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1999-12-11 03:00:00
2025-04-28 00:58:08
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A380605
Expansion of e.g.f. exp(2*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "2", "16", "260", "6544", "224672", "9797824", "518778752", "32332764160", "2319086302208", "188178044545024", "17043816700333568", "1704575787500099584", "186577340672207974400", "22185432394552519868416", "2847773562263558405439488", "392481896442656581445287936", "57805399208817471918851883008" ]
[ "nonn" ]
8
0
2
[ "A002293", "A251574", "A380515", "A380605", "A380606" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-28T08:38:29
oeisdata/seq/A380/A380605.seq
13cdc6fd2e7893a78192f4ff8c7a5b33
A380606
Expansion of e.g.f. exp(3*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "3", "27", "459", "11817", "411183", "18090459", "963856071", "60351513777", "4344290172891", "353515902334299", "32093341598006307", "3215888732193019353", "352572962113533923271", "41981774097966848444763", "5395346708265250105968927", "744369113570455426540767201", "109733083289828610273889269939" ]
[ "nonn" ]
8
0
2
[ "A002293", "A251574", "A380515", "A380605", "A380606" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-28T08:38:25
oeisdata/seq/A380/A380606.seq
5d7c0b162a805a2f051a2da17401bef3
A380607
a(0) = 1, a(n) = 5*binomial(6*(n-1),n-1), for n > 0.
[ "1", "5", "30", "330", "4080", "53130", "712530", "9738960", "134891640", "1886744970", "26589681300", "376970137830", "5370413979840", "76816421507280", "1102478371452150", "15868672192650600", "228978369822304080", "3311260421942706570" ]
[ "nonn" ]
23
0
2
[ "A004355", "A380607" ]
null
Karol A. Penson, Jan 28 2025
2025-02-02T08:48:44
oeisdata/seq/A380/A380607.seq
25f7428f1924e8e7368722dea3fe4183
A380608
a(n) is the number of distinct ways to cut a hexagon with edges of size n into diamonds with integer sides.
[ "2", "37", "6330", "12807773" ]
[ "nonn", "more" ]
10
0
1
[ "A045846", "A380608" ]
null
Craig Knecht, Jan 28 2025
2025-02-07T00:46:35
oeisdata/seq/A380/A380608.seq
de067a2b7942116cb50e5797bef1893b
A380609
Primes a single step away from a cycle under the mapping p-> gpf(2*p+1).
[ "2", "17", "31", "37", "67", "71", "73", "97", "103", "137", "149", "157", "181", "199", "211", "227", "241", "269", "283", "313", "337", "367", "379", "409", "487", "541", "563", "577", "587", "607", "617", "643", "661", "769", "787", "857", "877", "907", "929", "937", "977", "997", "1039", "1093", "1151", "1187", "1237", "1453", "1543", "1567", "1579", "1621" ]
[ "nonn" ]
23
1
1
[ "A006530", "A076565", "A287865", "A380609" ]
null
Johannes M.V.A. Koelman, Jan 28 2025
2025-02-16T19:36:35
oeisdata/seq/A380/A380609.seq
95df46d2435c6898be356ae7b318ab1e
A380610
Irregular triangle read by rows: T(n,k) is the number of non-isomorphic formulas in conjunctive normal form (CNF) with n variables and k distinct nonempty clauses up to permutations of the variables and clauses, 0 <= k < 3^n.
[ "1", "1", "2", "1", "1", "5", "16", "31", "38", "31", "16", "5", "1", "1", "9", "73", "500", "2676", "11390", "39256", "111252", "263014", "524677", "890602", "1294240", "1617050", "1741208", "1617050", "1294240", "890602", "524677", "263014", "111252", "39256", "11390", "2676", "500", "73", "9", "1", "1", "14", "238", "4320", "72225", "1039086", "12712546", "133231940", "1211353657" ]
[ "nonn", "tabf" ]
44
0
3
[ "A000244", "A371830", "A380518", "A380610", "A380630" ]
null
Frank Schwidom, Jan 28 2025
2025-02-26T06:32:22
oeisdata/seq/A380/A380610.seq
3e7ff0199fe13b3ddceada7ecc684464
A380611
Irregular triangle read by rows: T(r,c) is the product of the number of standard Young tableaux (A117506) and the number of semistandard Young tableaux (A262030) for partitions of r.
[ "1", "1", "3", "1", "10", "16", "1", "35", "135", "40", "45", "1", "126", "896", "875", "756", "375", "96", "1", "462", "5250", "10206", "8400", "2450", "14336", "2800", "875", "1701", "175", "1", "1716", "28512", "90552", "74250", "65856", "257250", "48000", "74088", "55566", "102900", "8100", "10976", "5488", "288", "1", "6435", "147147", "686400", "567567", "931392", "3244032", "606375", "194040", "2910600", "1448832", "2673000", "202125", "666792", "846720", "1029000", "491520", "19845", "24696", "65856", "14400", "441", "1" ]
[ "nonn", "tabf" ]
34
0
3
[ "A000041", "A000312", "A047874", "A059304", "A088218", "A117506", "A262030", "A365643", "A380611" ]
null
Wouter Meeussen, Jan 28 2025
2025-01-29T22:15:35
oeisdata/seq/A380/A380611.seq
d1dc00e4d4bd6b4170ffd395ade2f459
A380612
a(n) = (-1)^n*Product_{k=1..n} (2*k + 1)*(2*k - 3).
[ "1", "3", "-15", "315", "-14175", "1091475", "-127702575", "21070924875", "-4656674397375", "1327152203251875", "-473793336560919375", "207047688077121766875", "-108700036240488927609375", "67502722505343624045421875", "-48939473816374127432930859375", "40962339584305144661363129296875" ]
[ "sign", "easy" ]
35
0
2
[ "A001147", "A380570", "A380612" ]
null
Thomas Scheuerle, Jan 28 2025
2025-02-02T16:30:45
oeisdata/seq/A380/A380612.seq
b017ceace324a2f8537f9e1cfea27f38
A380613
Expansion of Product_{k>=1} (1 + x^k)^prime(k)#.
[ "1", "2", "7", "42", "291", "2970", "36950", "597100", "11070875", "248103940", "7018494836", "215718595582", "7881561212732", "320881902092122", "13754717161317416", "643588827524430916", "33926485821837232397", "1992916854095359256932", "121393059052727838936847", "8107963745977267426512386", "574571379331620422000295082" ]
[ "nonn" ]
8
0
2
[ "A002110", "A061152", "A261052", "A380497", "A380613", "A380614" ]
null
Ilya Gutkovskiy, Jan 28 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380613.seq
5143a00623dc364c1f8bb6f9c7c92141
A380614
Product_{n>=1} (1 + x^n)^a(n) = Sum_{n>=0} prime(n)# * x^n.
[ "2", "5", "20", "155", "1860", "24970", "444060", "8583935", "202071920", "5992773714", "186947632200", "7001535728810", "288868991951760", "12455290280871150", "587972068547997856", "31327583556949986095", "1856116108295418943020", "113366872636395467452840", "7619343577986975410930880", "541957669076266404650853414" ]
[ "nonn" ]
7
1
1
[ "A002110", "A168246", "A305871", "A380498", "A380613", "A380614" ]
null
Ilya Gutkovskiy, Jan 28 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380614.seq
4b9b8b0fe11a6d2e15b7867f0061e20d
A380615
Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
[ "1", "1", "1", "2", "2", "1", "5", "8", "5", "2", "18", "38", "34", "14", "3", "105", "275", "288", "154", "42", "6", "902", "2614", "3102", "1959", "705", "140", "14", "9749", "30346", "39242", "27898", "11956", "3142", "473", "34", "127072", "415360", "573654", "446078", "217000", "68544", "13886", "1670", "95", "1915951", "6513999", "9484003", "7911844", "4230802", "1523176", "373188", "60614", "5969", "280" ]
[ "nonn", "tabl" ]
12
0
4
[ "A002995", "A007769", "A053979", "A170946", "A379430", "A380237", "A380615", "A380616", "A380617", "A380618", "A380619" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-28T20:51:01
oeisdata/seq/A380/A380615.seq
34f555ecabcb68928804c25ef2d31468
A380616
Triangle read by rows: T(n,k) is the number of unsensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
[ "1", "1", "1", "2", "2", "1", "5", "8", "5", "2", "17", "33", "30", "13", "3", "79", "198", "208", "118", "35", "6", "554", "1571", "1894", "1232", "472", "104", "12", "5283", "16431", "21440", "15545", "6879", "1914", "315", "27", "65346", "213831", "296952", "233027", "115134", "37311", "7881", "1021", "65", "966156", "3288821", "4799336", "4019360", "2163112", "787065", "196267", "32857", "3407", "175" ]
[ "nonn", "tabl" ]
6
0
4
[ "A006082", "A053979", "A054499", "A214816", "A277741", "A380615", "A380616", "A380617", "A380620", "A380621" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-28T20:51:24
oeisdata/seq/A380/A380616.seq
39ea39f28e93aaad25f652a548877aca
A380617
Triangle read by rows: T(n,k) is the number of achiral combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
[ "1", "1", "1", "2", "2", "1", "5", "8", "5", "2", "16", "28", "26", "12", "3", "53", "121", "128", "82", "28", "6", "206", "528", "686", "505", "239", "68", "10", "817", "2516", "3638", "3192", "1802", "686", "157", "20", "3620", "12302", "20250", "19976", "13268", "6078", "1876", "372", "35", "16361", "63643", "114669", "126876", "95422", "50954", "19346", "5100", "845", "70" ]
[ "nonn", "tabl" ]
4
0
4
[ "A001405", "A018191", "A170947", "A379431", "A380615", "A380616", "A380617" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-28T20:51:14
oeisdata/seq/A380/A380617.seq
acd2bfd2382bb786d7d05edebdd062aa
A380618
Number of sensed combinatorial maps with n edges and 2 vertices.
[ "1", "2", "8", "38", "275", "2614", "30346", "415360", "6513999", "115063118", "2259975228", "48860184539", "1153140907207", "29502289676802", "813371784160602", "24040797257734161", "758379326971459945", "25432414455826532993", "903508909333199982128", "33897272145242834426910", "1339265974992611047296679" ]
[ "nonn" ]
6
1
2
[ "A380237", "A380615", "A380618", "A380619", "A380620" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-28T20:51:10
oeisdata/seq/A380/A380618.seq
25c7624f73a1ee95efe8c0c844be0dd6
A380619
Number of sensed combinatorial maps with n edges and 3 vertices.
[ "1", "5", "34", "288", "3102", "39242", "573654", "9484003", "175036065", "3568736050", "79697415569", "1935425955944", "50794210191337", "1432898704970561", "43244525933606928", "1390448844972918928", "47455314531812444788", "1713525997666221196906", "65266335503957271588042", "2615307907226341637828915" ]
[ "nonn" ]
7
2
2
[ "A380615", "A380618", "A380619", "A380621" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-28T20:51:06
oeisdata/seq/A380/A380619.seq
67ebf6ca992f4a9a5e15d6f27b9dd004
A380620
Number of unsensed combinatorial maps with n edges and 2 vertices.
[ "1", "2", "8", "33", "198", "1571", "16431", "213831", "3288821" ]
[ "nonn", "more" ]
4
1
2
[ "A380239", "A380616", "A380618", "A380620", "A380621" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-30T15:28:33
oeisdata/seq/A380/A380620.seq
82910d6d888ff989d2e9b6dec09e1263
A380621
Number of unsensed combinatorial maps with n edges and 3 vertices.
[ "1", "5", "30", "208", "1894", "21440", "296952", "4799336" ]
[ "nonn", "more" ]
4
2
2
[ "A380616", "A380619", "A380620", "A380621" ]
null
Andrew Howroyd, Jan 28 2025
2025-01-30T15:28:25
oeisdata/seq/A380/A380621.seq
27f6a34763919dea747a38be28f1bddd
A380622
Array read by antidiagonals: T(n,k) is the number of rooted k-regular combinatorial maps with n vertices, n >= 0, k >= 1.
[ "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "1", "3", "5", "1", "0", "1", "0", "24", "0", "1", "0", "1", "15", "189", "297", "60", "1", "0", "1", "0", "1695", "0", "4896", "0", "1", "0", "1", "105", "19305", "472200", "869400", "100278", "1105", "1", "0", "1", "0", "252000", "0", "242183775", "0", "2450304", "0", "1", "0", "1", "945", "3828825", "2465608950", "103694490900", "198147676875", "16482741030", "69533397", "27120", "1", "0" ]
[ "nonn", "tabl" ]
9
0
12
[ "A000012", "A053979", "A062980", "A269919", "A292186", "A380622", "A380623", "A380624", "A380625" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T16:35:34
oeisdata/seq/A380/A380622.seq
e13cb927517c4581cf9d2343821da6d3
A380623
Number of rooted 5-regular combinatorial maps with 2n vertices.
[ "1", "189", "869400", "16482741030", "811815704093520", "82428779884228798041", "14987637044586056537983800", "4438122232105976899960948809420", "1998996880327869592350459728071408800", "1300772228637464354810371940980750446850116", "1174611244368635468934806695142536970482225836000" ]
[ "nonn" ]
7
0
2
[ "A380622", "A380623" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T16:35:29
oeisdata/seq/A380/A380623.seq
52c91541b842e4bbc923cced4db4d674
A380624
Number of rooted 6-regular combinatorial maps with n vertices.
[ "1", "15", "1695", "472200", "242183775", "198147676875", "236869405180500", "389616942676537500", "844097335215098919375", "2329896471102350138203125", "7982322432441532563075684375", "33237663686231528596766478000000", "165317735601526459288582776594562500", "968055507884358705829008353504856562500" ]
[ "nonn" ]
7
0
2
[ "A380622", "A380624" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T16:35:25
oeisdata/seq/A380/A380624.seq
5c3a4a7e8d6e393c05806ca69f753941
A380625
Number of rooted regular combinatorial maps with n edges.
[ "1", "2", "4", "21", "130", "1135", "12448", "154441", "2283922", "38761556", "721082359", "14999247901", "345288253975", "8513996163751", "228807509644648", "6634125686206751", "203954623297226722", "6705169274925371251", "234777003656354137054", "8632415297513570062501", "335879068944350793715480" ]
[ "nonn" ]
9
0
2
[ "A380622", "A380625" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T16:35:20
oeisdata/seq/A380/A380625.seq
0cac5895f329247a82c83e676bdaf312
A380626
Array read by antidiagonals: T(n,k) is the number of sensed k-regular combinatorial maps with n vertices, n >= 0, k >= 1.
[ "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "1", "2", "3", "1", "0", "1", "0", "7", "0", "1", "0", "1", "5", "29", "36", "11", "1", "0", "1", "0", "174", "0", "365", "0", "1", "0", "1", "18", "1475", "26614", "44106", "5250", "81", "1", "0", "1", "0", "16162", "0", "10107019", "0", "103801", "0", "1", "0", "1", "105", "214215", "102762168", "3703659517", "6605320523", "549530780", "2492164", "1228", "1", "0" ]
[ "nonn", "tabl" ]
8
0
12
[ "A000012", "A007769", "A129114", "A170946", "A292206", "A380622", "A380626", "A380627", "A380628", "A380629" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T21:31:08
oeisdata/seq/A380/A380626.seq
ba26e955dc93bc120504fa866ae28685
A380627
Number of sensed 5-regular combinatorial maps with 2n vertices.
[ "1", "29", "44106", "549530780", "20295421909475", "1648575609240648557", "249793950749168438672432", "63401746172946552016801544036", "24987461004098373175802500801970565", "14453024762638492834399423828614955417596", "11746112443686354689351672116979783313870949792" ]
[ "nonn" ]
6
0
2
[ "A380623", "A380626", "A380627" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T21:31:04
oeisdata/seq/A380/A380627.seq
82f720d5f2926b657534d54b7d14f44f
A380628
Number of sensed 6-regular combinatorial maps with n vertices.
[ "1", "5", "174", "26614", "10107019", "6605320523", "6579728772912", "9276594775469270", "17585361213957551946", "43146230949730084319048", "133038707207639820811320335", "503600964942920889570482778054", "2296079661132313737232568593302086", "12410968049799470734493011986934972606" ]
[ "nonn" ]
7
0
2
[ "A380624", "A380626", "A380628" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T21:31:00
oeisdata/seq/A380/A380628.seq
f60802ce7a3159508cdbb78e6f715121
A380629
Number of sensed regular combinatorial maps with n edges.
[ "1", "2", "3", "9", "26", "135", "1124", "11225", "143600", "2156862", "36069006", "681844857", "14387370477", "327462904319", "8171705457024", "221137571070305", "6373582250114091", "197210862517274355", "6521583445100185049", "227168823675390365225", "8396976723995537706278", "327880018217851412105973" ]
[ "nonn" ]
5
0
2
[ "A170946", "A380625", "A380626", "A380629" ]
null
Andrew Howroyd, Jan 29 2025
2025-01-29T21:30:57
oeisdata/seq/A380/A380629.seq
e19d5913d7418fed80696b5e6f843023
A380630
Number of matrices with n columns, any number of distinct rows and entries in 0..2 and without an all zero row up to permutations of rows and columns.
[ "1", "4", "144", "11250688", "50371911404609819639808", "58894902159279477652776826941706227937004584169809397602591562463707136" ]
[ "nonn" ]
11
0
2
[ "A003180", "A380518", "A380610", "A380630" ]
null
Andrew Howroyd, Feb 19 2025
2025-03-02T16:03:55
oeisdata/seq/A380/A380630.seq
88ca515617e3f9df2c1d08e375e9ee84
A380631
Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with k cycles and each node a member of exactly one cycle, 0 <= k <= floor(n/3).
[ "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "2", "0", "1", "2", "2", "0", "1", "3", "5", "0", "1", "3", "10", "0", "1", "4", "17", "6", "0", "1", "4", "26", "18", "0", "1", "5", "38", "51", "0", "1", "5", "52", "106", "18", "0", "1", "6", "70", "205", "87", "0", "1", "6", "90", "350", "286", "0", "1", "7", "115", "579", "741", "66", "0", "1", "7", "142", "887", "1660", "406" ]
[ "nonn", "tabf" ]
15
0
18
[ "A000007", "A000012", "A008619", "A380631", "A380632", "A380633", "A380634", "A381467" ]
null
Andrew Howroyd, Feb 24 2025
2025-02-25T13:13:27
oeisdata/seq/A380/A380631.seq
8bd2be560ac4ed7b8290fa7c4844f708
A380632
Number of simple connected graphs on n unlabeled nodes with each node a member of exactly one cycle.
[ "1", "0", "0", "1", "1", "1", "2", "2", "3", "5", "9", "14", "28", "49", "95", "182", "369", "733", "1509", "3103", "6504", "13627", "28949", "61701", "132457", "285454", "618863", "1346022", "2940287", "6444364", "14172744", "31257883", "69142445", "153333476", "340880766", "759549740", "1696122213", "3795178540", "8508326129", "19109193805", "42991993545", "96881110654" ]
[ "nonn" ]
8
0
7
[ "A000083", "A380631", "A380632", "A380805" ]
null
Andrew Howroyd, Feb 24 2025
2025-02-24T16:32:30
oeisdata/seq/A380/A380632.seq
558501dad6baded015c0fc74bdfa05c9
A380633
Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes of degree at most 3 with k cycles and each node a member of exactly one cycle, 0 <= k <= floor(n/3).
[ "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "2", "0", "1", "2", "1", "0", "1", "3", "3", "0", "1", "3", "6", "0", "1", "4", "11", "2", "0", "1", "4", "17", "5", "0", "1", "5", "26", "17", "0", "1", "5", "36", "37", "2", "0", "1", "6", "50", "78", "12", "0", "1", "6", "65", "140", "44", "0", "1", "7", "85", "248", "131", "4", "0", "1", "7", "106", "396", "325", "23" ]
[ "nonn", "tabf" ]
9
0
18
[ "A000007", "A000012", "A000672", "A003453", "A004526", "A380631", "A380633", "A380805" ]
null
Andrew Howroyd, Feb 24 2025
2025-02-24T16:32:26
oeisdata/seq/A380/A380633.seq
f421a4a883a51589fc69a106b3761403
A380634
Number of unlabeled 2,3 cacti (triangular cacti with bridges) with n triangles and every node contained in exactly one triangle.
[ "1", "1", "1", "2", "6", "18", "66", "265", "1140", "5186", "24588", "120062", "600884", "3066490", "15907266", "83665520", "445317808", "2394928214", "12997988041", "71116953074", "391931826699", "2174062325068", "12130745830640", "68049392678632", "383601371168527", "2172093593344465", "12349917974708867" ]
[ "nonn" ]
10
0
4
[ "A091487", "A287891", "A380631", "A380634", "A381467" ]
null
Andrew Howroyd, Feb 24 2025
2025-02-25T01:56:24
oeisdata/seq/A380/A380634.seq
2cac16c21a431b696b37a51aab1ccd53
A380635
a(1) = 1; a(n+1) = Sum_{d^2|n} a(n/d^2).
[ "1", "1", "1", "1", "2", "2", "2", "2", "3", "4", "4", "4", "5", "5", "5", "5", "7", "7", "8", "8", "10", "10", "10", "10", "12", "13", "13", "14", "16", "16", "16", "16", "19", "19", "19", "19", "24", "24", "24", "24", "28", "28", "28", "28", "32", "34", "34", "34", "39", "40", "41", "41", "46", "46", "48", "48", "53", "53", "53", "53", "58", "58", "58", "60", "67", "67", "67", "67", "74", "74", "74", "74", "84", "84", "84", "85", "93", "93", "93", "93" ]
[ "nonn" ]
7
1
5
[ "A003238", "A076752", "A167865", "A307779", "A317240", "A380635" ]
null
Ilya Gutkovskiy, Jan 28 2025
2025-01-29T07:16:49
oeisdata/seq/A380/A380635.seq
45772cf4432a2162cd5f952e67849c19
A380636
Expansion of e.g.f. exp(x*C(2*x)^2) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers, A000108.
[ "1", "1", "9", "145", "3409", "105921", "4102681", "190630609", "10340890785", "641787925249", "44866443580201", "3489524955627921", "298914951848510449", "27966383049400396225", "2837759948683874979129", "310425081738609550495441", "36418950255827044479693121", "4561668082989623411575958529" ]
[ "nonn" ]
16
0
3
[ "A000108", "A251568", "A380636" ]
null
Seiichi Manyama, Jan 28 2025
2025-03-16T10:08:55
oeisdata/seq/A380/A380636.seq
229103712343fa0fdfebf2b0b701dfa1
A380637
Expansion of e.g.f. exp(x*G(3*x)^3) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
[ "1", "1", "19", "703", "39313", "2959921", "280935811", "32221238239", "4336213980673", "670088514363553", "116959281939738451", "22759439305951039231", "4885844614853182749649", "1147088485458553806981073", "292394958982688921734424323", "80420728320326634679448511391" ]
[ "nonn" ]
19
0
3
[ "A001764", "A380512", "A380637", "A380641" ]
null
Seiichi Manyama, Jan 28 2025
2025-03-16T10:08:59
oeisdata/seq/A380/A380637.seq
8327a63b30215b0980a52ad789ca5a7c
A380638
Expansion of e.g.f. exp(x*G(4*x)^4) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "1", "33", "2209", "226753", "31555521", "5557183201", "1185423664993", "297171500140929", "85638231765516673", "27896677183469054881", "10137203757416219332641", "4065668625283435566910273", "1783936343221839549449049409", "850091650335726912762794748513", "437197222292805469886634467693281" ]
[ "nonn" ]
13
0
3
[ "A002293", "A380516", "A380638" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-29T07:57:05
oeisdata/seq/A380/A380638.seq
2f41bb47c171ac6582bbdb390c816e71
A380639
Expansion of e.g.f. exp(x/(1 - 2*x)^2).
[ "1", "1", "9", "97", "1297", "20961", "398041", "8678209", "213337377", "5830560577", "175187949481", "5734893998241", "203021979225649", "7724154592735777", "314158263983430777", "13597375157683820161", "623802598335834369601", "30228101725367033318529", "1542430410234859308052297" ]
[ "nonn", "easy" ]
11
0
3
[ "A082579", "A380636", "A380639", "A380640" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-29T08:10:38
oeisdata/seq/A380/A380639.seq
37ce949c769c349cc2d995f57054dd66
A380640
Expansion of e.g.f. exp(x*G(2*x)^2) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
[ "1", "1", "9", "193", "6673", "319521", "19575001", "1461908449", "128828471073", "13086232224193", "1505486837413801", "193477959856396161", "27472294970916814129", "4271180551913140331233", "721640087945607030774393", "131656978622706616938932641", "25795404137789777215960879681", "5402020596794976601680149234049" ]
[ "nonn" ]
20
0
3
[ "A001764", "A080893", "A380511", "A380636", "A380639", "A380640", "A380643" ]
null
Seiichi Manyama, Jan 28 2025
2025-03-16T10:09:03
oeisdata/seq/A380/A380640.seq
f2b009dae43c31c6e5e0f9ac87fc7e5b
A380641
Expansion of e.g.f. exp(x/(1 - 3*x)^3).
[ "1", "1", "19", "379", "8857", "244801", "7904251", "292980619", "12257946289", "570627408097", "29212843607011", "1629314013114811", "98250285167099209", "6365331315043185889", "440712959779710869707", "32460639303987670526731", "2533396174719346231613281", "208776665140069914314618689" ]
[ "nonn", "easy" ]
12
0
3
[ "A091695", "A380637", "A380641" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-29T08:10:33
oeisdata/seq/A380/A380641.seq
ab539bef25b8767bfc45737f8f3c2f94
A380642
Numbers k such that the total number of digits d in the numbers from 1 to k is even for each d from 0 to 9.
[ "0", "122", "220", "440", "660", "880", "10022", "10100", "10198", "10202", "10918", "11000", "11098", "11122", "11220", "11440", "11660", "11880", "12002", "12120", "12222", "12344", "12442", "12662", "12882", "13244", "13322", "13424", "14140", "14242", "14324", "14422", "15522", "16160", "16262", "16622", "17722", "18180", "18282", "18822", "19018", "19922" ]
[ "base", "nonn" ]
16
1
2
[ "A360320", "A380642" ]
null
Max Alekseyev, Jan 28 2025
2025-01-29T19:29:35
oeisdata/seq/A380/A380642.seq
503ef5645f477459160108b0985a4cf5
A380643
Expansion of e.g.f. exp(x*G(3*x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "1", "19", "865", "63289", "6402421", "827951491", "130454402149", "24246255965905", "5193341198368489", "1259626725043888051", "341256073037890028041", "102138911537774675080969", "33470594059698797005874845", "11918817613356955871120346979", "4582850483720783516657005897741" ]
[ "nonn" ]
19
0
3
[ "A002293", "A080893", "A380637", "A380640", "A380643" ]
null
Seiichi Manyama, Jan 29 2025
2025-03-16T10:09:08
oeisdata/seq/A380/A380643.seq
c615d480fbb4511f0d4f89519e04e0c5
A380644
Numbers that can be expressed as 4*j*k+j+k, j,k >= 1, as well as 4*j*k-j-k, j,k >= 2.
[ "26", "41", "47", "56", "61", "68", "71", "74", "86", "89", "96", "101", "107", "110", "116", "128", "131", "140", "146", "151", "152", "155", "159", "161", "166", "173", "176", "182", "185", "191", "194", "201", "206", "208", "209", "215", "221", "224", "236", "239", "242", "250", "251", "257", "261", "263", "266", "271", "272", "278", "281", "290", "293", "296", "299" ]
[ "nonn" ]
6
1
1
[ "A054520", "A124934", "A125217", "A125218", "A380140", "A380509", "A380572", "A380644" ]
null
Hugo Pfoertner, Jan 29 2025
2025-01-29T07:53:46
oeisdata/seq/A380/A380644.seq
d77950e8b8ac5f19a0c101f3046834a3
A380645
The expansion of the Stieltjes continued fraction 1/(1 - x/(1 - a(A053645(0))*x/(1 - a(A053645(1))*x/(1 - a(A053645(2))*x/...)))) gives the sequence itself.
[ "1", "1", "2", "5", "15", "52", "201", "857", "4370", "34365", "478287", "9095996", "189526537", "4036216585", "87129122290", "2478683501397", "2450240534552191", "12482183328151728692", "65634092872761268943625", "345370818796643845031835465", "1817414952852912380501431441282" ]
[ "nonn" ]
26
0
3
[ "A053645", "A380645" ]
null
Thomas Scheuerle, Feb 06 2025
2025-02-07T15:58:12
oeisdata/seq/A380/A380645.seq
c636440ee4cc07f54d815c647433b798
A380646
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x)/(1 + x)^2 ).
[ "1", "4", "46", "932", "27568", "1080432", "52916176", "3115326496", "214470890496", "16914853191680", "1504252282653184", "148956086481767424", "16256865070022066176", "1938988214539948730368", "250943399365390735104000", "35026523834624205803491328", "5245178283068781060488298496", "838841884254236846183525646336" ]
[ "nonn" ]
13
0
2
[ "A065866", "A088690", "A097629", "A377829", "A377892", "A380646", "A380647", "A380648", "A380828" ]
null
Seiichi Manyama, Feb 06 2025
2025-02-06T09:01:29
oeisdata/seq/A380/A380646.seq
0d6992798cc7d58cece42621a65f4413
A380647
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x)/(1 + x)^3 ).
[ "1", "6", "105", "3246", "146637", "8780688", "657224901", "59140486800", "6223651526457", "750357182131200", "102014741343847329", "15443915464974191616", "2576937457466957107845", "469914373917914931984384", "92982800086882512621716925", "19843243096453465663599962112", "4543276116844426827394718716401" ]
[ "nonn" ]
15
0
2
[ "A088690", "A370055", "A377830", "A377893", "A380646", "A380647", "A380648" ]
null
Seiichi Manyama, Feb 06 2025
2025-02-06T09:01:21
oeisdata/seq/A380/A380647.seq
b722696cf18437c45d52f23b459d23da
A380648
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-4*x)/(1 + x)^4 ).
[ "1", "8", "188", "7816", "475096", "38289504", "3857806144", "467330651456", "66209818738176", "10747317030192640", "1967261819870112256", "400989528160028255232", "90087157573721153554432", "22119056538323287540637696", "5893098619063477612068864000", "1693364632974231188010697990144" ]
[ "nonn" ]
14
0
2
[ "A088690", "A370058", "A380646", "A380647", "A380648" ]
null
Seiichi Manyama, Feb 06 2025
2025-02-06T10:23:03
oeisdata/seq/A380/A380648.seq
97e86d19815f378f54e0b7ef02aaf151
A380649
Rectangular array ((-1)*D(i,j,1,2)) read by descending antidiagonals: D(i,j,s,n) denotes the determinant of the matrix described in Comments.
[ "1", "4", "3", "8", "7", "6", "13", "12", "11", "10", "19", "18", "17", "16", "15", "26", "25", "24", "23", "22", "21", "34", "33", "32", "31", "30", "29", "28", "43", "42", "41", "40", "39", "38", "37", "36", "53", "52", "51", "50", "49", "48", "47", "46", "45", "64", "63", "62", "61", "60", "59", "58", "57", "56", "55", "76", "75", "74", "73", "72", "71", "70", "69", "68", "67", "66" ]
[ "nonn", "tabl" ]
6
1
2
[ "A000027", "A000096", "A038722", "A185787", "A333029", "A380649", "A380660", "A380661" ]
null
Clark Kimberling, Jan 31 2025
2025-02-03T21:35:27
oeisdata/seq/A380/A380649.seq
d33b743b16e8fa9373c0c52920bce5a0
A380650
The largest number which is a linear combination of the divisors of n with nonnegative integer coefficients such that no linear combination with smaller nonnegative integer coefficients is equal to n.
[ "0", "1", "2", "3", "4", "7", "6", "7", "8", "13", "10", "17", "12", "19", "22", "15", "16", "25", "18", "31", "32", "31", "22", "37", "24", "37", "26", "45", "28", "60", "30", "31", "52", "49", "58", "59", "36", "55", "62", "67", "40", "85", "42", "73", "76", "67", "46", "77", "48", "73", "82", "87", "52", "79", "94", "97", "92", "85", "58" ]
[ "nonn" ]
29
1
3
[ "A000010", "A145388", "A380650" ]
null
Alexei Vernitski, Jan 29 2025
2025-02-14T14:25:10
oeisdata/seq/A380/A380650.seq
d75183ba14db2f80a12579f83761d743
A380651
a(n) = 4^n - n*3^(n-1).
[ "1", "3", "10", "37", "148", "619", "2638", "11281", "48040", "203095", "851746", "3544765", "14651452", "60200131", "246114934", "1001997289", "4065384784", "16448074927", "66394953802", "267516917653", "1076266398436", "4324824038683", "17362058273950", "69646979806657", "279215540418808" ]
[ "nonn", "easy" ]
31
0
2
[ "A000302", "A027471", "A380651" ]
null
Enrique Navarrete, Jan 29 2025
2025-02-06T08:21:54
oeisdata/seq/A380/A380651.seq
a132cba1497333c6a2d181f0f711c4a3
A380652
Shifts left one place under the inverse modulo 2 binomial transform.
[ "1", "1", "0", "-1", "-1", "-2", "-1", "1", "4", "3", "-1", "-4", "-1", "-3", "0", "5", "5", "4", "-1", "-5", "-2", "-5", "-1", "6", "9", "1", "-6", "-5", "13", "14", "11", "1", "-38", "-39", "-1", "38", "41", "81", "42", "-37", "-163", "-128", "37", "167", "56", "143", "11", "-214", "-253", "-219", "36", "257", "149", "328", "105", "-303", "-624", "-247", "313", "490", "-455", "-387", "-476", "-417", "1251", "1250" ]
[ "sign" ]
10
0
6
[ "A000587", "A010060", "A047999", "A166966", "A380652" ]
null
Ilya Gutkovskiy, Jan 29 2025
2025-02-11T16:36:56
oeisdata/seq/A380/A380652.seq
996cb784b463791ddcd3fc9b3275bb23
A380653
Number of positive integers less than or equal to n that have the same sum of prime factors (with repetition) as n.
[ "1", "1", "1", "1", "1", "2", "1", "1", "2", "2", "1", "3", "1", "1", "1", "2", "1", "3", "1", "2", "1", "2", "1", "3", "2", "1", "4", "2", "1", "3", "1", "4", "1", "2", "1", "5", "1", "1", "1", "3", "1", "2", "1", "2", "4", "1", "1", "5", "2", "3", "1", "2", "1", "6", "2", "3", "1", "2", "1", "4", "1", "1", "4", "5", "1", "3", "1", "2", "1", "3", "1", "6", "1", "1", "5", "2", "2", "3", "1", "6", "7", "2", "1", "4", "2", "1", "1", "3", "1", "7", "2", "1", "1", "1", "1", "8", "1", "4", "4", "5" ]
[ "nonn" ]
12
1
6
[ "A001414", "A058933", "A263025", "A380653", "A380654" ]
null
Ilya Gutkovskiy, Jan 29 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380653.seq
f6b1e23cffe14918e62198b372035f91
A380654
Number of positive integers less than or equal to n that have the same sum of distinct prime factors as n.
[ "1", "1", "1", "2", "1", "2", "1", "3", "2", "2", "1", "3", "1", "1", "1", "4", "1", "4", "1", "3", "1", "2", "1", "5", "6", "1", "3", "2", "1", "2", "1", "5", "1", "2", "1", "7", "1", "1", "1", "4", "1", "2", "1", "3", "2", "1", "1", "8", "5", "6", "1", "2", "1", "9", "2", "3", "1", "2", "1", "3", "1", "1", "4", "6", "1", "3", "1", "3", "1", "2", "1", "10", "1", "1", "3", "2", "2", "3", "1", "7", "4", "2", "1", "3", "2", "1", "1", "4", "1", "5", "2", "2", "1", "1", "1", "11", "1", "4", "3", "8" ]
[ "nonn" ]
11
1
4
[ "A008472", "A067003", "A263025", "A380653", "A380654" ]
null
Ilya Gutkovskiy, Jan 29 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380654.seq
5110e9bf0a636cc50a87d3636eb05af9
A380655
Smallest prime p > 10^(n-1) for which successive cyclic shifts of digits by 1, ..., n-1 positions to the left are all prime, or -1 if no such p exists.
[ "2", "11", "113", "1193", "11939", "193939", "71777393", "913311913", "93739179151", "317793117877", "731779311787", "1373779119729007" ]
[ "nonn", "base", "more" ]
61
1
1
[ "A247153", "A380655", "A380669" ]
null
Jean-Marc Rebert, Jan 29 2025
2025-02-25T11:24:46
oeisdata/seq/A380/A380655.seq
0ce6a30d2319a6304a6be4783fbe432b
A380656
a(n) is the number of divisors d such that -d^n mod n = d.
[ "0", "1", "0", "0", "0", "2", "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "2", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "3", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "2", "0", "1", "0", "0", "0", "4", "0", "0", "0", "4", "0", "1", "0", "1", "0", "1", "0", "2", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "2", "1", "1", "0", "1", "0", "1", "0", "1", "0", "0" ]
[ "nonn" ]
19
1
6
[ "A000005", "A371883", "A380656" ]
null
Juri-Stepan Gerasimov, Feb 03 2025
2025-02-05T21:59:33
oeisdata/seq/A380/A380656.seq
afa3ca3d8f4fabdba91707033d394beb
A380657
Numbers whose prime factorization has more Pythagorean prime factors than non-Pythagorean prime factors (including multiplicities).
[ "5", "13", "17", "25", "29", "37", "41", "50", "53", "61", "65", "73", "75", "85", "89", "97", "101", "109", "113", "125", "130", "137", "145", "149", "157", "169", "170", "173", "175", "181", "185", "193", "195", "197", "205", "221", "229", "233", "241", "250", "255", "257", "265", "269", "275", "277", "281", "289", "290", "293", "305", "313", "317", "325", "337" ]
[ "nonn" ]
6
1
1
[ "A000040", "A002144", "A002145", "A083025", "A376961", "A377625", "A378137", "A378139", "A378140", "A380657" ]
null
Clark Kimberling, Jan 30 2025
2025-01-31T13:42:02
oeisdata/seq/A380/A380657.seq
a60741be2d4a917dc32992ce036bb2ec
A380658
Rectangular array, read by descending antidiagonals: row n shows the numbers whose prime factorization includes n-1 Pythagorean primes (including multiplicities).
[ "2", "3", "1", "4", "5", "25", "6", "10", "50", "125", "7", "13", "65", "250", "625", "8", "15", "75", "325", "1250", "3125", "9", "17", "85", "375", "1625", "6250", "15625" ]
[ "nonn", "tabl", "more" ]
4
1
1
[ "A000040", "A002144", "A002145", "A083025", "A380658", "A380659" ]
null
Clark Kimberling, Jan 31 2025
2025-02-03T21:35:35
oeisdata/seq/A380/A380658.seq
910f62acb08ad16b7656960c98f81e15
A380659
Rectangular array, read by descending antidiagonals: row n shows the numbers whose prime factorization includes n-1 non-Pythagorean primes (including multiplicities).
[ "1", "5", "2", "13", "3", "4", "17", "7", "6", "8", "25", "10", "9", "12", "16", "29", "11", "14", "18", "24", "32", "37", "15", "20", "27", "36", "48", "64", "41", "19", "21", "28", "54", "72", "96", "128", "53", "23", "22", "40", "56", "108", "144", "192", "256", "61", "26", "30", "42", "80", "112", "216", "288", "384", "512", "65", "31", "33", "44", "81", "160", "224", "432", "576", "768", "1024", "73", "34", "38", "60", "84", "162", "320", "448", "864", "1152", "1536", "2048" ]
[ "nonn", "tabl" ]
5
1
2
[ "A000040", "A002144", "A002145", "A083025", "A380658", "A380659" ]
null
Clark Kimberling, Jan 31 2025
2025-02-03T21:35:44
oeisdata/seq/A380/A380659.seq
ac0bc9799ec6acc163860d77289fc982
A380660
Rectangular array pos(i,j,1,2) read by descending antidiagonals: pos( ) and neg() denote the positive part and negative part of a determinant; see Comments.
[ "5", "16", "27", "48", "65", "84", "119", "144", "171", "200", "253", "288", "325", "364", "405", "480", "527", "576", "627", "680", "735", "836", "897", "960", "1025", "1092", "1161", "1232", "1363", "1440", "1519", "1600", "1683", "1768", "1855", "1944", "2109", "2204", "2301", "2400", "2501", "2604", "2709", "2816", "2925", "3128", "3243", "3360" ]
[ "nonn", "tabl", "changed" ]
23
1
1
[ "A000027", "A380649", "A380660", "A380661" ]
null
Clark Kimberling, Feb 04 2025
2025-04-14T05:44:23
oeisdata/seq/A380/A380660.seq
c0d286a14d54e4dcaeabc710be98fe2e
A380661
Rectangular array neg(i,j,1,2) read by descending antidiagonals: pos() and neg() denote the positive part and negative part of a determinant; see Comments.
[ "6", "20", "30", "56", "72", "90", "132", "156", "182", "210", "272", "306", "342", "380", "420", "506", "552", "600", "650", "702", "756", "870", "930", "992", "1056", "1122", "1190", "1260", "1406", "1482", "1560", "1640", "1722", "1806", "1892", "1980", "2162", "2256", "2352", "2450", "2550", "2652", "2756", "2862", "2970", "3192", "3306", "3422" ]
[ "nonn", "tabl", "changed" ]
23
1
1
[ "A000027", "A380649", "A380660", "A380661" ]
null
Clark Kimberling, Feb 04 2025
2025-04-14T05:44:37
oeisdata/seq/A380/A380661.seq
4e2b697675882b9278c49ad791cc97d2
A380662
Numbers m such that Sum_{k>=0} floor(m/5^k) is prime.
[ "2", "3", "6", "11", "16", "25", "30", "34", "35", "39", "44", "49", "58", "68", "73", "79", "82", "84", "87", "89", "92", "103", "106", "111", "113", "121", "123", "126", "131", "146", "154", "155", "159", "160", "170", "183", "188", "193", "202", "207", "212", "217", "219", "224", "226", "228", "236", "248", "251", "266", "271", "279", "280", "284", "289", "295" ]
[ "nonn" ]
6
1
1
[ "A191610", "A380662", "A381239" ]
null
Clark Kimberling, Feb 19 2025
2025-03-04T23:25:19
oeisdata/seq/A380/A380662.seq
4792b62f75e6a086e3ae31a89a50679d
A380663
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x/(1 - x)) ).
[ "1", "2", "15", "208", "4285", "117936", "4075099", "169736960", "8282604537", "463604723200", "29287449579751", "2061571190059008", "160023548976361525", "13580237335641417728", "1250935473495646861875", "124307671411309327876096", "13255531892787507819759601", "1509841440567809574906101760" ]
[ "nonn" ]
9
0
2
[ "A052873", "A377831", "A380663", "A380664", "A380665" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T03:50:00
oeisdata/seq/A380/A380663.seq
51acb582fa58fb0ff65fde0e76e66871
A380664
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x/(1 - x)^2) ).
[ "1", "2", "17", "268", "6277", "196416", "7716109", "365398496", "20271580137", "1290027358720", "92653747607401", "7414981595716608", "654373744057368493", "63136350047908917248", "6612064512998173129125", "747016321343021395603456", "90564758322246657646854481", "11727981253987656671672008704" ]
[ "nonn" ]
9
0
2
[ "A361598", "A377831", "A380663", "A380664" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T03:50:54
oeisdata/seq/A380/A380664.seq
a5d96716c013d80ff6e3ea414bf09bc3
A380665
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x/(1 - x)) ).
[ "1", "3", "31", "586", "16401", "612336", "28678231", "1618268688", "106946168769", "8105456425600", "693228400344591", "66055574392722432", "6940237183385667409", "797165049089377683456", "99381018789002592800775", "13365207839280075801020416", "1928719845703457066672384769", "297293268794967068206087176192" ]
[ "nonn" ]
11
0
2
[ "A052873", "A377832", "A380663", "A380665" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T03:51:49
oeisdata/seq/A380/A380665.seq
122c33d9f637976d5bd82a098b610cee
A380666
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x/(1 - x)^2) ).
[ "1", "3", "33", "670", "20193", "812736", "41056921", "2499780144", "178288822305", "14584953692800", "1346528845766481", "138513476506770432", "15711724851356153857", "1948422564510092267520", "262263690685637016402825", "38082186820362623941236736", "5933845220766237850177220289", "987599486681637240983472930816" ]
[ "nonn" ]
8
0
2
[ "A380665", "A380666" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T03:52:37
oeisdata/seq/A380/A380666.seq
2c219373de7730e5c2b9fdbccfca6ff1
A380667
First differences of the Golay-Rudin-Shapiro sequence (A020985), divided by 2.
[ "0", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "-1", "0", "0", "1", "-1", "1", "0", "0", "-1", "1", "0", "-1", "1", "-1", "0", "0", "1", "0", "0", "-1", "1", "0", "0", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "-1", "0", "0", "1", "-1", "0", "0", "0", "1", "-1", "0", "1", "-1", "1", "0", "0", "-1", "0", "0", "1", "-1", "1", "0", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "-1", "0", "0", "1", "-1", "1", "0", "0", "-1", "1", "0" ]
[ "sign", "easy" ]
15
0
3
[ "A020985", "A020986", "A380667" ]
null
Paolo Xausa, Jan 30 2025
2025-01-30T15:28:10
oeisdata/seq/A380/A380667.seq
f5efd8d39a929d84aa5cb95a292279ac
A380668
Third center column of elementary triangular automaton rule 182, starting from a lone 1 cell.
[ "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1" ]
[ "nonn" ]
19
0
null
[ "A380173", "A380668", "A380670", "A381735" ]
null
Paul Cousin, Jan 30 2025
2025-04-12T09:19:49
oeisdata/seq/A380/A380668.seq
baa25f1d10f96b3d0f44c0b18b0690ca
A380669
Smallest prime p > 10^(n-1) for which successive cyclic shifts of digits by 1, ..., n-1 positions to the right are all prime, or -1 if no such p exists.
[ "2", "11", "113", "1193", "11939", "193939", "93717773", "139133119", "15193739179", "153991739117", "877317793117" ]
[ "nonn", "base", "more" ]
29
1
1
[ "A004023", "A247153", "A380655", "A380669" ]
null
Jean-Marc Rebert, Jan 30 2025
2025-02-25T11:26:39
oeisdata/seq/A380/A380669.seq
33e0aec8745ab597b12bffde7696e967
A380670
Population of elementary triangular automaton rule 182 at generation n, starting from a lone 1 cell at generation 0.
[ "1", "4", "10", "19", "28", "34", "52", "58", "82", "85", "124", "118", "181", "178", "223", "274", "283", "322", "355", "388", "421", "502", "493", "568", "577", "676", "739", "724", "865", "856", "931", "1006", "1069", "1162", "1141", "1342", "1339", "1450", "1387", "1648", "1603", "1756", "1801", "1960", "1945", "2230", "2125", "2404", "2251", "2374", "2395", "2746", "2683", "2884", "2983" ]
[ "nonn" ]
15
0
2
[ "A372581", "A380012", "A380668", "A380670" ]
null
Paul Cousin, Jan 30 2025
2025-03-09T12:52:58
oeisdata/seq/A380/A380670.seq
8f6ab8d14c29e64204eedc528006c17a
A380671
a(n) is the smallest number not yet in the sequence which is coprime to n and shares at least one decimal digit with n.
[ "1", "21", "13", "41", "51", "61", "17", "81", "19", "11", "10", "23", "3", "15", "14", "31", "7", "71", "9", "27", "2", "25", "12", "29", "22", "63", "20", "83", "24", "37", "16", "33", "32", "35", "34", "43", "30", "39", "38", "47", "4", "121", "36", "45", "44", "49", "40", "85", "46", "53", "5", "55", "50", "59", "52", "57", "56", "65", "54", "67", "6", "69", "26", "141", "58", "161", "60" ]
[ "nonn", "base", "easy" ]
11
1
2
[ "A065190", "A380671" ]
null
David James Sycamore and Michael De Vlieger, Jan 30 2025
2025-01-31T11:47:36
oeisdata/seq/A380/A380671.seq
30f2e76740fa595804cab81d37bec228
A380672
Triangle read by rows where row n lists divisors d | n such that rad(d) != rad(n), where rad = A007947.
[ "1", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "5", "1", "1", "2", "3", "4", "1", "1", "2", "7", "1", "3", "5", "1", "1", "1", "2", "3", "9", "1", "1", "2", "4", "5", "1", "3", "7", "1", "2", "11", "1", "1", "2", "3", "4", "8", "1", "1", "2", "13", "1", "1", "2", "4", "7", "1", "1", "2", "3", "5", "6", "10", "15", "1", "1", "1", "3", "11", "1", "2", "17", "1", "5", "7", "1", "2", "3", "4", "9", "1", "1", "2", "19" ]
[ "nonn", "tabf", "easy" ]
25
2
6
[ "A000005", "A005361", "A007947", "A027750", "A183093", "A284318", "A380672", "A380819" ]
null
Michael De Vlieger, Feb 13 2025
2025-02-16T23:01:56
oeisdata/seq/A380/A380672.seq
197841b880dd1b991e44148c90f474de
A380673
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x * (1 - x)) ).
[ "1", "2", "11", "106", "1501", "28416", "677839", "19566128", "663801849", "25897000960", "1142424023731", "56232973813248", "3055417111781269", "181644488496644096", "11728204122824976375", "817281148114199197696", "61136484485752079320561", "4886365932210442324672512", "415573028022035962921316059" ]
[ "nonn" ]
9
0
2
[ "A277184", "A377831", "A380663", "A380664", "A380673" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T11:23:45
oeisdata/seq/A380/A380673.seq
ce2c2853b3ce9a77290422bd7d683071
A380674
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x * (1 - x)^2) ).
[ "1", "3", "25", "370", "8097", "237096", "8733601", "388380000", "20253654945", "1212334652800", "81937521020841", "6172429566120192", "512850795552978625", "46594245206418954240", "4595466275857015549425", "488993161791784338804736", "55839856392986843905585089", "6811561624203525171739852800" ]
[ "nonn" ]
9
0
2
[ "A377832", "A380665", "A380666", "A380674", "A380675" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T11:23:40
oeisdata/seq/A380/A380674.seq
eccb25836bb5b62430e584b668efc03a
A380675
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x * (1 - x)) ).
[ "1", "3", "27", "436", "10377", "329016", "13079971", "626414496", "35132554449", "2259697340800", "164013549475371", "13263204195136512", "1182645846100592473", "115285805003164594176", "12197859187688440506675", "1392237638583170475298816", "170517388925776876433310369", "22307473046095249063001554944" ]
[ "nonn" ]
9
0
2
[ "A377832", "A380665", "A380666", "A380674", "A380675" ]
null
Seiichi Manyama, Jan 30 2025
2025-01-30T11:23:35
oeisdata/seq/A380/A380675.seq
488405ea88cf4079d10368cacdc84460
A380676
G.f. A(x) satisfies 2 = Sum_{n=-oo..+oo} (-1)^n * x^n * (A(x) + x^n)^(3*n+1).
[ "1", "2", "9", "76", "591", "5127", "46919", "444617", "4333010", "43132310", "436715297", "4483520704", "46564078707", "488335074439", "5164287656762", "55010054836724", "589682412920880", "6356441723399838", "68858811108713642", "749250723117079260", "8185098919015604558", "89739660783143322586", "987110817010576637569" ]
[ "nonn" ]
10
0
2
[ "A355866", "A380067", "A380676", "A380677" ]
null
Paul D. Hanna, Feb 02 2025
2025-02-03T02:22:26
oeisdata/seq/A380/A380676.seq
4082c4b41384cf898a6c9c3cf3da243f
A380677
G.f. A(x) satisfies 1 = Sum_{n=-oo..+oo} x^(2*n) * (x^n - A(x))^(3*n+1).
[ "1", "2", "8", "36", "198", "1128", "6837", "42690", "273960", "1792650", "11922735", "80342746", "547403208", "3764568202", "26097746670", "182183863242", "1279566641040", "9035527984360", "64109825254786", "456834687004440", "3267926616628182", "23458797921291994", "168936073477132102", "1220121029135864026", "8835737467337361482" ]
[ "nonn" ]
11
0
2
[ "A355866", "A380067", "A380676", "A380677" ]
null
Paul D. Hanna, Feb 02 2025
2025-02-03T02:22:31
oeisdata/seq/A380/A380677.seq
2692088cff55f332181a1bcbd8417469
A380678
G.f. A(x) satisfies A( x - A(x)^2/(1 - A(x)^2) ) = x.
[ "1", "1", "4", "25", "190", "1645", "15652", "160186", "1739032", "19838179", "236192158", "2920269202", "37352521348", "492799406899", "6690428699026", "93293086422514", "1334088426585850", "19538994465481000", "292775222237716612", "4484180296611470218", "70146488080451823382", "1119964903188050808163", "18239593214541431577550" ]
[ "nonn" ]
9
1
3
[ "A027383", "A213591", "A380558", "A380678" ]
null
Paul D. Hanna, Feb 14 2025
2025-02-15T09:47:39
oeisdata/seq/A380/A380678.seq
9125e95afe3e46faea1659609e1855d8
A380679
G.f. A(x) satisfies A(x) = Sum_{n>=0} x^n * (1+x)^(n*(3*n+1)/2) / A(x)^(n*(n+1)/2).
[ "1", "1", "2", "3", "7", "15", "48", "177", "792", "3985", "21616", "125845", "773128", "4995356", "33768501", "237936780", "1742684309", "13233752561", "103985325332", "843956110146", "7064063586175", "60895536312911", "539984607186223", "4919957726789582", "46013558733949708", "441315845699885259", "4336873914330888090", "43633249440459934580" ]
[ "nonn" ]
8
0
3
[ "A321099", "A380679" ]
null
Paul D. Hanna, Feb 22 2025
2025-02-23T01:59:47
oeisdata/seq/A380/A380679.seq
c692a236ea4ed75d3494b96113ac979b
A380680
G.f. A(x) = Sum_{n=-oo..+oo} x^(n^2) * (2 - x^n)^n/(1 - 2*x^n)^n.
[ "1", "4", "6", "12", "32", "48", "120", "192", "450", "784", "1704", "3072", "6624", "12288", "25536", "49404", "100544", "196608", "398982", "786432", "1584192", "3147924", "6316032", "12582912", "25226304", "50331712", "100780032", "201341856", "402908016", "805306368", "1611192192", "3221225472", "6443615490", "12884995776", "25772261376", "51539609952" ]
[ "nonn" ]
7
0
2
[ "A380060", "A380680" ]
null
Paul D. Hanna, Feb 06 2025
2025-02-07T05:41:10
oeisdata/seq/A380/A380680.seq
5b8d82ec545f14fa556828415d6343e4
A380681
G.f. A(x) satisfies 2*x = Sum_{n=-oo..+oo} (-1)^n * x^(2*n) * (A(x) + x^n)^(2*n) with A(0) = 1.
[ "1", "2", "7", "28", "122", "564", "2707", "13372", "67593", "347916", "1817244", "9607688", "51316353", "276485966", "1500906317", "8201237354", "45072131590", "248974971580", "1381605020061", "7698230495694", "43053083351989", "241588037857532", "1359801706168192", "7675245175662224", "43433685932208079", "246372179366760938", "1400586104620945564" ]
[ "nonn" ]
8
0
2
[ "A380681", "A380682", "A380683", "A380684", "A380685", "A380686" ]
null
Paul D. Hanna, Jan 30 2025
2025-01-31T04:26:14
oeisdata/seq/A380/A380681.seq
c4283c37913486a3e3ab2b38324a1213
A380682
G.f. A(x) satisfies 3*x = Sum_{n=-oo..+oo} (-1)^n * x^(3*n) * (A(x) + x^n)^(3*n) with A(0) = 1.
[ "1", "2", "5", "16", "61", "249", "1052", "4563", "20235", "91420", "419423", "1948712", "9149749", "43345282", "206922865", "994442783", "4807332168", "23360888569", "114048745449", "559114028719", "2751327072141", "13585135755721", "67287432632212", "334223723285970", "1664459140656762", "8309074228762074", "41571618824043394", "208418278965591903" ]
[ "nonn" ]
11
0
2
[ "A380681", "A380682", "A380683", "A380684", "A380685", "A380686" ]
null
Paul D. Hanna, Jan 30 2025
2025-01-31T12:17:03
oeisdata/seq/A380/A380682.seq
5131d2c9c6408248497b5c6988a15f9e
A380683
G.f. A(x) satisfies 5*x = Sum_{n=-oo..+oo} (-1)^n * x^(5*n) * (A(x) + x^n)^(5*n) with A(0) = 1.
[ "1", "3", "11", "44", "185", "806", "3620", "16732", "79540", "388643", "1949282", "10013543", "52527829", "280419434", "1518360693", "8313011022", "45902814834", "255113772507", "1424884037539", "7989178696699", "44934216024959", "253391300848307", "1432226630488773", "8112521901225671", "46044227635950537", "261841663108466812" ]
[ "nonn" ]
7
0
2
[ "A380681", "A380682", "A380683", "A380684", "A380685", "A380686" ]
null
Paul D. Hanna, Jan 30 2025
2025-01-31T04:25:52
oeisdata/seq/A380/A380683.seq
f6b26db24e7a70a5ff1a5b34a616b3a9
A380684
G.f. A(x) satisfies 7*x = Sum_{n=-oo..+oo} (-1)^n * x^(7*n) * (A(x) + x^n)^(7*n) with A(0) = 1.
[ "1", "4", "20", "110", "638", "3828", "23515", "146974", "930940", "5959555", "38485153", "250361331", "1639087576", "10791380549", "71409038308", "474737253262", "3169904556865", "21253752401187", "143071102097208", "966819122581869", "6558130910319694", "44650977592122241", "305125605291293360", "2092700240205257834" ]
[ "nonn" ]
7
0
2
[ "A380681", "A380682", "A380683", "A380684", "A380685", "A380686" ]
null
Paul D. Hanna, Jan 30 2025
2025-01-31T04:25:58
oeisdata/seq/A380/A380684.seq
6fc83917827c6bdb056ab5ab0a6c1809
A380685
G.f. A(x) satisfies 11*x = Sum_{n=-oo..+oo} (-1)^n * x^(11*n) * (A(x) + x^n)^(11*n) with A(0) = 1.
[ "1", "6", "46", "391", "3519", "32844", "314364", "3065049", "30309929", "303099290", "3058547381", "31095231714", "318128140148", "3272175165178", "33812476941532", "350804453372227", "3652493526423700", "38148267537614974", "399552938393084989", "4195306357570788627", "44150612881708715578", "465588400391644207583" ]
[ "nonn" ]
7
0
2
[ "A380681", "A380682", "A380683", "A380684", "A380685", "A380686" ]
null
Paul D. Hanna, Jan 30 2025
2025-01-31T04:26:04
oeisdata/seq/A380/A380685.seq
713dc44adf4316072cf20c4ac2bb985b
A380686
G.f. A(x) satisfies 13*x = Sum_{n=-oo..+oo} (-1)^n * x^(13*n) * (A(x) + x^n)^(13*n) with A(0) = 1.
[ "1", "7", "63", "630", "6678", "73458", "829026", "9533799", "111227655", "1312486329", "15630519009", "187566228108", "2265222908689", "27506278176946", "335576593759204", "4110813273569129", "50538822010972154", "623312138152980011", "7709386972340494155", "95596398467476043727", "1188126666895003363071", "14797577583300937454948" ]
[ "nonn" ]
9
0
2
[ "A380681", "A380682", "A380683", "A380684", "A380685", "A380686" ]
null
Paul D. Hanna, Jan 30 2025
2025-02-01T00:50:27
oeisdata/seq/A380/A380686.seq
1974d23f8f6a6d8a4bf605e5f7294b28
A380687
G.f. satisfies A(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / A(x)^(n*(n+1)).
[ "1", "1", "1", "1", "2", "3", "16", "50", "270", "1266", "7017", "40073", "243665", "1556727", "10394483", "72403198", "524195255", "3936080686", "30591479055", "245655102572", "2035083634357", "17369029459700", "152535273188651", "1376833447490442", "12760355850982450", "121311719667445606", "1182004361469302527", "11793836041463723717", "120413981027066126060" ]
[ "nonn" ]
7
0
5
[ "A321099", "A380679", "A380687" ]
null
Paul D. Hanna, Feb 23 2025
2025-02-24T08:51:57
oeisdata/seq/A380/A380687.seq
8d50eb956cec4d7289f50df03259d6e5
A380688
Decimal expansion of Sum_{p prime} (p + 1)^3/((p - 1)^2*p^3).
[ "4", "1", "5", "8", "6", "3", "9", "6", "6", "8", "8", "9", "6", "3", "1", "1", "7", "9", "7", "9", "2", "1", "4", "4", "5", "6", "6", "4", "7", "3", "5", "1", "5", "5", "2", "1", "7", "8", "5", "3", "4", "7", "2", "4", "8", "6", "5", "2", "9", "9", "1", "8", "4", "8", "8", "5", "1", "2", "2", "0", "8", "5", "4", "7", "3", "0", "6", "8", "3", "4", "0", "8", "9", "6", "0", "9", "3", "2", "5", "2", "2", "9", "3", "1", "4", "0", "9", "8", "0", "3", "5", "7", "6", "4", "3", "6", "1", "9", "4", "7", "9", "3", "4" ]
[ "cons", "nonn" ]
17
1
1
[ "A085541", "A085548", "A136141", "A152441", "A380688" ]
null
Artur Jasinski, Mar 31 2025
2025-04-02T06:29:18
oeisdata/seq/A380/A380688.seq
01ba8a13bb950b2b644c6d000c662602
A380689
Decimal expansion of Sum_{p prime} (p + 1)^3/((p - 1)^3*p^2).
[ "7", "8", "6", "6", "6", "6", "5", "3", "9", "7", "3", "3", "1", "8", "0", "4", "4", "9", "2", "4", "7", "6", "9", "1", "9", "3", "2", "2", "4", "7", "0", "6", "9", "0", "8", "5", "5", "9", "7", "8", "9", "3", "4", "7", "1", "6", "7", "5", "8", "8", "5", "2", "0", "7", "5", "4", "9", "9", "4", "5", "3", "1", "2", "1", "8", "2", "8", "4", "1", "5", "0", "1", "4", "6", "4", "5", "6", "3", "1", "9", "4", "2", "6", "1", "5", "4", "2", "2", "6", "9", "7", "9", "0", "0", "1", "9", "3", "1", "6", "7", "6", "5", "3", "8", "3", "6" ]
[ "nonn", "cons" ]
15
1
1
[ "A085548", "A086242", "A136141", "A380689", "A380840" ]
null
Artur Jasinski, Mar 31 2025
2025-04-02T06:30:35
oeisdata/seq/A380/A380689.seq
6e5711ada31962702dd13d136116ce23
A380690
a(0) = 0; a(n) = the number of times a(n-1) has all digits in common with a previous term.
[ "0", "0", "1", "0", "2", "0", "3", "0", "4", "0", "5", "0", "6", "0", "7", "0", "8", "0", "9", "0", "10", "0", "11", "1", "2", "1", "3", "1", "4", "1", "5", "1", "6", "1", "7", "1", "8", "1", "9", "1", "10", "1", "11", "12", "0", "12", "1", "13", "0", "13", "1", "14", "0", "14", "1", "15", "0", "15", "1", "16", "0", "16", "1", "17", "0", "17", "1", "18", "0", "18", "1", "19", "0", "19", "1", "20", "0", "20", "1", "21" ]
[ "nonn", "base" ]
12
0
5
[ "A309261", "A326834", "A364788", "A380690" ]
null
Sergio Pimentel, Jan 30 2025
2025-02-09T13:38:16
oeisdata/seq/A380/A380690.seq
344481e35c3c65a753357904a6a5c33d
A380691
Number of divisors d | k, d < k/d, such that (d, k/d) are neither unitary nor both coreful, where k is neither squarefree nor prime power (in A126706).
[ "1", "1", "1", "2", "1", "2", "2", "1", "1", "3", "1", "1", "2", "2", "2", "1", "1", "3", "1", "1", "3", "2", "2", "2", "1", "4", "1", "1", "2", "2", "3", "3", "1", "1", "4", "1", "2", "2", "2", "2", "2", "4", "1", "1", "2", "2", "1", "2", "4", "3", "1", "4", "1", "1", "1", "3", "5", "2", "1", "2", "5", "2", "2", "3", "2", "1", "3", "1", "4", "2", "4", "2", "2", "2", "2", "1", "6", "1", "1", "1", "2", "2", "5", "2", "1", "4", "1" ]
[ "nonn", "easy" ]
5
1
4
[ "A000005", "A001221", "A007947", "A013929", "A024619", "A034444", "A126706", "A361430", "A380691" ]
null
Michael De Vlieger, Feb 09 2025
2025-02-16T23:02:18
oeisdata/seq/A380/A380691.seq
e18e16124d9bbe7b20ea2b299e1d74a1
A380692
Numbers k such that the least prime dividing k is larger than the maximum exponent in the prime factorization of k; a(1) = 1 by convention.
[ "1", "2", "3", "5", "6", "7", "9", "10", "11", "13", "14", "15", "17", "19", "21", "22", "23", "25", "26", "29", "30", "31", "33", "34", "35", "37", "38", "39", "41", "42", "43", "45", "46", "47", "49", "51", "53", "55", "57", "58", "59", "61", "62", "63", "65", "66", "67", "69", "70", "71", "73", "74", "75", "77", "78", "79", "82", "83", "85", "86", "87", "89", "91", "93", "94", "95", "97", "99" ]
[ "nonn", "easy" ]
10
1
2
[ "A005117", "A005408", "A020639", "A051903", "A067259", "A136327", "A151800", "A368110", "A380692", "A380693", "A380694", "A380695" ]
null
Amiram Eldar, Jan 30 2025
2025-01-31T04:24:41
oeisdata/seq/A380/A380692.seq
54232f25e3ceb882fcda454aaa7e6441
A380693
Numbers k such that the least prime dividing k is larger than or equal to the maximum exponent in the prime factorization of k; a(1) = 1 by convention.
[ "1", "2", "3", "4", "5", "6", "7", "9", "10", "11", "12", "13", "14", "15", "17", "18", "19", "20", "21", "22", "23", "25", "26", "27", "28", "29", "30", "31", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "55", "57", "58", "59", "60", "61", "62", "63", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79" ]
[ "nonn", "easy" ]
9
1
2
[ "A007918", "A020639", "A047592", "A051903", "A187320", "A207481", "A255805", "A380692", "A380693", "A380694", "A380695" ]
null
Amiram Eldar, Jan 30 2025
2025-01-31T04:24:05
oeisdata/seq/A380/A380693.seq
a62985ee3f4329e422ab4d0a23bbd2ca
A380694
Numbers k such that the prime index of the least prime dividing k is larger than the maximum exponent in the prime factorization of k.
[ "3", "5", "7", "11", "13", "15", "17", "19", "21", "23", "25", "29", "31", "33", "35", "37", "39", "41", "43", "47", "49", "51", "53", "55", "57", "59", "61", "65", "67", "69", "71", "73", "77", "79", "83", "85", "87", "89", "91", "93", "95", "97", "101", "103", "105", "107", "109", "111", "113", "115", "119", "121", "123", "127", "129", "131", "133", "137", "139", "141", "143", "145", "149" ]
[ "nonn", "easy" ]
7
1
1
[ "A000720", "A020639", "A051903", "A055396", "A320055", "A320056", "A352830", "A380692", "A380693", "A380694", "A380695" ]
null
Amiram Eldar, Jan 30 2025
2025-01-31T04:24:21
oeisdata/seq/A380/A380694.seq
a9f347fd5764b529e0864f3877a4d91b
A380695
Numbers k such that the prime index of the least prime dividing k is larger than or equal to the maximum exponent in the prime factorization of k; a(1) = 1 by convention.
[ "1", "2", "3", "5", "6", "7", "9", "10", "11", "13", "14", "15", "17", "19", "21", "22", "23", "25", "26", "29", "30", "31", "33", "34", "35", "37", "38", "39", "41", "42", "43", "45", "46", "47", "49", "51", "53", "55", "57", "58", "59", "61", "62", "63", "65", "66", "67", "69", "70", "71", "73", "74", "75", "77", "78", "79", "82", "83", "85", "86", "87", "89", "91", "93", "94", "95", "97", "99" ]
[ "nonn", "easy" ]
9
1
2
[ "A000720", "A020639", "A051903", "A055396", "A368110", "A380692", "A380693", "A380694", "A380695" ]
null
Amiram Eldar, Jan 30 2025
2025-01-31T04:24:30
oeisdata/seq/A380/A380695.seq
49b4582c3fee3c95563c026091041e68
A380696
a(n) = A007598(floor(n/2) - (-1)^n).
[ "1", "1", "0", "1", "1", "4", "1", "9", "4", "25", "9", "64", "25", "169", "64", "441", "169", "1156", "441", "3025", "1156", "7921", "3025", "20736", "7921", "54289", "20736", "142129", "54289", "372100", "142129", "974169", "372100", "2550409", "974169", "6677056", "2550409", "17480761", "6677056", "45765225", "17480761", "119814916" ]
[ "nonn", "easy" ]
72
0
6
[ "A000045", "A001654", "A007598", "A053602", "A069921", "A123231", "A272912", "A380696" ]
null
Benjamin G. Brunsden, Jan 30 2025
2025-03-27T06:11:01
oeisdata/seq/A380/A380696.seq
5bc70861526752f378832a29ca0e80fd
A380697
Frobenius number of the set S = {e_i+2; 1 <= i <= m}, where the e_i are the exponents in the binary expansion n = Sum_{i=1..m} 2^e_i, or 0 if GCD(S) = A326674(2*n) > 1.
[ "0", "0", "1", "0", "0", "5", "1", "0", "3", "7", "1", "11", "3", "2", "1", "0", "0", "0", "1", "0", "0", "5", "1", "19", "3", "7", "1", "7", "3", "2", "1", "0", "5", "11", "1", "17", "5", "5", "1", "23", "3", "4", "1", "6", "3", "2", "1", "29", "5", "11", "1", "9", "5", "5", "1", "9", "3", "4", "1", "3", "3", "2", "1", "0", "0", "13", "1", "0", "0", "5", "1", "27", "3", "7", "1", "11", "3", "2", "1", "0", "0", "13", "1" ]
[ "nonn" ]
13
1
6
[ "A004767", "A065003", "A326674", "A380697" ]
null
Pontus von Brömssen, Jan 30 2025
2025-02-01T23:14:04
oeisdata/seq/A380/A380697.seq
e6a47a7a96d1e98787f6df0a6896571e
A380698
a(n) is the number of intervals making up the set {A377091(k), k = 0..n}.
[ "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "1", "1", "1", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "2", "3", "3", "2", "3", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "3", "3", "2", "2", "2", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
8
0
4
[ "A377091", "A380698", "A380699" ]
null
Rémy Sigrist, Jan 30 2025
2025-02-02T08:51:52
oeisdata/seq/A380/A380698.seq
936522ab3af3a2ac44cf91d07c2f8110
A380699
Numbers m such that the set {A377091(k), k = 0..m} is an integer interval.
[ "0", "1", "2", "4", "5", "6", "7", "9", "10", "11", "12", "16", "17", "18", "19", "20", "25", "26", "27", "28", "29", "30", "31", "36", "37", "38", "39", "40", "41", "42", "52", "53", "54", "55", "56", "57", "58", "59", "60", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "81", "82", "83", "84", "85", "86", "87", "88", "89", "90", "100", "101", "102", "103", "104", "105" ]
[ "nonn" ]
6
1
3
[ "A377091", "A380698", "A380699" ]
null
Rémy Sigrist, Jan 30 2025
2025-02-02T08:51:57
oeisdata/seq/A380/A380699.seq
44ce62272ec31280a1aa13c035951808
A380700
Decimal expansion of the acute vertex angles, in radians, in a triakis tetrahedron face.
[ "5", "8", "5", "6", "8", "5", "5", "4", "3", "4", "5", "7", "1", "5", "0", "9", "5", "9", "6", "1", "7", "7", "5", "7", "5", "3", "8", "4", "7", "7", "5", "1", "7", "7", "6", "6", "2", "0", "0", "3", "6", "1", "0", "6", "7", "1", "7", "1", "6", "4", "1", "5", "0", "2", "6", "5", "0", "5", "5", "9", "3", "2", "7", "2", "2", "1", "2", "6", "4", "9", "2", "2", "1", "3", "3", "2", "4", "0", "3", "3", "8", "8", "2", "2", "0", "0", "2", "6", "3", "3" ]
[ "nonn", "cons", "easy" ]
10
0
1
[ "A378204", "A378205", "A378206", "A378207", "A378208", "A380700", "A380701" ]
null
Paolo Xausa, Jan 30 2025
2025-01-30T17:44:03
oeisdata/seq/A380/A380700.seq
74686e247fe1f05073f0e1f13906be73
A380701
Decimal expansion of the obtuse vertex angle, in radians, in a triakis tetrahedron face.
[ "1", "9", "7", "0", "2", "2", "1", "5", "6", "6", "6", "7", "5", "4", "9", "1", "3", "1", "9", "2", "2", "7", "1", "2", "8", "3", "0", "6", "3", "2", "4", "4", "6", "7", "3", "5", "1", "7", "9", "6", "4", "4", "7", "2", "6", "5", "0", "3", "1", "8", "2", "2", "8", "1", "5", "6", "7", "3", "8", "2", "5", "9", "3", "7", "8", "6", "5", "2", "8", "6", "5", "6", "2", "0", "1", "9", "7", "2", "8", "3", "2", "0", "9", "8", "4", "0", "2", "9", "5", "5" ]
[ "nonn", "cons", "easy" ]
7
1
2
[ "A378204", "A378205", "A378206", "A378207", "A378208", "A380700", "A380701" ]
null
Paolo Xausa, Jan 30 2025
2025-01-30T17:43:59
oeisdata/seq/A380/A380701.seq
11ff7581b8cfc4ea65498e2a1a39512c
A380702
Decimal expansion of the acute vertex angles, in radians, in a (small) triakis octahedron face.
[ "5", "4", "8", "0", "2", "8", "4", "0", "7", "6", "2", "0", "3", "1", "2", "7", "4", "4", "5", "3", "0", "8", "6", "3", "2", "8", "2", "8", "2", "0", "6", "2", "8", "6", "7", "8", "4", "7", "9", "7", "1", "2", "3", "6", "3", "6", "5", "9", "2", "0", "4", "3", "1", "6", "9", "9", "5", "5", "4", "8", "4", "3", "8", "8", "6", "0", "3", "3", "9", "4", "3", "5", "5", "4", "6", "4", "8", "5", "4", "5", "5", "3", "8", "9", "9", "3", "5", "3", "1", "5" ]
[ "nonn", "cons", "easy" ]
8
0
1
[ "A020765", "A361601", "A378351", "A378352", "A378353", "A378354", "A380702", "A380703" ]
null
Paolo Xausa, Jan 30 2025
2025-01-30T17:44:11
oeisdata/seq/A380/A380702.seq
d8f324aa20384e8328cbb0530d6528d8
A380703
Decimal expansion of the obtuse vertex angle, in radians, in a (small) triakis octahedron face.
[ "2", "0", "4", "5", "5", "3", "5", "8", "3", "8", "3", "4", "9", "1", "6", "7", "7", "4", "9", "4", "0", "0", "9", "1", "6", "8", "1", "7", "6", "3", "8", "2", "4", "5", "5", "2", "7", "2", "3", "7", "7", "4", "4", "6", "7", "2", "0", "5", "6", "6", "9", "7", "1", "8", "6", "9", "8", "3", "8", "4", "7", "7", "1", "4", "5", "8", "7", "1", "3", "7", "5", "3", "5", "1", "9", "3", "2", "3", "8", "0", "8", "7", "8", "4", "8", "1", "6", "4", "1", "9" ]
[ "nonn", "cons", "easy" ]
8
1
1
[ "A010503", "A378351", "A378352", "A378353", "A378354", "A380702", "A380703" ]
null
Paolo Xausa, Jan 30 2025
2025-01-30T17:44:07
oeisdata/seq/A380/A380703.seq
62dd0810452c16348fff4893e51f29af
A380704
Decimal expansion of the acute vertex angles, in radians, in a deltoidal icositetrahedron face.
[ "1", "4", "2", "3", "8", "2", "1", "1", "3", "6", "1", "3", "1", "3", "9", "1", "5", "4", "9", "4", "4", "5", "5", "5", "7", "3", "5", "6", "6", "6", "6", "9", "0", "4", "6", "8", "4", "8", "8", "5", "7", "9", "7", "9", "9", "0", "2", "9", "5", "1", "0", "1", "3", "5", "9", "0", "4", "7", "9", "1", "8", "9", "5", "6", "3", "9", "5", "0", "2", "3", "1", "3", "5", "2", "9", "6", "2", "1", "8", "6", "1", "2", "5", "7", "8", "9", "9", "9", "6", "0" ]
[ "nonn", "cons", "easy" ]
6
1
2
[ "A020765", "A378390", "A378391", "A378392", "A378393", "A378394", "A380704", "A380705" ]
null
Paolo Xausa, Jan 31 2025
2025-01-31T04:20:55
oeisdata/seq/A380/A380704.seq
ade7e829f57f6e0794f2bea176f7b7dc