
[ "1", "4", "3", "34872", "18", "792" ]
[ "nonn", "more" ]
7
1
2
null
null
Eric W. Weisstein, Apr 27 2025
2025-06-19T18:35:24
oeisdata/seq/A383/A383435.seq
bc31fd9bd180480faffbbc962a3648ea
A383436
a(1) = 1; a(n) = 2 + n * Sum_{k=1..n-1} a(k).
[ "1", "4", "17", "90", "562", "4046", "33042", "302098", "3058742", "33986022", "411230866", "5383385882", "75816017838", "1143072268942", "18370804322282", "313528393766946", "5663106612415462", "107932149554271158", "2164639221616216002", "45571352034025600042", "1004848312350264480926", "23159361103691809941342" ]
[ "nonn" ]
12
1
2
[ "A001339", "A007808", "A074143", "A082425", "A082427", "A082428", "A082430", "A383436", "A383437" ]
null
Seiichi Manyama, Apr 27 2025
2025-04-27T09:55:25
oeisdata/seq/A383/A383436.seq
42365bc2faf0a3bf6e5096dd3e9bd501
A383437
a(1) = 1; a(n) = 5 + n * Sum_{k=1..n-1} a(k).
[ "1", "7", "29", "153", "955", "6875", "56145", "513325", "5197415", "57749055", "698763565", "9147450305", "128826591795", "1942308614755", "31215674165705", "532747505761365", "9622751822814655", "183398328858349895", "3678155373214684005", "77434849962414400105", "1707438441671237522315" ]
[ "nonn" ]
12
1
2
[ "A001339", "A007808", "A074143", "A082425", "A082427", "A082428", "A082430", "A383436", "A383437" ]
null
Seiichi Manyama, Apr 27 2025
2025-04-27T09:55:01
oeisdata/seq/A383/A383437.seq
c58b7ac060d5928e1e8aa5d515e51862
A383438
a(n) = Sum_{k=1..n} Product_{p|k, p prime} k/p.
[ "1", "2", "3", "5", "6", "12", "13", "17", "20", "30", "31", "55", "56", "70", "85", "93", "94", "148", "149", "189", "210", "232", "233", "329", "334", "360", "369", "425", "426", "1326", "1327", "1343", "1376", "1410", "1445", "1661", "1662", "1700", "1739", "1899", "1900", "3664", "3665", "3753", "3888", "3934", "3935", "4319", "4326", "4576", "4627", "4731" ]
[ "nonn" ]
12
1
2
[ "A205959", "A383438" ]
null
Peter Luschny, Apr 27 2025
2025-04-27T15:02:32
oeisdata/seq/A383/A383438.seq
b15f460576ae87359430b3376d43cad7
A383439
a(n) = (5*n)!/((n!)^2*(3*n + 1)!).
[ "1", "5", "180", "10010", "678300", "51482970", "4206302100", "361913666400", "32356261929420", "2979510862285100", "280884023785324960", "26990111025198348300", "2634899457411931245900", "260690108634780944767200", "26088052554768282442056000", "2636591265602354831196585600", "268771779551047800167424355500" ]
[ "nonn" ]
14
0
2
[ "A104978", "A383439", "A383440" ]
null
Peter Luschny, May 03 2025
2025-05-04T03:18:35
oeisdata/seq/A383/A383439.seq
930b1e91860b5ef17da21a24a90df56f
A383440
a(n) = (5*n + 3)!/((8*n^2 + 10*n + 3)*(n!)^2*(3*n + 2)!).
[ "1", "16", "702", "42432", "3010700", "235282320", "19615029280", "1712821144320", "154870831986156", "14388837044278400", "1366276815032189060", "132069279628944665280", "12957831870375876372252", "1287484157116598357029120", "129316124278441748161584000", "13111175417326191857901849600" ]
[ "nonn" ]
12
0
2
[ "A383439", "A383440", "A383453" ]
null
Peter Luschny, May 03 2025
2025-05-04T03:19:01
oeisdata/seq/A383/A383440.seq
33da40a76b7e57b2dde3ed84c01fe7fa
A383441
a(n) is the total of iterations needed in the binary GCD algorithm to compute gcd(n, k) for k = 0..n. The corresponding row of gcds is row n of A109004.
[ "0", "0", "0", "2", "1", "5", "5", "12", "5", "11", "12", "23", "13", "29", "27", "31", "17", "38", "26", "47", "31", "42", "51", "70", "35", "63", "64", "72", "62", "96", "69", "104", "49", "80", "84", "86", "64", "123", "103", "118", "77", "130", "94", "152", "115", "128", "151", "174", "90", "163", "138", "164", "144", "197", "157", "188", "144", "187", "206", "229", "157", "251" ]
[ "nonn" ]
18
0
4
[ "A000265", "A109004", "A383441" ]
null
Peter Luschny, May 16 2025
2025-05-18T08:13:05
oeisdata/seq/A383/A383441.seq
e2a0ed5ae4b0bf1e38ad93c7132d4aed
A383442
a(0) = 0; thereafter a(n) is the least integer (in absolute value) not yet in the sequence such that the absolute difference between a(n-1) and a(n) is a triangular number; in case of a tie, preference is given to the positive value.
[ "0", "1", "2", "-1", "-2", "-3", "3", "4", "5", "-5", "-4", "6", "7", "8", "-7", "-6", "9", "10", "11", "-10", "-9", "-8", "-11", "-12", "-13", "-14", "14", "13", "12", "15", "16", "17", "18", "-18", "-15", "-16", "-17", "19", "20", "21", "22", "23", "-22", "-19", "-20", "-21", "24", "25", "26", "27", "28", "-27", "-24", "-23", "-26", "-25", "-28", "-29", "-30", "-31", "-32", "-33", "33", "30", "29", "32", "31", "34", "35", "36", "37", "38", "39", "-39", "-36", "-35", "-34", "-37", "-38", "40" ]
[ "sign" ]
33
0
3
[ "A000217", "A000290", "A001477", "A377091", "A383442", "A383443", "A383688" ]
null
N. J. A. Sloane, May 03 2025
2025-05-05T11:45:30
oeisdata/seq/A383/A383442.seq
689e9120dd5ebb016264d88ca22156c0
A383443
First differences of A383442.
[ "1", "1", "-3", "-1", "-1", "6", "1", "1", "-10", "1", "10", "1", "1", "-15", "1", "15", "1", "1", "-21", "1", "1", "-3", "-1", "-1", "-1", "28", "-1", "-1", "3", "1", "1", "1", "-36", "3", "-1", "-1", "36", "1", "1", "1", "1", "-45", "3", "-1", "-1", "45", "1", "1", "1", "1", "-55", "3", "1", "-3", "1", "-3", "-1", "-1", "-1", "-1", "-1", "66", "-3", "-1", "3", "-1", "3", "1", "1", "1", "1", "1", "-78", "3", "1", "1", "-3", "-1", "78", "1", "1", "1", "1", "1", "1", "-91", "3", "1", "1", "-3", "-1", "91" ]
[ "sign" ]
13
0
3
[ "A383442", "A383443", "A383688" ]
null
N. J. A. Sloane, May 03 2025
2025-05-05T11:45:38
oeisdata/seq/A383/A383443.seq
cb47e6c2ab6001c7c84acadc175079a7
A383444
First differences of A377090.
[ "2", "-3", "2", "-3", "5", "-7", "-2", "3", "7", "2", "-11", "-2", "-2", "17", "-3", "2", "2", "-17", "-2", "-2", "23", "2", "-3", "2", "-23", "-2", "-2", "29", "2", "2", "-3", "-29", "-2", "-2", "37", "-2", "3", "-37", "-2", "-2", "43", "2", "-3", "-41", "-2", "-2", "47", "2", "2", "-53", "3", "-2", "-2", "53", "2", "2", "-59", "-2", "3", "-2", "59", "2", "2", "-67", "2", "67", "-3", "2", "-67", "-2", "71", "-73", "-2", "3", "73", "2", "-79", "2", "79", "-3", "2", "2", "-83", "-2", "-2", "3", "-2", "89" ]
[ "sign" ]
11
0
1
[ "A377090", "A380311", "A383444" ]
null
N. J. A. Sloane, Apr 27 2025
2025-05-02T10:56:32
oeisdata/seq/A383/A383444.seq
3fa63f0667d9e5df26249c7f2e01874f
A383445
Index of n in A377090, or -1 if n does not appear there.
[ "0", "3", "1", "5", "9", "15", "10", "16", "14", "17", "23", "21", "24", "22", "28", "31", "29", "36", "30", "35", "37", "43", "41", "47", "42", "48", "54", "49", "55", "61", "56", "62", "67", "63", "68", "66", "71", "75", "80", "76", "81", "79", "82", "89", "91", "88", "90", "92", "99", "93", "98", "100", "105", "111", "106", "112", "110", "113", "124", "122", "125", "123", "126", "128", "121", "127", "133", "138", "134", "139", "137", "147", "150", "148", "146", "149", "153" ]
[ "nonn" ]
14
0
2
[ "A377090", "A383445", "A383446" ]
null
N. J. A. Sloane, Apr 30 2025
2025-04-30T12:42:58
oeisdata/seq/A383/A383445.seq
37f8db584ea9a022678eee66b2b632f6
A383446
Index of -n in A377090, or -1 if -n does not appear there.
[ "0", "2", "4", "8", "6", "11", "7", "12", "18", "13", "19", "25", "20", "26", "32", "27", "33", "38", "34", "39", "44", "40", "45", "51", "46", "52", "50", "53", "59", "57", "60", "58", "65", "69", "64", "70", "74", "72", "78", "73", "77", "83", "86", "84", "87", "85", "95", "97", "94", "96", "101", "104", "102", "107", "103", "108", "114", "109", "115", "118", "116", "119", "117", "120", "129", "132", "130", "136", "131", "135", "140", "143", "141", "144", "142", "145", "156" ]
[ "nonn" ]
13
0
2
[ "A377090", "A383445", "A383446" ]
null
N. J. A. Sloane, Apr 30 2025
2025-04-30T13:41:38
oeisdata/seq/A383/A383446.seq
c0b02aa47a27d4602b6af60cf3f2e2ff
A383447
Number of "peerless" trees on n nodes.
[ "1", "0", "1", "1", "2", "3", "6", "9", "19", "33", "67", "130", "270", "547", "1165", "2456", "5314", "11521", "25357", "56022", "125067", "280471", "633490", "1437340", "3278912", "7510503", "17277697", "39890262", "92427559", "214835923", "500879602", "1171013350", "2744946654", "6450077870" ]
[ "nonn", "more", "changed" ]
50
1
5
[ "A000055", "A383447", "A383448" ]
null
N. J. A. Sloane, May 01 2025, based on postings to the SeqFan Mailing List in April and May 2025 by Victor S. Miller, Allan C. Wechsler, Brendan McKay, and others
2025-07-09T05:09:07
oeisdata/seq/A383/A383447.seq
710e4fa1adc3005a9528f5037c3c63ea
A383448
Irregular triangle read by rows: T(n,k) (n>=1, k>=0) is the number of trees with n nodes in which there are k edges whose end-vertices have the same degree.
[ "1", "0", "1", "1", "1", "1", "2", "0", "1", "3", "2", "0", "1", "6", "3", "1", "0", "1", "9", "7", "5", "1", "0", "1", "19", "12", "10", "4", "1", "0", "1", "33", "33", "18", "15", "5", "1", "0", "1", "67", "66", "54", "26", "15", "5", "1", "0", "1", "130", "154", "128", "77", "36", "18", "6", "1", "0", "1", "270", "344", "309", "199", "110", "40", "21", "6", "1", "0", "1", "547", "806", "752", "530", "294", "147", "50", "24", "7", "1", "0", "1" ]
[ "nonn", "tabf" ]
31
1
7
[ "A000055", "A383447", "A383448" ]
null
N. J. A. Sloane, May 01 2025
2025-05-04T12:48:53
oeisdata/seq/A383/A383448.seq
e74fc64533e49761e98e56ddbda24a69
A383449
Number of permutations of length n which avoid the patterns 123 and 4321.
[ "1", "1", "2", "5", "13", "25", "25", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn" ]
4
1
3
null
null
N. J. A. Sloane, May 01 2025
2025-05-01T23:15:00
oeisdata/seq/A383/A383449.seq
ec0404726ee4640657d7f55d1a7449b7
A383450
2nd diagonal (from right) in A104978.
[ "2", "21", "180", "1430", "10920", "81396", "596904", "4326300", "31081050", "221760825", "1573537680", "11114897976", "78215948720", "548652722520", "3838040704080", "26784871943928", "186537501038070", "1296717366119175", "8999440181955300", "62366467037593950", "431633967218324640", "2983755440056831440", "20603495011611002400", "142131208489591604400" ]
[ "nonn" ]
7
0
1
[ "A104987", "A383450" ]
null
N. J. A. Sloane, May 02 2025
2025-05-04T08:02:15
oeisdata/seq/A383/A383450.seq
a2d042516eaa8114c8648f2f6064f801
A383451
3nd diagonal (from right) in A104978.
[ "5", "84", "990", "10010", "92820", "813960", "6864396", "56241900", "450675225", "3548173200", "27536909400", "211183061544", "1603426948760", "12070359895440", "90193956545880", "669621798598200", "4943243777508855", "36308086251336900", "265483485367681350", "1933360478165412450", "14028103934595550800", "101447684961932268960", "731424072912190585200", "5258854714114889362800" ]
[ "nonn" ]
9
0
1
[ "A104987", "A383451" ]
null
N. J. A. Sloane, May 02 2025
2025-05-04T08:02:23
oeisdata/seq/A383/A383451.seq
b16363cfc66e9380deb39a05b428cb24
A383452
Column 3 in A104978.
[ "0", "0", "0", "12", "165", "1430", "10010", "61880", "352716", "1899240", "9806280", "49031400", "239028075", "1141710570", "5362579950", "24837212400", "113678010600", "515030986800", "2312957340720", "10307744670600", "45626928615450", "200758485907980", "878623171119540", "3826892034209552", "16596215454480200", "71691488703052400", "308585103547921200", "1323929637802371600" ]
[ "nonn" ]
17
0
4
[ "A104987", "A383452" ]
null
N. J. A. Sloane, May 02 2025
2025-05-09T02:36:35
oeisdata/seq/A383/A383452.seq
be8e8372e8afd8b2225f49bd99add25f
A383453
The Geode Bi-Tri infinite rectangular array, read by upward antidiagonals.
[ "1", "2", "3", "5", "16", "12", "14", "70", "110", "55", "42", "288", "702", "728", "273", "132", "1155", "3850", "6160", "4760", "1428", "429", "4576", "19448", "42432", "50388", "31008", "7752", "1430", "18018", "93366", "259350", "418950", "395010", "201894", "43263", "4862", "70720", "433160", "1466080", "3010700", "3853696", "3010700", "1315600", "246675" ]
[ "nonn", "tabl" ]
46
0
2
[ "A000108", "A001764", "A243660", "A383453", "A383454", "A383457" ]
null
N. J. A. Sloane, May 02 2025
2025-05-09T15:07:32
oeisdata/seq/A383/A383453.seq
165cb54b586f52a848d080f1c6b5d99e
A383454
Row 1 of the array in A383453.
[ "2", "16", "110", "728", "4760", "31008" ]
[ "nonn", "more" ]
3
0
1
[ "A383453", "A383454" ]
null
N. J. A. Sloane, May 02 2025
2025-05-02T17:37:12
oeisdata/seq/A383/A383454.seq
ff0d8c2b35f5c9bff5fcebfdca7fa2eb
A383455
Row 2 of the array in A383453.
[ "5", "70", "702", "6160", "50388", "395010" ]
[ "nonn", "more" ]
5
0
1
[ "A383453", "A383455" ]
null
N. J. A. Sloane, May 02 2025
2025-05-02T17:40:45
oeisdata/seq/A383/A383455.seq
37b66334af9554687eae57f2bad5a3be
A383456
a(n) = 2*binomial(2*n+4,n)*(n+3)/(n+2).
[ "3", "16", "70", "288", "1155", "4576", "18018", "70720", "277134", "1085280", "4249388", "16640960", "65189475", "255487680", "1001800650", "3930284160", "15427730010", "60591880800", "238098549780", "936100651200", "3682173186510", "14490838080576", "57053452670100", "224729967000448", "885568808835900", "3491063797713856", "13767643081368792", "54315062063687040", "214354554086311331" ]
[ "nonn", "more" ]
7
0
1
[ "A383453", "A383456" ]
null
N. J. A. Sloane, May 02 2025
2025-05-03T20:48:53
oeisdata/seq/A383/A383456.seq
17b2f0f066ae553b07a4acfb7f4b04c6
A383457
Column 2 of the array in A383453.
[ "12", "110", "702", "3850", "19448", "93366", "433160", "1961256" ]
[ "nonn", "more" ]
3
0
1
[ "A383453", "A383457" ]
null
N. J. A. Sloane, May 02 2025
2025-05-02T17:47:35
oeisdata/seq/A383/A383457.seq
a6ee4256771ec3f0f543815b012fd3b9
A383458
Maximum number of cycles in any permutation in S_n of the highest order (A000793(n)).
[ "1", "1", "1", "1", "2", "3", "2", "2", "2", "3", "4", "3", "4", "3", "3", "3", "4", "5", "4", "5", "6", "7", "4", "5", "4" ]
[ "nonn", "more" ]
7
1
5
[ "A000793", "A074059", "A074064", "A383458", "A383459" ]
null
Anand Jain, Mar 22 2025
2025-05-27T19:21:43
oeisdata/seq/A383/A383458.seq
163da9917b88b50826dea9dbf1e7e902
A383459
Minimum number of cycles in any permutation in S_n of the highest order (A000793(n)).
[ "1", "1", "1", "1", "2", "1", "2", "2", "2", "3", "2", "3", "4", "3", "3", "3", "4", "3", "4", "5", "5", "4", "4", "5", "4" ]
[ "nonn", "more" ]
7
1
5
[ "A000793", "A074059", "A074064", "A383458", "A383459" ]
null
Anand Jain, Mar 22 2025
2025-05-27T19:21:13
oeisdata/seq/A383/A383459.seq
d789e213274236adcd29ac71ff1ec556
A383460
13 X oo array read by antidiagonals, giving the values of the standard mod 13 Ackermann function.
[ "1", "2", "2", "3", "3", "3", "5", "5", "4", "4", "0", "0", "7", "5", "5", "5", "5", "3", "9", "6", "6", "9", "9", "6", "9", "11", "7", "7", "9", "9", "5", "2", "8", "0", "8", "8", "9", "9", "9", "9", "3", "6", "2", "9", "9", "9", "9", "9", "9", "5", "9", "2", "4", "10", "10", "9", "9", "9", "9", "9", "9", "11", "7", "6", "11", "11", "9", "9", "9", "9", "9", "9", "5", "1", "4", "8", "12", "12" ]
[ "nonn", "tabf" ]
15
0
2
[ "A085119", "A383460" ]
null
N. J. A. Sloane, May 30 2025
2025-06-05T00:31:32
oeisdata/seq/A383/A383460.seq
30f53a66ba396f3bc2cce1f83f84c775
A383461
Number of vertices in graph G_n formed by taking a regular n-gon with all its chords extended to infinity (the n-th graph in A344857) and inverting it in its circumscribing circle.
[ "4", "5", "16", "37", "92", "145", "334", "471", "892", "901", "1964", "2185", "3796", "3969", "6682", "5563", "10964", "11141", "17032", "17293", "25324", "21913", "36326", "36479", "50572", "50485", "68644", "51661", "91172", "90753", "118834", "118355", "152356", "139861", "192512", "191445", "240124", "238481" ]
[ "nonn", "changed" ]
102
3
1
[ "A146212", "A344857", "A345025", "A383461", "A383462" ]
null
Scott R. Shannon and N. J. A. Sloane, Jun 02 2025
2025-07-09T05:09:14
oeisdata/seq/A383/A383461.seq
321fbaf2faf80b8158894abd30e0773f
A383462
Triangle read by rows: T(n,k) (n >= 3, 2 <= k <= n-1) = number of vertices where k lines cross in the planar graph formed when every pair of vertices of a regular n-gon are joined by an infinite line.
[ "3", "1", "4", "10", "0", "5", "30", "1", "0", "6", "84", "0", "0", "0", "7", "120", "16", "1", "0", "0", "8", "324", "0", "0", "0", "0", "0", "9", "420", "40", "0", "1", "0", "0", "0", "10", "880", "0", "0", "0", "0", "0", "0", "0", "11", "708", "156", "24", "0", "1", "0", "0", "0", "0", "12", "1950", "0", "0", "0", "0", "0", "0", "0", "0", "0", "13", "1890", "280", "0", "0", "0", "1", "0", "0", "0", "0", "0", "14" ]
[ "nonn", "tabl" ]
27
3
1
[ "A007569", "A146212", "A146213", "A292105", "A344857", "A383462" ]
null
Scott R. Shannon and N. J. A. Sloane, Jun 07 2025
2025-06-21T14:15:42
oeisdata/seq/A383/A383462.seq
e8cb53f8bb7934c2d6193c301a452117
A383464
a(n) = 8*n^2 - 5*n + 1.
[ "1", "4", "23", "58", "109", "176", "259", "358", "473", "604", "751", "914", "1093", "1288", "1499", "1726", "1969", "2228", "2503", "2794", "3101", "3424", "3763", "4118", "4489", "4876", "5279", "5698", "6133", "6584", "7051", "7534", "8033", "8548", "9079", "9626", "10189", "10768", "11363", "11974", "12601", "13244", "13903", "14578", "15269" ]
[ "nonn", "easy" ]
28
0
2
[ "A130083", "A139272", "A140064", "A383464" ]
null
N. J. A. Sloane, Jun 26 2025
2025-06-30T09:27:55
oeisdata/seq/A383/A383464.seq
7f2b5c81bd300a0f432e841d18c2f16d
A383465
a(n) = 25*n^2/2 - 11*n/2 + 1.
[ "1", "8", "40", "97", "179", "286", "418", "575", "757", "964", "1196", "1453", "1735", "2042", "2374", "2731", "3113", "3520", "3952", "4409", "4891", "5398", "5930", "6487", "7069", "7676", "8308", "8965", "9647", "10354", "11086", "11843", "12625", "13432", "14264", "15121", "16003", "16910", "17842", "18799", "19781", "20788", "21820", "22877", "23959", "25066", "26198", "27355", "28537", "29744", "30976", "32233", "33515", "34822" ]
[ "nonn", "easy", "new" ]
24
0
2
null
null
N. J. A. Sloane, Jul 16 2025
2025-07-18T01:52:25
oeisdata/seq/A383/A383465.seq
b8e0c5f642e3a9e1a83bc317d76e764c
A383467
Primes p such that gcd(ord_p(2), ord_p(6)) = 1.
[ "5", "7", "31", "43", "135607", "153649", "270841", "1489441", "1505447", "25781083", "127236649", "558062249", "745988807", "27989941729", "29512739491", "47206579351" ]
[ "nonn", "hard", "more" ]
10
1
1
[ "A014664", "A211242", "A344202", "A382414", "A383411", "A383467" ]
null
Li GAN, Apr 27 2025
2025-05-03T09:38:39
oeisdata/seq/A383/A383467.seq
88cfa4d467d9af5375e2d8779f18099f
A383468
Semiprimes s = A001358(k) such that k, s - k and s + k are also semiprimes.
[ "10", "15", "141", "166", "274", "298", "299", "687", "995", "1115", "1227", "1299", "1345", "1891", "1945", "2194", "2661", "2998", "3093", "3287", "3566", "3781", "3902", "4174", "4262", "4497", "4798", "5378", "5414", "5758", "6609", "7094", "7666", "8354", "8434", "9566", "10041", "10342", "11051", "11091", "11486", "11582", "11702", "12279", "12574", "13154", "13346", "13387", "13466" ]
[ "nonn" ]
7
1
1
[ "A001358", "A383468", "A383469" ]
null
Zak Seidov and Robert Israel, Apr 27 2025
2025-04-29T13:27:59
oeisdata/seq/A383/A383468.seq
ef3bd5564e4758dbc83e22cbc4f33157
A383469
Semiprimes k such that A001358(k) + k and A001358(k) - k are also semiprimes.
[ "4", "6", "46", "55", "87", "93", "94", "206", "298", "326", "362", "382", "394", "542", "562", "629", "758", "841", "866", "926", "993", "1046", "1079", "1147", "1167", "1234", "1317", "1469", "1477", "1561", "1774", "1895", "2047", "2227", "2245", "2515", "2638", "2705", "2894", "2902", "3007", "3031", "3063", "3202", "3269", "3409", "3453", "3466", "3487", "3809", "3891", "4058", "4174", "4207" ]
[ "nonn" ]
6
1
1
[ "A001358", "A383468", "A383469" ]
null
Zak Seidov and Robert Israel, Apr 27 2025
2025-04-29T13:28:09
oeisdata/seq/A383/A383469.seq
04697a420e81ae6b6962af3b952077fa
A383470
Numbers k which are divisible by the number of squares mod k.
[ "1", "2", "4", "12", "16", "24", "48", "60", "72", "112", "144", "168", "192", "224", "240", "360", "528", "576", "672", "720", "792", "1188", "1344", "1456", "2016", "2184", "2376", "2448", "2880", "3360", "4032", "4560", "4752", "5940", "6336", "6840", "7392", "8448", "8832", "10080", "11880", "13200", "13248", "15456", "16632", "17472", "19008", "19800" ]
[ "nonn" ]
13
1
2
[ "A000224", "A383470" ]
null
Allan C. Wechsler, Apr 27 2025
2025-04-28T11:32:12
oeisdata/seq/A383/A383470.seq
78b82723b7cb9a01d747f01ed70672da
A383473
Integers k such that d*2^k + 1 is prime for some divisor of k.
[ "1", "2", "4", "6", "8", "12", "14", "15", "16", "18", "25", "30", "36", "51", "55", "63", "66", "69", "75", "81", "85", "134", "141", "162", "189", "201", "209", "220", "245", "276", "324", "408", "438", "446", "456", "534", "616", "675", "693", "726", "892", "900", "1305", "1326", "1494", "1824", "2208", "2394", "2766", "2826", "3024", "3168", "3189", "3690", "3703", "3880", "3912", "3927", "4410", "4543", "4713" ]
[ "nonn" ]
10
1
2
[ "A002064", "A005849", "A027750", "A382811", "A383473" ]
null
Juri-Stepan Gerasimov, Apr 27 2025
2025-05-04T12:40:19
oeisdata/seq/A383/A383473.seq
32ce01ec4e29228b91ca33f1d60bf8cc
A383474
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(2,0),(3,0),(0,1),(0,2),(0,3).
[ "1", "1", "1", "2", "2", "2", "4", "5", "5", "4", "7", "12", "14", "12", "7", "13", "26", "37", "37", "26", "13", "24", "56", "89", "106", "89", "56", "24", "44", "118", "209", "277", "277", "209", "118", "44", "81", "244", "477", "698", "784", "698", "477", "244", "81", "149", "499", "1063", "1700", "2113", "2113", "1700", "1063", "499", "149", "274", "1010", "2329", "4026", "5469", "6040", "5469", "4026", "2329", "1010", "274" ]
[ "nonn", "tabl" ]
14
0
4
[ "A000073", "A007318", "A036355", "A073778", "A122680", "A383474", "A383477" ]
null
Seiichi Manyama, Apr 27 2025
2025-04-28T08:45:21
oeisdata/seq/A383/A383474.seq
da7bd634cea0bc8bd57333b30fc770bd
A383475
Numbers k such that k*2^d is the average of a twin prime pair for some divisor d of k.
[ "2", "3", "6", "9", "12", "15", "18", "21", "24", "30", "36", "39", "42", "45", "48", "51", "54", "60", "69", "72", "75", "78", "81", "90", "96", "99", "105", "108", "114", "120", "129", "132", "135", "141", "144", "150", "156", "165", "168", "174", "180", "186", "192", "201", "210", "216", "228", "231", "234", "240", "252", "258", "261", "264", "270", "282", "285", "288", "300" ]
[ "nonn" ]
16
1
1
[ "A002822", "A014574", "A027750", "A060212", "A382811", "A383473", "A383475" ]
null
Juri-Stepan Gerasimov, Apr 27 2025
2025-05-04T00:01:28
oeisdata/seq/A383/A383475.seq
fe3546cb8f2e2575a4797fdca4fe0c35
A383476
Numbers k such that binomial(2k,k) + k is prime.
[ "1", "3", "5", "23", "55", "61", "191", "1933", "3049", "8011", "10589", "58687", "100469" ]
[ "nonn", "hard", "more" ]
19
1
2
[ "A134758", "A309289", "A383476" ]
null
Juri-Stepan Gerasimov, Apr 28 2025
2025-05-04T12:40:53
oeisdata/seq/A383/A383476.seq
da57311b4eb772b2c18b0a9549ae3dd3
A383477
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(2,0),(3,0),(0,1).
[ "1", "1", "1", "1", "2", "2", "1", "3", "5", "4", "1", "4", "9", "12", "7", "1", "5", "14", "25", "26", "13", "1", "6", "20", "44", "63", "56", "24", "1", "7", "27", "70", "125", "153", "118", "44", "1", "8", "35", "104", "220", "336", "359", "244", "81", "1", "9", "44", "147", "357", "646", "864", "819", "499", "149", "1", "10", "54", "200", "546", "1134", "1800", "2144", "1830", "1010", "274" ]
[ "nonn", "tabl" ]
16
0
5
[ "A000073", "A038137", "A073778", "A292326", "A383474", "A383477", "A383478" ]
null
Seiichi Manyama, Apr 28 2025
2025-04-28T08:45:11
oeisdata/seq/A383/A383477.seq
d1deb22ab0f6944b32f06b7138b9abe5
A383478
Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(3,0),(0,1).
[ "1", "2", "9", "44", "220", "1134", "5950", "31608", "169488", "915420", "4972825", "27141036", "148711836", "817516196", "4506838380", "24906188912", "137933068572", "765324011736", "4253501563156", "23675286219200", "131955035141160", "736347621539310", "4113559552360230", "23003228298637080" ]
[ "nonn" ]
16
0
2
[ "A063018", "A383477", "A383478" ]
null
Seiichi Manyama, Apr 28 2025
2025-05-28T16:22:41
oeisdata/seq/A383/A383478.seq
891ad5f43a13fcae69dd30f4a0c829b2
A383479
Number of lattice paths from (0,0) to (n,n) using steps (1,0),(3,0),(0,1).
[ "1", "2", "6", "24", "100", "420", "1792", "7752", "33858", "148940", "658944", "2929056", "13070876", "58521344", "262754040", "1182619280", "5334172518", "24104916504", "109111142376", "494630028200", "2245300152480", "10204575481320", "46429481139000", "211460450151600", "963971663881200", "4398118872144192" ]
[ "nonn" ]
18
0
2
[ "A038112", "A049140", "A144401", "A370624", "A383479", "A383480" ]
null
Seiichi Manyama, Apr 28 2025
2025-05-29T08:06:11
oeisdata/seq/A383/A383479.seq
2b6401888959faaa2b103e443b3f7b8e
A383480
Number of lattice paths from (0,0) to (n,n) using steps (1,0),(4,0),(0,1).
[ "1", "2", "6", "20", "75", "294", "1176", "4752", "19350", "79310", "326898", "1353768", "5628441", "23478700", "98217840", "411879264", "1730924700", "7287941340", "30736775190", "129825892000", "549096132585", "2325216522420", "9857299586700", "41830206233400", "177673556967075", "755307883986084", "3213402383779812" ]
[ "nonn" ]
19
0
2
[ "A038112", "A063021", "A383479", "A383480", "A383481" ]
null
Seiichi Manyama, Apr 28 2025
2025-05-29T10:42:07
oeisdata/seq/A383/A383480.seq
3bde8413a442917c078a27a2dd9099c9
A383481
Coefficient of x^n in the expansion of 1 / (1-x-x^4)^n.
[ "1", "1", "3", "10", "39", "156", "630", "2556", "10431", "42823", "176748", "732810", "3049722", "12732188", "53299284", "223645200", "940355391", "3961092906", "16712516565", "70615352330", "298761296064", "1265504676810", "5366250376710", "22777466596560", "96768003904650", "411451657313931", "1750809473690436", "7455339422353396" ]
[ "nonn" ]
16
0
3
[ "A003269", "A063021", "A370624", "A383481" ]
null
Seiichi Manyama, Apr 28 2025
2025-05-28T16:34:21
oeisdata/seq/A383/A383481.seq
97fea9e834fa87e3e5ec531495ef7063
A383482
Integers k such that sigma(k)/k - 1 is a rational square.
[ "1", "6", "9", "28", "216", "360", "496", "2016", "2401", "8128", "16758", "182520", "884736", "1022112", "1352328", "1571328", "1935360", "2678400", "33550336", "54758400", "101382400", "119533176", "136808280", "163298502", "198288000", "618591192", "691022088", "782481673", "796663296", "1137067008", "1275418369", "1303102080" ]
[ "nonn" ]
27
1
2
[ "A000203", "A000396", "A046060", "A069070", "A218404", "A381321", "A383482" ]
null
Michel Marcus, Apr 28 2025
2025-05-04T23:44:16
oeisdata/seq/A383/A383482.seq
5ec382d5c27893b487382cab22a04052
A383483
Numbers k such that k = sigma(m)-m where m = sigma(3*k)-3*k.
[ "3", "15", "5919", "118719", "179871", "33750303" ]
[ "nonn", "more" ]
27
1
1
[ "A063990", "A259180", "A383239", "A383483" ]
null
S. I. Dimitrov, Apr 28 2025
2025-05-16T14:32:48
oeisdata/seq/A383/A383483.seq
6fc80fe930782aab3d0540be4b282346
A383484
Integers k such that there exists an integer 0<m<k such that sigma(m)^2 + sigma(k)^2 = (m+k)^2.
[ "3", "33", "69", "77", "133", "161", "235", "267", "287", "321", "385", "699", "715", "1235", "1379", "1437", "1529", "1595", "1653", "1719", "2047", "2233", "2241", "2569", "2727", "2829", "3237", "3269", "3999", "4585", "4683", "4911", "5075", "5163", "5215", "5497", "5667", "5691", "7085", "7089", "7587", "7761", "7797", "7945", "8259", "9159", "9659", "10653" ]
[ "nonn" ]
42
1
1
[ "A063990", "A259180", "A383239", "A383484" ]
null
S. I. Dimitrov, Apr 28 2025
2025-06-02T05:01:59
oeisdata/seq/A383/A383484.seq
5b681b5de4769be291e8d55ce4071f6b
A383485
a(n) = 2*(2*(n - 1)! + n + 2) (mod n*(n + 2)).
[ "1", "4", "3", "12", "5", "16", "0", "20", "31", "24", "11", "28", "0", "32", "49", "36", "17", "40", "0", "44", "67", "48", "0", "52", "54", "56", "85", "60", "29", "64", "0", "68", "70", "72", "109", "76", "0", "80", "121", "84", "41", "88", "0", "92", "139", "96", "0", "100", "102", "104", "157", "108", "0", "112", "114", "116", "175", "120", "59", "124", "0", "128", "130", "132", "199", "136", "0", "140" ]
[ "nonn" ]
6
1
2
[ "A001359", "A005563", "A067774", "A073830", "A383485" ]
null
Giorgos Kalogeropoulos, Apr 28 2025
2025-05-04T12:39:53
oeisdata/seq/A383/A383485.seq
ac38d226f23279269d839570a7e866b9
A383486
Decimal expansion Sum_{p primes} (p^2 + p^4)*log(p)^3/(p^6 - 3*p^4 + 3*p^2 -1).
[ "1", "9", "5", "0", "1", "3", "5", "8", "3", "2", "6", "7", "3", "1", "8", "9", "9", "5", "7", "9", "5", "4", "5", "2", "2", "1", "2", "5", "2", "5", "6", "8", "7", "4", "5", "9", "6", "0", "3", "3", "4", "1", "3", "5", "8", "8", "0", "5", "5", "0", "2", "8", "7", "1", "6", "0", "5", "2", "3", "1", "3", "9", "0", "4", "4", "3", "1", "2", "7", "7", "4", "1", "6", "5", "4", "7", "9", "2", "3", "6", "3", "3", "1", "4", "2", "6", "3", "9", "8", "7", "7", "1", "1", "0", "4", "1", "7", "8", "2", "5", "5", "1", "5", "8", "8" ]
[ "nonn", "cons" ]
20
1
2
[ "A345364", "A383224", "A383486" ]
null
Artur Jasinski, Apr 28 2025
2025-04-29T04:52:08
oeisdata/seq/A383/A383486.seq
ff54601fd311ebb1933ea5b9294baef1
A383487
Prime powers p^r such that p (mod 4) = 3 and r is even.
[ "9", "49", "81", "121", "361", "529", "729", "961", "1849", "2209", "2401", "3481", "4489", "5041", "6241", "6561", "6889", "10609", "11449", "14641", "16129", "17161", "19321", "22801", "26569", "27889", "32041", "36481", "39601", "44521", "49729", "51529", "57121", "59049", "63001", "69169", "73441", "80089", "94249", "96721" ]
[ "nonn" ]
30
1
1
null
null
Eric W. Weisstein, Apr 30 2025
2025-05-01T08:31:35
oeisdata/seq/A383/A383487.seq
37e1387d852eec50707bc4f67b9736dd
A383488
Numbers k that have at least one divisor d_i(k) for which a divisor d_j(k) exists such that d_i(k) < d_j(k) < sigma(d_i(k)).
[ "12", "18", "20", "24", "30", "36", "40", "42", "48", "54", "56", "60", "66", "70", "72", "78", "80", "84", "88", "90", "96", "99", "100", "102", "104", "105", "108", "110", "112", "114", "120", "126", "130", "132", "138", "140", "144", "150", "154", "156", "160", "162", "168", "170", "174", "176", "180", "186", "189", "192", "196", "198", "200", "204", "208", "210", "216" ]
[ "nonn" ]
8
1
1
[ "A000203", "A002808", "A008594", "A008600", "A008602", "A008606", "A027750", "A044102", "A109042", "A135628", "A383360", "A383488", "A383489" ]
null
Felix Huber, May 03 2025
2025-05-08T21:06:15
oeisdata/seq/A383/A383488.seq
632bcb1380881419c8f189ee28d744dd
A383489
a(n) is the number of divisors d_i(m) for which a divisor d_j(m) exists such that d_i(m) < d_j(m) < sigma(d_i(m)) where m = A383488(n).
[ "1", "1", "1", "4", "2", "5", "3", "2", "6", "2", "1", "7", "2", "1", "8", "1", "6", "7", "1", "6", "8", "1", "2", "1", "1", "1", "8", "1", "4", "1", "11", "4", "1", "7", "1", "6", "11", "5", "1", "6", "8", "3", "11", "1", "1", "3", "13", "1", "1", "10", "1", "5", "5", "6", "3", "9", "12", "4", "1", "7", "1", "6", "4", "1", "15", "1", "13", "1", "1", "4", "11", "1", "10", "1", "6", "11", "1", "1", "1", "14", "4", "2", "13" ]
[ "nonn" ]
11
1
4
[ "A000203", "A002808", "A027750", "A109042", "A383360", "A383488", "A383489" ]
null
Felix Huber, May 08 2025
2025-05-13T23:59:10
oeisdata/seq/A383/A383489.seq
2472f9d8ae3dcaee188a3cc739feea5e
A383490
Number of polyforms with n cells on the faces of a rhombic triacontahedron up to rotation and reflection.
[ "1", "1", "1", "3", "4", "12", "24", "65", "156", "422", "1057", "2708", "6574", "15399", "33438", "66787", "118242", "180602", "227896", "226652", "169294", "97224", "44324", "16416", "5005", "1247", "261", "46", "8", "1", "1" ]
[ "nonn", "fini", "full" ]
21
0
4
[ "A030135", "A030136", "A340635", "A383490", "A383491", "A383492", "A383494", "A383496", "A383974" ]
null
Peter Kagey, Apr 28 2025
2025-05-23T10:13:14
oeisdata/seq/A383/A383490.seq
a838500c04fbc8ca6ee544b1f35f6827
A383491
Number of polyforms with n cells on the faces of a rhombic triacontahedron up to rotation.
[ "1", "1", "1", "4", "6", "19", "43", "119", "300", "818", "2083", "5357", "13078" ]
[ "nonn", "fini", "more" ]
10
0
4
[ "A030137", "A030138", "A383490", "A383491", "A383493", "A383495", "A383497", "A383498" ]
null
Peter Kagey, Apr 28 2025
2025-04-29T04:50:01
oeisdata/seq/A383/A383491.seq
a7fbe8505078222ba1dc562cea4acd7e
A383492
Number of polyforms with n cells on the faces of a triakis icosahedron up to rotation and reflection.
[ "1", "1", "2", "2", "4", "4", "10", "13", "29", "47", "99", "175", "358", "669", "1346", "2600", "5191", "10137", "20093", "39320", "77437", "151314", "295745", "574011", "1110144", "2130239", "4059919", "7662738", "14316799", "26413683", "48057066", "86015788", "151180505", "260256043", "437720722", "716963561", "1139830037", "1751982279", "2592522277" ]
[ "nonn", "fini", "full" ]
17
0
3
[ "A030135", "A030136", "A057784", "A340635", "A383490", "A383492", "A383493", "A383494", "A383496" ]
null
Peter Kagey, Apr 28 2025
2025-06-10T13:54:39
oeisdata/seq/A383/A383492.seq
259371e14f70c3b8e0871ead0a4142e5
A383493
Number of polyforms with n cells on the faces of a triakis icosahedron up to rotation.
[ "1", "1", "2", "3", "5", "7", "15", "24", "49", "91", "182", "344", "688", "1328", "2641", "5182", "10288", "20240", "40014", "78577", "154562", "302511", "590930", "1147805", "2219309", "4260085", "8118169", "15324786", "28630807", "52826179", "96109611", "172029602", "302353990", "520508934", "875430977", "1433922264", "2279645080", "3503957379" ]
[ "nonn", "fini", "full" ]
16
0
3
[ "A030137", "A030138", "A151531", "A383491", "A383492", "A383493", "A383495", "A383497", "A383498" ]
null
Peter Kagey, Apr 28 2025
2025-06-10T13:54:45
oeisdata/seq/A383/A383493.seq
d82595292f78918894307cc87855a0dd
A383494
Number of polyforms with n cells on the faces of a pentakis dodecahedron up to rotation and reflection.
[ "1", "1", "2", "2", "6", "10", "27", "56", "149", "352", "915", "2285", "5919", "15084", "38908", "99627", "255728", "653113", "1664892", "4221090", "10648018", "26658710", "66154031", "162272380", "392491903", "933148405", "2173804324", "4943689469", "10932561700", "23403033225", "48251790080", "95274168428" ]
[ "nonn", "fini", "more" ]
16
0
3
[ "A030135", "A030136", "A340635", "A383490", "A383492", "A383494", "A383495", "A383496" ]
null
Peter Kagey, Apr 28 2025
2025-06-12T15:19:23
oeisdata/seq/A383/A383494.seq
6c3149f45a801a3f22a577327e130c1e
A383495
Number of polyforms with n cells on the faces of a pentakis dodecahedron up to rotation.
[ "1", "1", "2", "3", "8", "18", "46", "108", "280", "694", "1788", "4544", "11740", "30105", "77584", "199102", "510910", "1305859", "3328504", "8441297", "21293077", "53315322", "132301407", "324539916", "784969397", "1866286028", "4347578908", "9887356006", "21865065180", "46806020153", "96503472390", "190548248699" ]
[ "nonn", "fini", "more" ]
14
0
3
[ "A030137", "A030138", "A383491", "A383493", "A383494", "A383495", "A383497", "A383498" ]
null
Peter Kagey, Apr 28 2025
2025-06-12T15:19:10
oeisdata/seq/A383/A383495.seq
c3bafdb0fde8c96e84452470a4225e30
A383496
Number of polyforms with n cells on the faces of a disdyakis triacontahedron up to rotation and reflection.
[ "1", "1", "3", "3", "9", "14", "38", "74", "185", "414", "1025", "2430", "6012", "14640", "36294", "89531", "222452", "552015", "1374367", "3421955", "8535077", "21296556", "53184718", "132846918", "331913842", "829176301", "2071018243", "5170617085", "12902719975", "32176288808" ]
[ "nonn", "more", "fini" ]
27
0
3
[ "A030135", "A030136", "A197462", "A340635", "A383490", "A383492", "A383494", "A383496", "A383497" ]
null
Peter Kagey, Apr 28 2025
2025-06-13T14:25:12
oeisdata/seq/A383/A383496.seq
c118a951e782c253d9c8e0329ae9932a
A383497
Number of polyforms with n cells on the faces of a disdyakis triacontahedron up to rotation.
[ "1", "2", "3", "6", "13", "28", "66", "148", "349", "828", "2004", "4860", "11919", "29280", "72348", "179062", "444357", "1104030", "2747476", "6843910", "17067229", "42593112", "106362575", "265693836", "663811498", "1658352602", "4141998151", "10341234170", "25805349073", "64352577616" ]
[ "nonn", "fini", "more" ]
19
0
2
[ "A030137", "A030138", "A197463", "A383491", "A383493", "A383495", "A383496", "A383497", "A383498" ]
null
Peter Kagey, Apr 28 2025
2025-06-13T22:07:47
oeisdata/seq/A383/A383497.seq
a25741c5768b96b8cd3b519144d51d6c
A383498
Number of polyforms with n cells on the faces of a deltoidal hexecontahedron up to rotation.
[ "1", "1", "2", "6", "16", "48", "149", "460", "1471", "4702", "15126", "48607", "156417", "502137", "1608406", "5130178", "16278890", "51297616", "160220536", "494647640", "1504567216", "4491151455", "13098763174", "37146270208", "101880559018", "268650665645" ]
[ "nonn", "fini", "more" ]
14
0
3
[ "A030137", "A030138", "A340635", "A383491", "A383493", "A383495", "A383497", "A383498" ]
null
Peter Kagey, Apr 28 2025
2025-06-13T14:25:39
oeisdata/seq/A383/A383498.seq
5aa96ada719f50fd15678fcfccbd34ba
A383499
Expansion of 1/sqrt( (1-x) * (1-x-4*x^2)^3 ).
[ "1", "2", "9", "22", "71", "186", "537", "1434", "3957", "10586", "28603", "76266", "203767", "540986", "1435533", "3796050", "10026015", "26422350", "69544765", "182759750", "479731113", "1257750486", "3294264627", "8619879726", "22535782953", "58869786162", "153671378139", "400861115498", "1045005290059", "2722601576322" ]
[ "nonn" ]
22
0
2
[ "A026569", "A377204", "A383254", "A383499", "A383503" ]
null
Seiichi Manyama, May 05 2025
2025-05-05T07:18:30
oeisdata/seq/A383/A383499.seq
df706c432d5a77194d663880d9e1f001
A383500
Positive integers that contain the digit 9, or an odd digit d immediately preceded by a digit <= d.
[ "9", "11", "13", "15", "17", "19", "23", "25", "27", "29", "33", "35", "37", "39", "45", "47", "49", "55", "57", "59", "67", "69", "77", "79", "89", "90", "91", "92", "93", "94", "95", "96", "97", "98", "99", "101", "103", "105", "107", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "123", "125", "127", "129", "130", "131", "132", "133", "134", "135", "136", "137" ]
[ "nonn", "base", "easy" ]
17
1
1
[ "A347298", "A382464", "A382623", "A382935", "A382937", "A383061", "A383245", "A383247", "A383249", "A383500", "A383501" ]
null
Paolo Xausa, Apr 29 2025
2025-05-11T11:57:39
oeisdata/seq/A383/A383500.seq
5d95093a07bc494fbc7ea3fce97c5bb1
A383501
Nonnegative integers without the digit 9 such that every odd digit except the leftmost is immediately preceded by a larger digit.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "12", "14", "16", "18", "20", "21", "22", "24", "26", "28", "30", "31", "32", "34", "36", "38", "40", "41", "42", "43", "44", "46", "48", "50", "51", "52", "53", "54", "56", "58", "60", "61", "62", "63", "64", "65", "66", "68", "70", "71", "72", "73", "74", "75", "76", "78", "80", "81", "82", "83", "84", "85", "86", "87", "88", "100", "102", "104", "106", "108" ]
[ "nonn", "base", "easy" ]
7
1
3
[ "A377912", "A382465", "A382624", "A382935", "A382938", "A383062", "A383246", "A383248", "A383250", "A383500", "A383501" ]
null
Paolo Xausa, Apr 29 2025
2025-04-29T13:39:57
oeisdata/seq/A383/A383501.seq
188029909ee1459f947989564a881c75
A383502
Position of the first instance of prime(n), in base 3, in the ternary representation of Pi after the ternary point.
[ "2", "4", "6", "2", "12", "20", "6", "10", "27", "16", "85", "3", "35", "78", "95", "6", "38", "96", "19", "27", "9", "66", "157", "171", "81", "191", "12", "127", "52", "3", "36", "275", "88", "589", "283", "40", "290", "952", "47", "10", "1213", "750", "572", "84", "126", "2", "282", "162", "125", "480", "26", "66", "185", "157", "1490", "1310", "832", "1321", "352" ]
[ "base", "nonn" ]
18
1
1
[ "A000040", "A004601", "A004602", "A007089", "A178707", "A383502" ]
null
James S. DeArmon, Apr 28 2025
2025-05-30T00:49:35
oeisdata/seq/A383/A383502.seq
46527ef5ce9cadeb5235566655ceba9b
A383503
Expansion of 1/sqrt( (1-x) * (1-x-4*x^3)^3 ).
[ "1", "2", "3", "10", "23", "42", "97", "218", "435", "918", "1977", "4062", "8393", "17590", "36303", "74614", "154211", "317334", "650505", "1335054", "2736453", "5595950", "11439475", "23370270", "47681965", "97217882", "198110199", "403383026", "820820215", "1669405626", "3393344257", "6893850650", "13999109715", "28414742790" ]
[ "nonn" ]
35
0
2
[ "A217615", "A377213", "A383254", "A383499", "A383503" ]
null
Seiichi Manyama, May 05 2025
2025-05-07T08:27:00
oeisdata/seq/A383/A383503.seq
1d884cd83d284e60e963d7387a171c00
A383504
Sum of next a(n) successive prime squares is prime.
[ "2", "5", "7", "25", "11", "13", "7", "7", "35", "7", "19", "31", "25", "11", "5", "19", "5", "11", "5", "139", "37", "17", "19", "19", "13", "5", "7", "7", "19", "13", "11", "5", "7", "11", "5", "5", "5", "13", "47", "43", "5", "23", "13", "11", "11", "79", "31", "35", "5", "5", "25", "5", "37", "95", "31", "13", "43", "17", "5", "35", "17", "23", "11", "41", "59", "7", "47", "5", "13", "7", "11" ]
[ "nonn" ]
75
1
1
[ "A001248", "A073684", "A383504", "A384161" ]
null
Abhiram R Devesh, May 18 2025
2025-06-09T14:42:07
oeisdata/seq/A383/A383504.seq
b6112c87925189922e852c37fa84221f
A383505
Least integer k >= 0 such that binomial(k*n,k+1) = -1 mod n, or -1 if no such integer exists.
[ "0", "1", "2", "3", "4", "341", "6", "79", "8", "19599", "10" ]
[ "nonn", "more" ]
51
1
3
[ "A000430", "A059288", "A099905", "A383505" ]
null
Jason Bard, May 05 2025
2025-05-22T17:06:25
oeisdata/seq/A383/A383505.seq
fda1bfaae74adf13d3bf66b6f1bfd1a6
A383506
Number of non Wilf section-sum partitions of n.
[ "0", "0", "0", "0", "1", "2", "1", "3", "4", "4", "7", "9", "12", "18", "25", "32", "42", "55", "64", "87", "101", "128", "147", "192", "218", "273", "314", "394", "450", "552", "631", "772", "886", "1066", "1221", "1458", "1677", "1980", "2269", "2672", "3029" ]
[ "nonn", "more" ]
10
0
6
[ "A000009", "A000041", "A047966", "A048767", "A098859", "A122111", "A130091", "A130092", "A239455", "A320348", "A325324", "A325325", "A336866", "A351293", "A351294", "A351295", "A351592", "A353837", "A381431", "A381432", "A381433", "A383506", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383514", "A383515", "A383516", "A383517", "A383518", "A383519", "A383520", "A383530", "A383709", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-18T14:37:28
oeisdata/seq/A383/A383506.seq
fa9bb3674b14fdafc4baf8407c8d8ee1
A383507
Number of Wilf and conjugate Wilf integer partitions of n.
[ "1", "1", "2", "2", "3", "3", "6", "7", "9", "12", "14", "19", "20", "27", "30", "31", "40", "50", "56", "68", "76", "86", "112", "126", "139", "170", "197", "216", "251", "297", "317", "378", "411", "466", "521", "607", "621", "745", "791", "892", "975", "1123", "1163", "1366", "1439", "1635", "1757", "2021", "2080", "2464", "2599", "2882", "3116", "3572", "3713" ]
[ "nonn" ]
7
0
3
[ "A047966", "A048767", "A048768", "A098859", "A111133", "A130091", "A130092", "A217605", "A239455", "A320348", "A325324", "A325325", "A325349", "A325351", "A325366", "A325367", "A325368", "A325388", "A336866", "A351293", "A351294", "A381431", "A381432", "A381433", "A383506", "A383507", "A383512", "A383513", "A383534", "A383709" ]
null
Gus Wiseman, May 14 2025
2025-05-15T08:23:11
oeisdata/seq/A383/A383507.seq
456cf40fb811082c45a5cf98af62de1a
A383508
Number of integer partitions of n that are both Look-and-Say and section-sum partitions.
[ "1", "1", "2", "2", "3", "3", "6", "7", "9", "12", "14", "19", "22", "27", "30", "35", "42", "50", "58", "68", "82", "92", "112", "126", "149", "174", "199", "225", "263", "299", "337", "388", "435", "488", "545", "635", "681", "775", "841", "948", "1051", "1181", "1271", "1446", "1553", "1765", "1896", "2141", "2285", "2608", "2799" ]
[ "nonn" ]
13
0
3
[ "A000009", "A000041", "A033461", "A047966", "A047993", "A048767", "A098859", "A106529", "A122111", "A130091", "A130092", "A239455", "A320348", "A325324", "A325325", "A336866", "A351293", "A351294", "A351295", "A351592", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383515", "A383516", "A383517", "A383518", "A383519", "A383530", "A383709", "A384006", "A384007" ]
null
Gus Wiseman, May 17 2025
2025-05-18T14:37:34
oeisdata/seq/A383/A383508.seq
b262e6d2807adf4cb8195d01d0839510
A383509
Number of Look-and-Say partitions of n that are not section-sum partitions.
[ "0", "0", "0", "0", "1", "2", "1", "3", "4", "4", "7", "9", "11", "18", "25", "30", "41", "55", "63", "87", "98", "125", "147", "192", "213", "271", "313", "389", "444", "551", "621", "767", "874", "1055", "1209", "1444", "1646", "1965", "2244", "2644", "2991" ]
[ "nonn", "more" ]
9
0
6
[ "A000009", "A000041", "A047966", "A048767", "A098859", "A130091", "A130092", "A239455", "A320348", "A325324", "A325325", "A336866", "A351293", "A351294", "A351295", "A351592", "A353837", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383515", "A383516", "A383517", "A383519", "A383520", "A383530", "A383709", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-18T14:37:19
oeisdata/seq/A383/A383509.seq
34e9d95a6c78f1378fb7ce8c1f97d39b
A383510
Number of integer partitions of n that are neither Look-and-Say nor section-sum.
[ "0", "0", "0", "1", "0", "0", "3", "2", "5", "10", "14", "19", "33", "38", "55", "81", "107", "137", "201", "248", "349", "450", "596", "745", "1000", "1242", "1611", "2007", "2567", "3164", "4025", "4920", "6166", "7545", "9347", "11360", "14004", "16932", "20686", "24949", "30305", "36366", "43939", "52521", "63098", "75221" ]
[ "nonn" ]
9
0
7
[ "A000009", "A000041", "A033461", "A047966", "A048767", "A048768", "A098859", "A122111", "A130092", "A217605", "A239455", "A320348", "A325324", "A325325", "A336866", "A351293", "A351294", "A351295", "A351592", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383513", "A383515", "A383516", "A383517", "A383519", "A383520", "A383530", "A383531", "A383709", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-18T14:37:23
oeisdata/seq/A383/A383510.seq
19b0671108ab72e1847b13a140388d43
A383511
Number of integer partitions of n that are Look-and-Say and section-sum but not Wilf.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "2", "1", "0", "1", "0", "3", "3", "0", "0", "5", "2", "1", "5", "6", "1", "10", "5", "12", "11", "12", "14", "31", "15", "25", "28", "38" ]
[ "nonn", "more" ]
7
0
16
[ "A000009", "A000041", "A033461", "A047966", "A048767", "A098859", "A122111", "A130091", "A130092", "A217605", "A239455", "A320348", "A325324", "A325325", "A336866", "A351293", "A351294", "A351295", "A351592", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383515", "A383516", "A383517", "A383518", "A383519", "A383520", "A383530", "A383709", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-18T14:37:13
oeisdata/seq/A383/A383511.seq
957f738887f10d1d58f2b6175af44589
A383512
Heinz numbers of conjugate Wilf partitions.
[ "1", "2", "3", "4", "5", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "19", "20", "22", "23", "25", "26", "27", "28", "29", "31", "32", "33", "34", "35", "37", "38", "39", "40", "41", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "64", "67", "68", "69", "71", "73", "74", "75", "76", "77", "79", "80", "81", "82", "83", "85" ]
[ "nonn" ]
10
1
2
[ "A000040", "A000720", "A001222", "A001223", "A005117", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A109298", "A112798", "A122111", "A130091", "A130092", "A239455", "A320348", "A325324", "A325325", "A325349", "A325351", "A325355", "A325366", "A325367", "A325368", "A325388", "A336866", "A351293", "A351294", "A351295", "A381431", "A383506", "A383507", "A383512", "A383513", "A383530", "A383531", "A383532", "A383534", "A383535", "A383709", "A383712" ]
null
Gus Wiseman, May 13 2025
2025-05-15T08:23:15
oeisdata/seq/A383/A383512.seq
56bc01e1d8233251faa24f52c3af83bb
A383513
Heinz numbers of non conjugate Wilf partitions.
[ "6", "12", "18", "21", "24", "30", "36", "42", "48", "54", "60", "63", "65", "66", "70", "72", "78", "84", "90", "96", "102", "105", "108", "110", "114", "120", "126", "132", "133", "138", "140", "144", "147", "150", "154", "156", "162", "165", "168", "174", "180", "186", "189", "192", "198", "204", "210", "216", "220", "222", "228", "231", "234", "238", "240", "246" ]
[ "nonn" ]
10
1
1
[ "A000040", "A000720", "A001222", "A001223", "A005117", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A238745", "A239455", "A320348", "A325324", "A325325", "A325351", "A325355", "A325366", "A325367", "A325368", "A325388", "A336866", "A351293", "A351294", "A351295", "A381431", "A383506", "A383507", "A383512", "A383513", "A383530", "A383531", "A383532", "A383534", "A383535", "A383709", "A383712" ]
null
Gus Wiseman, May 13 2025
2025-05-15T08:23:23
oeisdata/seq/A383/A383513.seq
3268265834e1169cc06c04d90ce4f531
A383514
Heinz numbers of non Wilf section-sum partitions.
[ "10", "14", "15", "22", "26", "33", "34", "35", "38", "39", "46", "51", "55", "57", "58", "62", "65", "69", "74", "77", "82", "85", "86", "87", "91", "93", "94", "95", "100", "106", "111", "115", "118", "119", "122", "123", "129", "130", "133", "134", "141", "142", "143", "145", "146", "155", "158", "159", "161", "166", "170", "177", "178", "182", "183", "185", "187", "190" ]
[ "nonn" ]
5
1
1
[ "A000720", "A001222", "A001223", "A048767", "A051903", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A212166", "A239455", "A320348", "A325366", "A325368", "A336866", "A351293", "A351592", "A381431", "A381432", "A381433", "A383506", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383514", "A383515", "A383516", "A383517", "A383518", "A383519", "A383520", "A383531", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-19T09:44:14
oeisdata/seq/A383/A383514.seq
71613968e2e3f710b9baa1aac8da0572
A383515
Heinz numbers of integer partitions that are both Look-and-Say and section-sum.
[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "20", "23", "25", "27", "28", "29", "31", "32", "37", "40", "41", "43", "44", "45", "47", "49", "50", "52", "53", "56", "59", "61", "64", "67", "68", "71", "73", "75", "76", "79", "80", "81", "83", "88", "89", "92", "97", "98", "99", "101", "103", "104", "107", "109", "112", "113", "116", "117", "121", "124", "125" ]
[ "nonn" ]
5
1
2
[ "A000720", "A001222", "A001223", "A047966", "A048767", "A048768", "A051903", "A055396", "A056239", "A061395", "A098859", "A109298", "A112798", "A122111", "A130091", "A130092", "A212166", "A217605", "A238745", "A239455", "A325368", "A336866", "A351293", "A351294", "A351295", "A351592", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383515", "A383516", "A383517", "A383518", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-19T09:44:07
oeisdata/seq/A383/A383515.seq
aafb3042b2acb13444aa547acc5833c2
A383516
Heinz numbers of Look-and-Say partitions that are not section-sum partitions.
[ "12", "18", "24", "48", "54", "63", "72", "96", "108", "144", "147", "162", "189", "192", "216", "288", "324", "360", "384", "432", "486", "504", "540", "567", "576", "600", "648", "720", "756", "768", "792", "864", "936", "972", "1008", "1029", "1152", "1176", "1188", "1200", "1224", "1296", "1323", "1350", "1368", "1400", "1404", "1440", "1458", "1500" ]
[ "nonn" ]
6
1
1
[ "A000720", "A001222", "A001223", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A212166", "A217605", "A238745", "A239455", "A325368", "A336866", "A351293", "A351294", "A351295", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383514", "A383515", "A383516", "A383517", "A383518", "A383520", "A383531", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-19T09:44:11
oeisdata/seq/A383/A383516.seq
f33bdc69ba2cef7dffb53c1327e060a6
A383517
Heinz numbers of integer partitions that are neither Look-and-Say nor section-sum partitions.
[ "6", "21", "30", "36", "42", "60", "66", "70", "78", "84", "90", "102", "105", "110", "114", "120", "126", "132", "138", "140", "150", "154", "156", "165", "168", "174", "180", "186", "198", "204", "210", "220", "222", "228", "231", "234", "238", "240", "246", "252", "258", "264", "270", "273", "276", "280", "282", "286", "294", "300", "306", "308", "312", "315" ]
[ "nonn" ]
5
1
1
[ "A000720", "A001222", "A001223", "A048767", "A048768", "A051903", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A212166", "A217605", "A238745", "A239455", "A325368", "A336866", "A351293", "A351294", "A351295", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383512", "A383513", "A383514", "A383515", "A383516", "A383517", "A383518", "A383520", "A384006", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-19T09:44:03
oeisdata/seq/A383/A383517.seq
4a728fb79c72516e46f2519d028c6130
A383518
Heinz numbers of integer partitions that are Look-and-Say and section-sum but not conjugate Wilf partitions.
[ "325", "845", "931", "1625", "2527", "3509", "6253", "6517", "8125", "9251" ]
[ "nonn", "more" ]
6
1
1
[ "A001222", "A047966", "A048767", "A048768", "A051903", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A212166", "A217605", "A238745", "A239455", "A325368", "A336866", "A351293", "A351294", "A351295", "A351592", "A381431", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383513", "A383515", "A383516", "A383517", "A383518", "A383531", "A384007" ]
null
Gus Wiseman, May 18 2025
2025-05-20T21:58:42
oeisdata/seq/A383/A383518.seq
795303af59616b99bb8880f9e9da2d43
A383519
Number of section-sum partitions of n that have all distinct multiplicities (Wilf).
[ "1", "1", "2", "2", "3", "3", "6", "7", "9", "12", "14", "19", "21", "27", "30", "33", "41", "50", "57", "68", "79", "89", "112", "126", "144", "172", "198", "220", "257", "298", "327", "383", "423", "477", "533", "621", "650", "760", "816", "920", "1013" ]
[ "nonn", "more" ]
7
0
3
[ "A000009", "A000041", "A047966", "A098859", "A130091", "A130092", "A239455", "A320348", "A325324", "A325325", "A336866", "A351293", "A351294", "A351295", "A351592", "A353837", "A381431", "A381432", "A381433", "A383506", "A383512", "A383513", "A383514", "A383519", "A383520", "A383530", "A383709", "A384006" ]
null
Gus Wiseman, May 19 2025
2025-05-20T21:58:37
oeisdata/seq/A383/A383519.seq
09b3d10514dc4f847fc6a6ea5ceae87a
A383520
Heinz numbers of section-sum partitions with distinct multiplicities (Wilf).
[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "20", "23", "25", "27", "28", "29", "31", "32", "37", "40", "41", "43", "44", "45", "47", "49", "50", "52", "53", "56", "59", "61", "64", "67", "68", "71", "73", "75", "76", "79", "80", "81", "83", "88", "89", "92", "97", "98", "99", "101", "103", "104", "107", "109", "112", "113", "116", "117", "121", "124", "125" ]
[ "nonn" ]
8
1
2
[ "A000720", "A001222", "A001223", "A048767", "A051903", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A212166", "A239455", "A320348", "A325366", "A325368", "A336866", "A351293", "A351592", "A381431", "A381432", "A381433", "A383506", "A383512", "A383513", "A383514", "A383519", "A383520", "A384006" ]
null
Gus Wiseman, May 19 2025
2025-05-20T23:43:53
oeisdata/seq/A383/A383520.seq
e61cff300c6254750e5073649a59a168
A383521
Integers m such that phi(m) = (2/3)*(m+1).
[ "5", "35", "1295", "1679615" ]
[ "nonn", "hard", "more" ]
14
1
1
[ "A000010", "A383521" ]
null
Michel Marcus, Apr 29 2025
2025-05-02T08:01:42
oeisdata/seq/A383/A383521.seq
e4172d2d6611b871705ecc783a4b9fb0
A383522
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k,k).
[ "1", "1", "1", "4", "9", "16", "40", "99", "217", "508", "1236", "2905", "6864", "16537", "39663", "94969", "228953", "552892", "1334704", "3229545", "7828684", "18989079", "46110109", "112104531", "272771536", "664217441", "1618774405", "3947949499", "9634554687", "23526909403", "57484583145", "140529667636" ]
[ "nonn" ]
9
0
4
[ "A000984", "A002426", "A383522", "A383523" ]
null
Seiichi Manyama, Apr 29 2025
2025-04-29T08:53:54
oeisdata/seq/A383/A383522.seq
2d0e2f599197703645d9ffb75c07697a
A383523
a(n) = Sum_{k=0..floor(n/4)} binomial(n,k) * binomial(n-3*k,k).
[ "1", "1", "1", "1", "5", "11", "19", "29", "69", "163", "341", "639", "1319", "2913", "6343", "13061", "27029", "57699", "124813", "265583", "560385", "1191233", "2557743", "5486007", "11713623", "25013061", "53632099", "115219909", "247312763", "530489403", "1139262389", "2450199453", "5271832533", "11341427571", "24407218989" ]
[ "nonn" ]
6
0
5
[ "A000984", "A002426", "A383522", "A383523" ]
null
Seiichi Manyama, Apr 29 2025
2025-04-29T08:53:58
oeisdata/seq/A383/A383523.seq
72cdfaf502f2f290c7b8931c32912532
A383524
a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n-k,k)^2.
[ "1", "1", "3", "13", "43", "171", "711", "2913", "12363", "53203", "230593", "1010703", "4463119", "19827679", "88594299", "397741893", "1793063883", "8113429419", "36832823289", "167701920759", "765577205433", "3503296744233", "16065995216109", "73824301464939", "339844364816559", "1567063753104471", "7237078197034221" ]
[ "nonn" ]
9
0
3
[ "A000172", "A181545", "A275027", "A383524" ]
null
Seiichi Manyama, Apr 29 2025
2025-04-29T08:55:00
oeisdata/seq/A383/A383524.seq
9b92f52f0bf09baf14181469a100985c