Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
sequencelengths
1
348
keywords
sequencelengths
1
8
score
int64
1
2.31k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
sequencelengths
1
128
⌀
former_ids
sequencelengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-28 00:58:08
filename
stringlengths
29
29
hash
stringlengths
32
32
A004001
Hofstadter-Conway $10000 sequence: a(n) = a(a(n-1)) + a(n-a(n-1)) with a(1) = a(2) = 1.
[ "1", "1", "2", "2", "3", "4", "4", "4", "5", "6", "7", "7", "8", "8", "8", "8", "9", "10", "11", "12", "12", "13", "14", "14", "15", "15", "15", "16", "16", "16", "16", "16", "17", "18", "19", "20", "21", "21", "22", "23", "24", "24", "25", "26", "26", "27", "27", "27", "28", "29", "29", "30", "30", "30", "31", "31", "31", "31", "32", "32", "32", "32", "32", "32", "33", "34", "35", "36", "37", "38", "38", "39", "40", "41", "42" ]
[ "nonn", "easy", "nice" ]
186
1
3
[ "A004001", "A004074", "A005185", "A005229", "A005350", "A005707", "A051135", "A055748", "A080677", "A086841", "A087686", "A088359", "A093878", "A093879", "A188163", "A249071", "A265332", "A265901", "A265903", "A266341", "A267111", "A267112" ]
[ "M0276" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A004/A004001.seq
d8d0d7b8da23519b7351095144718aa7
A004002
Benford numbers: a(n) = e^e^...^e (n times) rounded to nearest integer.
[ "1", "3", "15", "3814279" ]
[ "nonn" ]
35
0
2
[ "A004002", "A056072", "A073236", "A225053" ]
[ "M3010" ]
N. J. A. Sloane
2024-07-20T19:46:06
oeisdata/seq/A004/A004002.seq
00864e7d9a611be3470e6bc785f0bee8
A004003
Number of domino tilings (or dimer coverings) of a 2n X 2n square.
[ "1", "2", "36", "6728", "12988816", "258584046368", "53060477521960000", "112202208776036178000000", "2444888770250892795802079170816", "548943583215388338077567813208427340288", "1269984011256235834242602753102293934298576249856" ]
[ "nonn", "easy", "nice" ]
144
0
2
[ "A004003", "A006125", "A006253", "A028420", "A065072", "A099390", "A124997", "A187596", "A239273", "A256043" ]
[ "M2160" ]
N. J. A. Sloane, Greg Huber
2025-02-16T08:32:27
oeisdata/seq/A004/A004003.seq
11a0eacbe04bc95cd5939fb858c76d93
A004004
a(n) = (3^(2*n+1) - 8*n - 3)/16.
[ "0", "1", "14", "135", "1228", "11069", "99642", "896803", "8071256", "72641337", "653772070", "5883948671", "52955538084", "476599842805", "4289398585298", "38604587267739", "347441285409712", "3126971568687473", "28142744118187326", "253284697063686007", "2279562273573174140", "20516060462158567341" ]
[ "nonn", "easy" ]
48
0
3
[ "A004004", "A162005", "A162008", "A162009", "A162010", "A162011", "A162014" ]
[ "M4943" ]
N. J. A. Sloane, Simon Plouffe
2025-02-08T15:32:15
oeisdata/seq/A004/A004004.seq
7a4892ec22e2be190f6f9bfbd17d37af
A004005
Coefficients of elliptic function sn.
[ "1", "135", "5478", "165826", "4494351", "116294673", "2949965020", "74197080276", "1859539731885", "46535238000235", "1163848723925346", "29100851707716150", "727566807977891803", "18189614152200873621", "454744658216502193656" ]
[ "nonn", "nice", "easy" ]
45
2
2
[ "A004005", "A060628" ]
[ "M5397" ]
N. J. A. Sloane, Simon Plouffe
2022-04-13T13:25:17
oeisdata/seq/A004/A004005.seq
a5eaa0c8996713f02d461881049496e1
A004006
a(n) = C(n,1) + C(n,2) + C(n,3), or n*(n^2 + 5)/6.
[ "0", "1", "3", "7", "14", "25", "41", "63", "92", "129", "175", "231", "298", "377", "469", "575", "696", "833", "987", "1159", "1350", "1561", "1793", "2047", "2324", "2625", "2951", "3303", "3682", "4089", "4525", "4991", "5488", "6017", "6579", "7175", "7806", "8473", "9177", "9919", "10700", "11521", "12383", "13287", "14234", "15225" ]
[ "nonn", "nice", "easy", "changed" ]
168
0
3
[ "A000124", "A000217", "A000292", "A000447", "A000578", "A001477", "A004006", "A004068", "A004126", "A004188", "A004466", "A004467", "A005900", "A006003", "A006527", "A006552", "A007310", "A007588", "A051576", "A055795", "A062025", "A063521", "A063522", "A063523", "A128834", "A144329", "A228074" ]
null
Albert D. Rich (AlbertRich(AT)msn.com)
2025-04-15T04:00:27
oeisdata/seq/A004/A004006.seq
bf3614ef72f8abbf3140935521657e2a
A004007
Theta series of E_6 lattice.
[ "1", "72", "270", "720", "936", "2160", "2214", "3600", "4590", "6552", "5184", "10800", "9360", "12240", "13500", "17712", "14760", "25920", "19710", "26064", "28080", "36000", "25920", "47520", "37638", "43272", "45900", "59040", "46800", "75600", "51840", "69264", "73710", "88560", "62208", "108000", "85176" ]
[ "nonn" ]
29
0
2
[ "A004007", "A005129" ]
[ "M5349" ]
N. J. A. Sloane
2018-01-11T01:09:04
oeisdata/seq/A004/A004007.seq
ea15484d7703c806722f5889dd0a5e02
A004008
Expansion of theta series of E_7 lattice in powers of q^2.
[ "1", "126", "756", "2072", "4158", "7560", "11592", "16704", "24948", "31878", "39816", "55944", "66584", "76104", "99792", "116928", "133182", "160272", "177660", "205128", "249480", "265104", "281736", "350784", "382536", "390726", "470232", "505568", "532800", "615384", "640080", "701568", "799092", "809424", "853776" ]
[ "nonn", "easy" ]
29
0
2
[ "A003781", "A004008", "A005875", "A228746" ]
[ "M5388" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A004/A004008.seq
c9d071be9f10fa5aaf2bc5d2a1acc89d
A004009
Expansion of Eisenstein series E_4(q) (alternate convention E_2(q)); theta series of E_8 lattice.
[ "1", "240", "2160", "6720", "17520", "30240", "60480", "82560", "140400", "181680", "272160", "319680", "490560", "527520", "743040", "846720", "1123440", "1179360", "1635120", "1646400", "2207520", "2311680", "2877120", "2920320", "3931200", "3780240", "4747680", "4905600", "6026880" ]
[ "nonn", "easy", "nice" ]
168
0
2
[ "A000143", "A001158", "A004009", "A006352", "A007331", "A008410", "A008411", "A013973", "A013974", "A029828", "A029829", "A029830", "A029831", "A035016", "A046948", "A058550", "A108091" ]
[ "M5416" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A004/A004009.seq
cdad89efeade98eae7851e1d31b76ea3
A004010
Theta series of 12-dimensional Coxeter-Todd lattice K_12.
[ "1", "0", "756", "4032", "20412", "60480", "139860", "326592", "652428", "1020096", "2000376", "3132864", "4445532", "7185024", "10747296", "13148352", "21003948", "27506304", "33724404", "48009024", "64049832", "70709184", "102958128", "124782336", "142254252", "189423360", "237588120", "248250240", "344391264" ]
[ "easy", "nonn", "nice" ]
39
0
3
[ "A004010", "A004046", "A008657", "A107658" ]
[ "M5478" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A004/A004010.seq
b175d63b431930340e9bc0f1dbcfc003
A004011
Theta series of D_4 lattice; Fourier coefficients of Eisenstein series E_{gamma,2}.
[ "1", "24", "24", "96", "24", "144", "96", "192", "24", "312", "144", "288", "96", "336", "192", "576", "24", "432", "312", "480", "144", "768", "288", "576", "96", "744", "336", "960", "192", "720", "576", "768", "24", "1152", "432", "1152", "312", "912", "480", "1344", "144", "1008", "768", "1056", "288", "1872", "576", "1152", "96", "1368", "744", "1728", "336" ]
[ "nonn", "easy", "core", "nice" ]
144
0
2
[ "A000118", "A000593", "A002388", "A004011", "A004016", "A005882", "A005928", "A008658", "A046949", "A096727", "A108092", "A108096" ]
[ "M5140" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A004/A004011.seq
12efcc333e4b3e849818158add35a923
A004012
Theta series of hexagonal close-packing.
[ "1", "0", "0", "12", "0", "0", "6", "0", "2", "18", "0", "12", "6", "0", "0", "12", "0", "12", "6", "6", "12", "24", "6", "0", "0", "12", "0", "12", "0", "24", "12", "12", "2", "12", "6", "24", "6", "12", "0", "24", "0", "12", "0", "6", "24", "12", "12", "24", "6", "12", "0", "24", "0", "24", "18", "12", "12", "24", "0", "12", "0", "12", "0", "36", "0", "24", "12", "18", "12", "24", "12", "48", "2", "0", "0", "36", "0", "0", "24", "12", "12" ]
[ "nonn", "easy", "nice" ]
27
0
4
null
[ "M4817" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004012.seq
3dda759f67324fa2afc988d6cbf51260
A004013
Theta series of body-centered cubic (b.c.c.) lattice.
[ "1", "0", "0", "8", "6", "0", "0", "0", "12", "0", "0", "24", "8", "0", "0", "0", "6", "0", "0", "24", "24", "0", "0", "0", "24", "0", "0", "32", "0", "0", "0", "0", "12", "0", "0", "48", "30", "0", "0", "0", "24", "0", "0", "24", "24", "0", "0", "0", "8", "0", "0", "48", "24", "0", "0", "0", "48", "0", "0", "72", "0", "0", "0", "0", "6", "0", "0", "24", "48", "0", "0", "0", "36", "0", "0", "56", "24", "0", "0", "0", "24", "0", "0", "72", "48", "0", "0", "0", "24", "0", "0" ]
[ "nonn", "easy", "nice" ]
58
0
4
[ "A004011", "A004013", "A004014", "A004015", "A005875", "A008422", "A008423", "A008424", "A008425", "A008426", "A008427", "A008443", "A023916", "A023936", "A045826", "A045828", "A045834", "A213056" ]
[ "M4473" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004013.seq
0be917e60a80d65fc0992fca2342560d
A004014
Norms of vectors in the b.c.c. lattice.
[ "0", "3", "4", "8", "11", "12", "16", "19", "20", "24", "27", "32", "35", "36", "40", "43", "44", "48", "51", "52", "56", "59", "64", "67", "68", "72", "75", "76", "80", "83", "84", "88", "91", "96", "99", "100", "104", "107", "108", "115", "116", "120", "123", "128", "131", "132", "136", "139", "140", "144", "147", "148", "152", "155", "160", "163", "164", "168" ]
[ "nonn", "nice", "easy" ]
43
0
2
[ "A004013", "A004014", "A004215", "A017101", "A034045", "A047458" ]
[ "M2347" ]
N. J. A. Sloane
2022-11-07T07:41:40
oeisdata/seq/A004/A004014.seq
ad82a1e1cce2c914065362acf84e469f
A004015
Theta series of face-centered cubic (f.c.c.) lattice.
[ "1", "12", "6", "24", "12", "24", "8", "48", "6", "36", "24", "24", "24", "72", "0", "48", "12", "48", "30", "72", "24", "48", "24", "48", "8", "84", "24", "96", "48", "24", "0", "96", "6", "96", "48", "48", "36", "120", "24", "48", "24", "48", "48", "120", "24", "120", "0", "96", "24", "108", "30", "48", "72", "72", "32", "144", "0", "96", "72", "72", "48", "120", "0", "144", "12", "48", "48", "168", "48", "96" ]
[ "nonn", "easy", "nice" ]
68
0
2
[ "A000007", "A000122", "A004013", "A004015", "A004016", "A005875", "A005901", "A008444", "A008445", "A008446", "A008447", "A008448", "A008449", "A045828", "A055039" ]
[ "M4821" ]
N. J. A. Sloane
2025-02-24T18:04:25
oeisdata/seq/A004/A004015.seq
11f064f725eea8f1e3942649ee88d804
A004016
Theta series of planar hexagonal lattice A_2.
[ "1", "6", "0", "6", "6", "0", "0", "12", "0", "6", "0", "0", "6", "12", "0", "0", "6", "0", "0", "12", "0", "12", "0", "0", "0", "6", "0", "6", "12", "0", "0", "12", "0", "0", "0", "0", "6", "12", "0", "12", "0", "0", "0", "12", "0", "0", "0", "0", "6", "18", "0", "0", "12", "0", "0", "0", "0", "12", "0", "0", "0", "12", "0", "12", "6", "0", "0", "12", "0", "0", "0", "0", "0", "12", "0", "6", "12", "0", "0", "12", "0" ]
[ "nonn", "nice", "easy" ]
139
0
2
[ "A000007", "A000122", "A002324", "A003051", "A003215", "A004015", "A004016", "A005881", "A005882", "A005928", "A008444", "A008445", "A008446", "A008447", "A008448", "A008449", "A008458", "A033685", "A033687", "A035019", "A038587", "A038591", "A186706" ]
[ "M4042" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004016.seq
ad1ce85b576485b5231c233c71bc9a1c
A004017
Theta series of E_8 lattice with respect to deep hole.
[ "16", "128", "448", "1024", "2016", "3584", "5504", "8192", "12112", "16128", "21312", "28672", "35168", "44032", "56448", "65536", "78624", "96896", "109760", "129024", "154112", "170496", "194688", "229376", "252016", "281344", "327040", "352256", "390240", "451584", "476672", "524288", "596736", "628992" ]
[ "nonn", "easy" ]
23
1
1
[ "A004017", "A007331" ]
[ "M5009" ]
N. J. A. Sloane
2024-10-14T12:22:44
oeisdata/seq/A004/A004017.seq
7e973f3b90c98072fe5c7e700d89fb3c
A004018
Theta series of square lattice (or number of ways of writing n as a sum of 2 squares). Often denoted by r(n) or r_2(n).
[ "1", "4", "4", "0", "4", "8", "0", "0", "4", "4", "8", "0", "0", "8", "0", "0", "4", "8", "4", "0", "8", "0", "0", "0", "0", "12", "8", "0", "0", "8", "0", "0", "4", "0", "8", "0", "4", "8", "0", "0", "8", "8", "0", "0", "0", "8", "0", "0", "0", "4", "12", "0", "8", "8", "0", "0", "0", "0", "8", "0", "0", "8", "0", "0", "4", "16", "0", "0", "8", "0", "0", "0", "4", "8", "8", "0", "0", "0", "0", "0", "8", "4", "8", "0", "0", "16", "0", "0", "0", "8", "8", "0", "0", "0", "0", "0", "0", "8", "4", "0", "12", "8" ]
[ "nonn", "easy", "nice", "core" ]
240
0
2
[ "A001481", "A002654", "A004018", "A004020", "A005883", "A014198", "A057655", "A057961", "A057962", "A071383", "A071385", "A104271", "A105673", "A122141", "A286815", "A319574" ]
[ "M3218" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004018.seq
c5fa63db4d14657980038ace8800df5e
A004019
a(0) = 0; for n > 0, a(n) = (a(n-1) + 1)^2.
[ "0", "1", "4", "25", "676", "458329", "210066388900", "44127887745906175987801", "1947270476915296449559703445493848930452791204", "3791862310265926082868235028027893277370233152247388584761734150717768254410341175325352025" ]
[ "nonn", "easy", "nice" ]
105
0
3
[ "A000290", "A001699", "A003095", "A004019", "A056207", "A091980", "A355108" ]
[ "M3611" ]
N. J. A. Sloane
2025-01-16T11:30:20
oeisdata/seq/A004/A004019.seq
5cf8feff7845eacfeb6539b11795729a
A004020
Theta series of square lattice with respect to edge.
[ "2", "4", "2", "4", "4", "0", "6", "4", "0", "4", "4", "4", "2", "4", "0", "4", "8", "0", "4", "0", "2", "8", "4", "0", "4", "4", "0", "4", "4", "4", "2", "8", "0", "0", "4", "0", "8", "4", "4", "4", "0", "0", "6", "4", "0", "4", "8", "0", "4", "4", "0", "8", "0", "0", "0", "8", "6", "4", "4", "0", "4", "4", "0", "0", "4", "4", "8", "4", "0", "4", "4", "0", "6", "4", "0", "0", "8", "0", "4", "4", "0", "12", "0", "4", "4", "0", "0", "4", "4", "0", "2", "8", "4", "4", "8", "0", "0", "4", "0", "4", "4", "4", "4", "0" ]
[ "nonn" ]
35
0
1
[ "A000122", "A000700", "A000796", "A004020", "A004531", "A008441", "A010054", "A121373" ]
[ "M0931" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004020.seq
0b5444aca99fe8699f6898cafd8a77fb
A004021
Theta series of packing P_{10c}.
[ "1", "372", "768", "5684", "6144", "28608", "23040", "91956", "61440", "224680", "140544", "458688", "276480", "358240", "480768", "1467188", "798720", "2329012", "1251072", "3590952", "1843200" ]
[ "nonn" ]
11
0
2
null
[ "M5448" ]
N. J. A. Sloane
2023-10-24T06:09:16
oeisdata/seq/A004/A004021.seq
ecaceeb28ea43f5908f5dc960497f1ad
A004022
Primes of the form (10^k - 1)/9. Also called repunit primes or repdigit primes.
[ "11", "1111111111111111111", "11111111111111111111111" ]
[ "nonn", "nice", "bref" ]
94
1
1
[ "A004022", "A004023", "A046413", "A116692" ]
[ "M4816" ]
N. J. A. Sloane
2024-11-05T12:12:55
oeisdata/seq/A004/A004022.seq
fad50e4021e85e0821165c8d80da8a06
A004023
Indices of prime repunits: numbers k such that 11...111 (with k 1's) = (10^k - 1)/9 is prime.
[ "2", "19", "23", "317", "1031", "49081", "86453", "109297", "270343", "5794777", "8177207" ]
[ "hard", "nonn", "nice", "more", "changed" ]
279
1
1
[ "A002275", "A004022", "A004023", "A055557", "A085104" ]
[ "M2114" ]
N. J. A. Sloane
2025-04-25T04:27:28
oeisdata/seq/A004/A004023.seq
6df5521cb9893cb21f41fd4922ee3b1b
A004024
Theta series of b.c.c. lattice with respect to deep hole.
[ "4", "4", "8", "12", "4", "12", "12", "12", "16", "16", "8", "8", "28", "12", "20", "24", "8", "16", "28", "12", "16", "28", "20", "32", "20", "16", "16", "32", "20", "24", "28", "8", "36", "44", "12", "32", "36", "16", "24", "20", "28", "20", "56", "28", "16", "40", "20", "40", "44", "12", "36", "40", "20", "32", "40", "16", "24", "60", "32", "36", "40", "24", "32", "60", "24", "40", "24", "20", "60", "36", "24", "32", "56", "32" ]
[ "nonn", "easy", "nice" ]
33
0
1
[ "A004024", "A045831" ]
[ "M3227" ]
N. J. A. Sloane
2017-07-07T03:45:09
oeisdata/seq/A004/A004024.seq
27dfd2cf2c426b5f1433860958fef180
A004025
Theta series of b.c.c. lattice with respect to long edge.
[ "2", "4", "0", "0", "8", "8", "0", "0", "10", "8", "0", "0", "8", "16", "0", "0", "16", "12", "0", "0", "16", "8", "0", "0", "10", "24", "0", "0", "24", "16", "0", "0", "16", "16", "0", "0", "8", "24", "0", "0", "32", "16", "0", "0", "24", "16", "0", "0", "18", "28", "0", "0", "24", "32", "0", "0", "16", "8", "0", "0", "24", "32", "0", "0", "32", "32", "0", "0", "32", "16", "0", "0", "16", "40", "0", "0", "32" ]
[ "nonn", "easy" ]
38
1
1
[ "A004025", "A045828", "A045834", "A045836" ]
[ "M0928" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004025.seq
a966a570183d06ba2c306c59fea2371c
A004026
Number of perfect quadratic forms or lattices in dimension n.
[ "1", "1", "1", "2", "3", "7", "33", "10916" ]
[ "hard", "more", "nonn", "nice" ]
44
1
4
[ "A004026", "A033689", "A037075", "A065535", "A065536", "A122079", "A122080" ]
[ "M0862" ]
N. J. A. Sloane
2021-05-04T12:03:12
oeisdata/seq/A004/A004026.seq
87b5c75f9ed4632923ac4f962544dc9e
A004027
Number of arithmetic n-dimensional crystal classes.
[ "1", "2", "13", "73", "710", "6079", "85308" ]
[ "nonn", "hard", "nice", "more" ]
45
0
2
[ "A004027", "A004028", "A004029", "A006227", "A307288" ]
[ "M2060" ]
N. J. A. Sloane
2023-10-06T07:33:02
oeisdata/seq/A004/A004027.seq
d25c2134036dffce148a421ca17fbec5
A004028
Number of geometric n-dimensional crystal classes.
[ "1", "2", "10", "32", "227", "955", "7103" ]
[ "nonn", "hard", "nice", "more" ]
47
0
2
[ "A004027", "A004028", "A004029" ]
[ "M1965" ]
N. J. A. Sloane
2023-09-28T02:02:22
oeisdata/seq/A004/A004028.seq
82ec9deacfef696bc04b02b8b415eb03
A004029
Number of n-dimensional space groups.
[ "1", "2", "17", "219", "4783", "222018", "28927915" ]
[ "nonn", "hard", "more", "nice" ]
62
0
2
[ "A004027", "A004029", "A006227", "A293060" ]
[ "M2103" ]
N. J. A. Sloane
2023-10-04T22:25:51
oeisdata/seq/A004/A004029.seq
95311f2c207c0a55e7fdbe8b16fe1db4
A004030
Erroneous version of A256413.
[ "1", "1", "5", "14", "64", "189", "826" ]
[ "dead" ]
48
0
3
[ "A004030", "A256413" ]
[ "M3847" ]
null
2017-07-09T04:08:22
oeisdata/seq/A004/A004030.seq
874b7d73d1e1cbee81d6c1c748c38158
A004031
Number of n-dimensional crystal systems.
[ "1", "1", "4", "7", "33", "59", "251" ]
[ "nonn", "hard", "more", "nice" ]
29
0
3
[ "A004026", "A004029", "A004031", "A004032", "A006226", "A006227", "A080738" ]
[ "M3317" ]
N. J. A. Sloane
2022-05-01T02:25:17
oeisdata/seq/A004/A004031.seq
5e32ae5208540e61a54c7c6dead5914a
A004032
Number of n-dimensional crystal families.
[ "1", "1", "4", "6", "23", "32", "91" ]
[ "hard", "nonn", "nice" ]
21
0
3
[ "A004027", "A004031", "A004032", "A006226", "A006227" ]
[ "M3289" ]
N. J. A. Sloane
2022-01-31T01:26:44
oeisdata/seq/A004/A004032.seq
1996cc0f236eb1cc8614bd5f1aa1eae6
A004033
Theta series of lattice A_2 tensor E_8 (dimension 16, det. 6561, min. norm 4). Also theta series of Eisenstein version of E_8 lattice.
[ "1", "0", "720", "13440", "97200", "455040", "1714320", "4821120", "12380400", "29043840", "58980960", "114076800", "219310320", "367338240", "621878400", "1037727360", "1583679600", "2401816320", "3747180240", "5232470400", "7551983520", "10938261120", "14715224640", "19930775040", "28073386800", "35727920640" ]
[ "nonn", "easy" ]
41
0
3
[ "A004016", "A004033", "A007332", "A037150" ]
[ "M5472" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004033.seq
b01d5e5141b9def704881a13da785ac3
A004034
Theta series of Leech lattice with respect to deep hole of type A_1.
[ "48", "4096", "97152", "1130496", "8400704", "45785088" ]
[ "nonn" ]
13
0
1
null
[ "M5294" ]
N. J. A. Sloane
2023-10-24T06:10:14
oeisdata/seq/A004/A004034.seq
fce02052cae6b799a11df0ec7132c6b3
A004035
The coding-theoretic function A(n,4,5).
[ "0", "1", "1", "3", "8", "18", "36", "66", "80" ]
[ "nonn", "hard", "more" ]
25
4
4
null
[ "M2729" ]
N. J. A. Sloane
2018-12-14T09:48:11
oeisdata/seq/A004/A004035.seq
2aaec9bb4021d06fe8ef43163d212db8
A004036
The coding-theoretic function A(n,4,6).
[ "1", "1", "4", "12", "30", "66", "132" ]
[ "nonn", "hard" ]
20
6
3
null
[ "M3438" ]
N. J. A. Sloane
2023-10-24T07:11:18
oeisdata/seq/A004/A004036.seq
e8582de3472dcad3e2822e2425520e6a
A004037
The coding-theoretic function A(n,6,4).
[ "1", "1", "1", "2", "2", "3", "5", "6", "9", "13", "14", "15", "20", "20", "22", "25", "30", "31", "37", "40", "42", "50", "52", "54", "63", "65", "67", "76", "80", "82", "92", "96", "99", "111", "114", "117", "130", "133", "136", "149", "154", "157", "171", "176", "180", "196", "200", "204", "221", "225", "229", "246", "252", "256", "274", "280", "285", "305", "310", "315", "336" ]
[ "nonn" ]
48
4
4
null
[ "M0291", "N0104" ]
N. J. A. Sloane
2024-02-27T09:53:24
oeisdata/seq/A004/A004037.seq
a9b929405b6afc9616ac0bd1c63d8a27
A004038
The coding-theoretic function A(n,6,5).
[ "1", "1", "2", "3", "6", "11", "12", "18", "28", "42", "48", "68" ]
[ "nonn", "hard" ]
16
6
3
null
[ "M0779" ]
N. J. A. Sloane
2023-10-24T06:12:03
oeisdata/seq/A004/A004038.seq
abc48c6f448e5601c435da04e7526c4d
A004039
The coding-theoretic function A(n,6,6).
[ "1", "1", "1", "3", "5", "11", "22", "26", "42", "70", "112" ]
[ "nonn", "hard" ]
16
6
4
null
[ "M2483" ]
N. J. A. Sloane
2023-10-24T06:14:36
oeisdata/seq/A004/A004039.seq
608c38051234a98ef8fde45817bd2c05
A004040
Inversion of A000257.
[ "1", "2", "6", "23", "103", "512", "2740", "15485", "91245", "555662", "3475090", "22214707", "144640291", "956560748", "6411521056", "43478151737", "297864793993", "2059159989914", "14350039389022", "100726680316559", "711630547589023", "5057282786190872", "36132861123763276", "259423620328055093", "1870954187618001253" ]
[ "nonn" ]
13
0
2
[ "A000257", "A004040", "A022558" ]
null
N. J. A. Sloane
2023-10-24T07:10:46
oeisdata/seq/A004/A004040.seq
399db805942d9c789546a792c6749969
A004041
Scaled sums of odd reciprocals: a(n) = (2*n + 1)!!*(Sum_{k=0..n} 1/(2*k + 1)).
[ "1", "4", "23", "176", "1689", "19524", "264207", "4098240", "71697105", "1396704420", "29985521895", "703416314160", "17901641997225", "491250187505700", "14459713484342175", "454441401368236800", "15188465029114325025", "537928935889764226500" ]
[ "nonn" ]
51
0
2
[ "A000254", "A002428", "A004041", "A024199", "A028338", "A049034", "A109692", "A161198" ]
null
Joe Keane (jgk(AT)jgk.org)
2024-12-28T00:06:48
oeisdata/seq/A004/A004041.seq
54750df325846ee6e50838ed17afd080
A004042
Periods of reciprocals of A006883, starting with first nonzero digit.
[ "0", "142857", "5882352941176470", "526315789473684210", "4347826086956521739130", "3448275862068965517241379310", "2127659574468085106382978723404255319148936170", "1694915254237288135593220338983050847457627118644067796610" ]
[ "nonn", "base" ]
29
1
2
[ "A004042", "A180340" ]
null
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A004/A004042.seq
b7c2e95fd8e95ee80e35aeb545a32154
A004043
The coding-theoretic function A(n,8,8).
[ "1", "1", "1", "1", "3", "3", "7", "15", "30", "34" ]
[ "nonn", "hard" ]
17
8
5
[ "A004043", "A005851", "A005852", "A005853", "A005866", "A030069" ]
null
N. J. A. Sloane
2023-10-24T06:13:42
oeisdata/seq/A004/A004043.seq
45947ec029b54fc2e21b9e77f7ba07fe
A004044
The classic football pool problem: size of minimal covering code in {0,1,2}^n with covering radius 1.
[ "1", "1", "3", "5", "9", "27" ]
[ "nonn", "hard", "more", "nice" ]
88
0
3
[ "A004044", "A060439" ]
null
N. J. A. Sloane
2021-08-08T11:28:46
oeisdata/seq/A004/A004044.seq
efb0a3a449abe661cf1e541d2eadcf52
A004045
Minimal size of binary code of length n such that every vector is within distance 1 of at least 2 codewords.
[ "2", "3", "4", "8", "12", "20", "32" ]
[ "nonn", "hard", "more" ]
28
1
1
null
null
N. J. A. Sloane
2020-03-03T23:38:39
oeisdata/seq/A004/A004045.seq
81724e103597b8912acc48e79b8b3952
A004046
Theta series of extremal 3-modular even 24-dimensional lattice with minimal norm 6 and det = 3^12.
[ "1", "0", "0", "26208", "530712", "6368544", "47331648", "256864608", "1116087336", "4092877152", "12996075456", "37058557536", "96952754808", "232778774592", "526258264896", "1128148021728", "2286143305992", "4451523096384", "8386247967552", "15130902687264", "26614339616592", "45684687301344" ]
[ "nonn" ]
33
0
4
[ "A004046", "A107657" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004046.seq
14d893cfa58382b6f7f05948cfe43caf
A004047
The coding-theoretic function A(n,10,9).
[ "1", "1", "1", "1", "1", "2", "3", "4", "6", "10", "19" ]
[ "nonn", "hard" ]
11
9
6
null
null
N. J. A. Sloane
2023-10-24T06:15:33
oeisdata/seq/A004/A004047.seq
f7f6e4517979b14cd50a5a16a108abfc
A004048
Theta series of 14-dimensional extremal 3-modular lattice with det 3^7, minimal norm 4, group 2 X G_2(3).
[ "1", "0", "756", "8736", "44226", "187488", "531468", "1314144", "3097332", "6141408", "10968048", "21258720", "34038186", "53778816", "88943400", "131804064", "184024386", "289650816", "387420516", "524343456", "756139104", "992308512" ]
[ "nonn" ]
14
0
3
null
null
N. J. A. Sloane
2024-06-14T22:31:09
oeisdata/seq/A004/A004048.seq
7f7f44592cdc254bbfe06211064b5d1a
A004049
Erroneous version of A006967.
[ "1", "1", "4", "4", "8", "24", "32", "40", "120", "296" ]
[ "dead" ]
10
1
3
null
null
N. J. A. Sloane
2023-10-24T06:17:06
oeisdata/seq/A004/A004049.seq
ecbebae0b0f3a235e40870043048c9df
A004050
Numbers of the form 2^j + 3^k, for j and k >= 0.
[ "2", "3", "4", "5", "7", "9", "10", "11", "13", "17", "19", "25", "28", "29", "31", "33", "35", "41", "43", "59", "65", "67", "73", "82", "83", "85", "89", "91", "97", "113", "129", "131", "137", "145", "155", "209", "244", "245", "247", "251", "257", "259", "265", "275", "283", "307", "337", "371", "499", "513", "515", "521", "539", "593", "730", "731", "733", "737", "745", "755" ]
[ "nonn" ]
53
1
1
[ "A000079", "A000243", "A004050", "A004051", "A085634", "A219835", "A226806", "A226832" ]
null
N. J. A. Sloane
2022-10-28T07:15:48
oeisdata/seq/A004/A004050.seq
d34b6cbd548f3f3df0f03ebe7efbab64
A004051
Primes of the form 2^a + 3^b.
[ "2", "3", "5", "7", "11", "13", "17", "19", "29", "31", "41", "43", "59", "67", "73", "83", "89", "97", "113", "131", "137", "251", "257", "283", "307", "337", "499", "521", "593", "733", "761", "857", "1033", "1051", "1753", "2129", "2203", "2251", "2699", "2777", "4099", "4177", "4339", "6563", "6569", "6577", "6689", "8219", "8273", "8609", "10657", "14753" ]
[ "nonn" ]
28
1
1
[ "A004050", "A004051", "A010051" ]
null
N. J. A. Sloane
2016-04-25T12:04:59
oeisdata/seq/A004/A004051.seq
7597797d8f919555ad470bda207c19ff
A004052
The coding-theoretic function A(n,14,8).
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "4", "4", "4", "4", "5", "5", "5", "6", "6", "7", "9", "9", "9", "10", "10", "11", "12", "12", "13", "15", "17", "18", "19", "21", "25", "26" ]
[ "nonn" ]
17
8
8
null
null
N. J. A. Sloane
2024-02-26T17:17:50
oeisdata/seq/A004/A004052.seq
f99aca38662acae793d42a0c82e68ad6
A004053
For m=2,3,..., write m in bases 2,3,..,m.
[ "10", "11", "10", "100", "11", "10", "101", "12", "11", "10", "110", "20", "12", "11", "10", "111", "21", "13", "12", "11", "10", "1000", "22", "20", "13", "12", "11", "10", "1001", "100", "21", "14", "13", "12", "11", "10", "1010", "101", "22", "20", "14", "13", "12", "11", "10", "1011", "102", "23", "21", "15", "14", "13", "12", "11", "10", "1100", "110", "30", "22", "20", "15", "14", "13", "12", "11", "10" ]
[ "nonn", "base", "tabl" ]
23
2
1
[ "A004053", "A007088", "A007090", "A007091", "A007092", "A007093", "A007094", "A007095" ]
null
Johan Boye (johbo(AT)ida.liu.se)
2024-12-01T15:40:01
oeisdata/seq/A004/A004053.seq
83857a11d932bf1d51e3097ca6ab2591
A004054
Expansion of (1-x)/((1+x)*(1-2*x)*(1-3*x)).
[ "1", "3", "11", "35", "111", "343", "1051", "3195", "9671", "29183", "87891", "264355", "794431", "2386023", "7163531", "21501515", "64526391", "193622863", "580955971", "1743042675", "5229477551", "15689131703", "47068793211", "141209175835", "423633119911", "1270910544543", "3812754003251", "11438306748995" ]
[ "nonn", "easy" ]
57
0
2
[ "A000244", "A001045", "A001047", "A004054", "A078008" ]
null
N. J. A. Sloane
2023-12-02T15:23:13
oeisdata/seq/A004/A004054.seq
836d4590e3a20c18bdc513e4d72b8aaa
A004055
((p-1)/2)! mod p for odd primes p.
[ "1", "2", "6", "10", "5", "13", "18", "1", "12", "1", "31", "9", "42", "46", "23", "1", "11", "66", "1", "27", "78", "1", "34", "22", "91", "102", "1", "33", "15", "126", "130", "37", "1", "44", "1", "129", "162", "1", "80", "178", "162", "190", "81", "183", "198", "1", "1", "226", "122", "144", "1", "64", "1", "16", "262", "187", "1", "217", "53", "1", "138", "1", "1", "288", "114", "1", "189" ]
[ "nonn" ]
36
1
2
[ "A004055", "A058302", "A065091" ]
null
Jeffrey Shallit, Dec 11 1996
2025-01-16T13:01:42
oeisdata/seq/A004/A004055.seq
e3b250b50c3a81c13e4c56a8ed7db5ec
A004056
The coding-theoretic function A(n,14,12).
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "3", "4", "4", "6", "8", "13" ]
[ "nonn", "hard" ]
11
12
8
null
null
N. J. A. Sloane
2023-10-24T06:17:55
oeisdata/seq/A004/A004056.seq
3adbf6f9211f32d1ae23a3926b8e0928
A004057
Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)).
[ "1", "7", "39", "191", "875", "3843", "16423", "68887", "285219", "1170059", "4768127", "19336863", "78141883", "314953555", "1266977751", "5089412519", "20422176467", "81882328731", "328110270895", "1314184126255", "5261965982571", "21063553061987" ]
[ "nonn", "easy" ]
17
0
2
[ "A004057", "A099110" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004057.seq
8c4d81a116668c59cff8ba5f2e3b9a06
A004058
Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)).
[ "1", "12", "99", "686", "4305", "25368", "143263", "785202", "4211229", "22226204", "115899147", "598832598", "3072304873", "15676477920", "79649367351", "403336249274", "2037103422837", "10267399442916", "51665107485475" ]
[ "nonn", "easy" ]
14
0
2
[ "A004058", "A099111" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004058.seq
98253abb30cecc116e99303844296ecc
A004059
a(n) gives position of first n in A057561.
[ "1", "2", "4", "5", "6", "8", "9", "11", "13", "14", "15", "17", "18", "20", "22", "23", "24", "26", "28", "29", "30", "32", "34", "35", "36", "38", "40", "41", "42", "43", "45", "47", "48", "50", "51", "53", "55", "56", "57", "59", "60", "61", "64" ]
[ "nonn" ]
20
1
2
[ "A004059", "A057561", "A094708" ]
[ "M0949" ]
N. J. A. Sloane
2023-10-24T06:19:00
oeisdata/seq/A004/A004059.seq
7db7551557b7d1067314df4a84af68dc
A004060
Erroneous version of A028491.
[ "3", "7", "13", "71", "103", "541", "1019", "1367", "1627", "4177", "9011", "9551" ]
[ "dead" ]
4
1
1
null
null
null
1999-12-11T03:00:00
oeisdata/seq/A004/A004060.seq
e6866d16647ae7346a81bdee0c4a701a
A004061
Numbers k such that (5^k - 1)/4 is prime.
[ "3", "7", "11", "13", "47", "127", "149", "181", "619", "929", "3407", "10949", "13241", "13873", "16519", "201359", "396413", "1888279", "3300593" ]
[ "hard", "nonn", "more", "changed" ]
73
1
1
[ "A004061", "A080130" ]
[ "M2620" ]
N. J. A. Sloane
2025-04-25T04:27:24
oeisdata/seq/A004/A004061.seq
c640d83ee79b969f33261f4a01fd5eed
A004062
Numbers k such that (6^k - 1)/5 is prime.
[ "2", "3", "7", "29", "71", "127", "271", "509", "1049", "6389", "6883", "10613", "19889", "79987", "608099", "1365019", "3360347" ]
[ "hard", "more", "nonn", "changed" ]
69
1
1
null
[ "M0861" ]
N. J. A. Sloane
2025-04-25T04:33:19
oeisdata/seq/A004/A004062.seq
0eb793623a23a2212c311ff319514885
A004063
Numbers k such that (7^k - 1)/6 is prime.
[ "5", "13", "131", "149", "1699", "14221", "35201", "126037", "371669", "1264699" ]
[ "nonn", "hard", "more", "changed" ]
58
1
1
null
[ "M3836" ]
N. J. A. Sloane
2025-04-25T05:26:38
oeisdata/seq/A004/A004063.seq
541eaef3ebdc1fa17eb86373f2407ceb
A004064
Numbers k such that (12^k - 1)/11 is prime.
[ "2", "3", "5", "19", "97", "109", "317", "353", "701", "9739", "14951", "37573", "46889", "769543" ]
[ "nonn", "hard", "more", "changed" ]
56
1
1
null
[ "M0744" ]
N. J. A. Sloane
2025-04-25T05:26:56
oeisdata/seq/A004/A004064.seq
6e869cd602a43d1dd38139e427234ba3
A004065
Define predecessors of n, P(n), to consist of numbers whose binary representation is obtained from that of n by replacing 10 with 01 or changing a final 1 to a 0; then a(0)=1, a(n) = Sum a(P(n)), n>0.
[ "1", "1", "1", "1", "1", "2", "2", "2", "1", "3", "5", "7", "5", "12", "12", "12", "1", "4", "9", "16", "14", "42", "54", "66", "14", "56", "110", "176", "110", "286", "286", "286", "1", "5", "14", "30", "28", "100", "154", "220", "42", "198", "462", "858", "572", "1716", "2002", "2288", "42", "240", "702", "1560", "1274", "4550", "6552", "8840", "1274", "5824", "12376" ]
[ "nonn", "base" ]
28
0
6
[ "A003121", "A004065" ]
null
David W. Wilson, Jan 29 2000
2024-08-28T09:37:31
oeisdata/seq/A004/A004065.seq
300133209131d870f910ea5acef29f25
A004066
Number of simple regular trivalent bicolored graphs with 2n nodes.
[ "0", "0", "1", "1", "2", "6", "14", "41", "157", "725", "4196", "29817", "246646", "2297088", "23503564", "260265650", "3090341095", "39101587595", "524783295041", "7443251159470", "111222017297268", "1746166043555813", "28734210790531045", "494526547845483641", "8883866458982018870", "166286444108288113541", "3237719185652343485853", "65477290060076644381373" ]
[ "nonn" ]
19
1
5
[ "A000512", "A000840", "A004066", "A006823", "A008325" ]
null
Gunnar Brinkmann, Brendan McKay and Eric Rogoyski
2020-04-03T17:25:42
oeisdata/seq/A004/A004066.seq
c37116cf2ddee6f52d9347ceda8a13dc
A004067
The coding-theoretic function A(n,6,7).
[ "1", "1", "1", "3", "6", "12", "26", "42", "69" ]
[ "nonn", "hard" ]
17
7
4
null
null
N. J. A. Sloane
2018-12-24T06:21:40
oeisdata/seq/A004/A004067.seq
0385ceca8a4e61ea8d608736f5bd310a
A004068
Number of atoms in a decahedron with n shells.
[ "0", "1", "7", "23", "54", "105", "181", "287", "428", "609", "835", "1111", "1442", "1833", "2289", "2815", "3416", "4097", "4863", "5719", "6670", "7721", "8877", "10143", "11524", "13025", "14651", "16407", "18298", "20329", "22505", "24831", "27312", "29953", "32759", "35735", "38886", "42217", "45733", "49439" ]
[ "nonn", "easy" ]
78
0
3
[ "A000292", "A000447", "A000578", "A004006", "A004068", "A004126", "A004188", "A004466", "A004467", "A005891", "A005900", "A006003", "A006322", "A006527", "A007588", "A010001", "A062025", "A063521", "A063522", "A063523", "A081436", "A100145", "A215630" ]
null
Albert D. Rich (AlbertRich(AT)msn.com)
2025-04-02T03:04:32
oeisdata/seq/A004/A004068.seq
39483443ba589fa4a32bf75dd4f1e35c
A004069
Numbers of points in nontrivial partial geometries.
[ "15", "27", "40", "45", "64" ]
[ "nonn", "hard" ]
6
1
1
null
null
N. J. A. Sloane
2023-10-24T06:19:30
oeisdata/seq/A004/A004069.seq
1b6ed0df8e380ada1d5dcbfd19fa0ddb
A004070
Table of Whitney numbers W(n,k) read by antidiagonals, where W(n,k) is maximal number of pieces into which n-space is sliced by k hyperplanes, n >= 0, k >= 0.
[ "1", "1", "1", "1", "2", "1", "1", "2", "3", "1", "1", "2", "4", "4", "1", "1", "2", "4", "7", "5", "1", "1", "2", "4", "8", "11", "6", "1", "1", "2", "4", "8", "15", "16", "7", "1", "1", "2", "4", "8", "16", "26", "22", "8", "1", "1", "2", "4", "8", "16", "31", "42", "29", "9", "1", "1", "2", "4", "8", "16", "32", "57", "64", "37", "10", "1", "1", "2", "4", "8", "16", "32", "63", "99", "93", "46", "11", "1", "1", "2", "4", "8", "16", "32", "64", "120", "163" ]
[ "tabl", "nonn", "easy", "nice" ]
85
0
5
[ "A000012", "A000027", "A000071", "A000079", "A000124", "A000125", "A000127", "A000225", "A000295", "A002662", "A002663", "A002664", "A004070", "A006261", "A007799", "A008859", "A008860", "A008861", "A008862", "A008863", "A035038", "A035039", "A035040", "A035041", "A035042", "A052509", "A178522", "A178524" ]
null
N. J. A. Sloane
2025-01-08T09:27:46
oeisdata/seq/A004/A004070.seq
82063c90ef761116c5c022c8ac763d39
A004071
Start with a(0)=1; replace each i with 12...i, then add 1 to final digit.
[ "1", "2", "13", "1124", "11121235", "1111211212312346", "11111211121121231121231234123457", "1111112111121112112123111211212311212312341121231234123451234568" ]
[ "nonn", "base" ]
15
0
2
null
null
N. J. A. Sloane
2017-03-31T22:51:27
oeisdata/seq/A004/A004071.seq
5595df7de744d85ad5cd57168274ae9a
A004072
Read the terms of A004071 backwards.
[ "1", "2", "31", "4211", "53212111", "6432132121121111", "75432143213212113212112111211111", "8654321543214321321211432132121132121121113212112111211112111111" ]
[ "nonn" ]
12
0
2
null
null
N. J. A. Sloane
2023-10-24T06:20:43
oeisdata/seq/A004/A004072.seq
4d9ed232c0b90e546e5e359a1097856d
A004073
Start with a(1)=1; to get a(n) replace each i in a(n-1) with 12...i, then append n.
[ "1", "12", "1123", "11121234", "1111211212312345", "11111211121121231121231234123456", "1111112111121112112123111211212311212312341121231234123451234567" ]
[ "nonn", "base" ]
15
1
2
null
null
N. J. A. Sloane
2017-03-31T22:50:57
oeisdata/seq/A004/A004073.seq
47b46ed7f4fdada0364e4b9c1dd23239
A004074
a(n) = 2*A004001(n) - n, where A004001 is the Hofstadter-Conway $10000 sequence.
[ "1", "0", "1", "0", "1", "2", "1", "0", "1", "2", "3", "2", "3", "2", "1", "0", "1", "2", "3", "4", "3", "4", "5", "4", "5", "4", "3", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "4", "5", "6", "7", "6", "7", "8", "7", "8", "7", "6", "7", "8", "7", "8", "7", "6", "7", "6", "5", "4", "5", "4", "3", "2", "1", "0", "1", "2", "3", "4", "5", "6", "5", "6", "7", "8", "9", "8", "9", "10", "11", "10", "11", "12", "11", "12", "11", "10", "11", "12", "13", "12", "13", "14", "13", "14", "13", "12" ]
[ "nonn" ]
35
1
6
[ "A004001", "A004074", "A082590", "A213057", "A233270", "A249071" ]
null
N. J. A. Sloane
2019-11-23T04:08:51
oeisdata/seq/A004/A004074.seq
1cc41593f4fb8a0756dcdff3cbf934c6
A004075
Number of Skolem sequences of order n.
[ "1", "0", "0", "6", "10", "0", "0", "504", "2656", "0", "0", "455936", "3040560", "0", "0", "1400156768", "12248982496", "0", "0", "11435578798976", "123564928167168", "0", "0", "204776117691241344", "2634563519776965376", "0", "0", "7064747252076429464064", "105435171495207196553472", "0", "0" ]
[ "nonn", "more" ]
45
1
4
[ "A004075", "A014552", "A059106", "A176127", "A268537" ]
null
N. J. A. Sloane
2023-10-24T06:22:21
oeisdata/seq/A004/A004075.seq
fc6ff109044aef988bf8343437f41c3c
A004076
Number of hooked Skolem sequences of order n.
[ "0", "1", "2", "0", "0", "38", "124", "0", "0", "12808", "72648", "0", "0", "21878816", "168870048", "0", "0", "113071735648", "1105816948032", "0", "0", "1395701792232832" ]
[ "nonn", "more" ]
27
1
3
null
null
N. J. A. Sloane
2023-10-24T19:24:00
oeisdata/seq/A004/A004076.seq
fb50caaed5e679e3c597da5c773ef7e5
A004077
Number of extended Skolem sequences of order n.
[ "2", "2", "6", "22", "48", "160", "636", "3556", "19488", "95872", "594320", "4459888", "32131648", "227072544", "1875064880", "17851780784", "165367171136", "1506506453568", "15540217445728", "179708231523680", "2034547787823488", "22716589497430656" ]
[ "nonn", "more" ]
30
1
1
null
null
N. J. A. Sloane
2023-10-24T07:02:09
oeisdata/seq/A004/A004077.seq
c467836ee445ea443c3ff0f40e17a237
A004078
Number of Tuscan squares of order n.
[ "1", "0", "1", "0", "736", "466144" ]
[ "nonn", "hard" ]
10
2
5
null
null
N. J. A. Sloane
2023-10-24T10:09:43
oeisdata/seq/A004/A004078.seq
a893181bbc133da1ac4812326f932117
A004079
a(n) = maximal m such that an m X n Florentine rectangle exists.
[ "1", "2", "2", "4", "4", "6", "6", "7", "8", "10", "10", "12" ]
[ "nonn", "hard" ]
7
1
2
null
null
N. J. A. Sloane
2023-10-24T06:27:25
oeisdata/seq/A004/A004079.seq
cf4c8233936c6edcb7c690ff1f228d08
A004080
Least k such that H(k) >= n, where H(k) is the harmonic number Sum_{i=1..k} 1/i.
[ "0", "1", "4", "11", "31", "83", "227", "616", "1674", "4550", "12367", "33617", "91380", "248397", "675214", "1835421", "4989191", "13562027", "36865412", "100210581", "272400600", "740461601", "2012783315", "5471312310", "14872568831", "40427833596", "109894245429", "298723530401", "812014744422" ]
[ "nonn", "nice" ]
82
0
3
[ "A002387", "A004080" ]
null
N. J. A. Sloane, Clark Kimberling
2025-02-16T08:32:28
oeisdata/seq/A004/A004080.seq
0e9b14189f9d298e985ae46273df6250
A004081
a(n) = n-th positive integer such that only one integer lies between exp(s(m)) and exp(s(m+1)), where s(m) = 1 + 1/2 + 1/3 + . . . + 1/m.
[ "4", "8", "13", "17", "22", "26", "31", "36", "40", "45", "49", "54", "58", "63", "68", "72", "77", "81", "86", "90", "95", "99", "104", "109", "113", "118", "122", "127", "131", "136", "141", "145", "150", "154", "159", "163", "168", "173", "177", "182", "186", "191", "195", "200" ]
[ "nonn" ]
13
1
1
null
null
Clark Kimberling
2013-05-30T16:57:29
oeisdata/seq/A004/A004081.seq
3ab2e266da1955c020ec4c1491924721
A004082
Numbers k such that sin(k-1) <= 0 and sin(k) > 0.
[ "1", "7", "13", "19", "26", "32", "38", "44", "51", "57", "63", "70", "76", "82", "88", "95", "101", "107", "114", "120", "126", "132", "139", "145", "151", "158", "164", "170", "176", "183", "189", "195", "202", "208", "214", "220", "227", "233", "239", "246", "252", "258", "264", "271", "277", "283", "290", "296" ]
[ "nonn" ]
46
1
2
[ "A004082", "A004084", "A038130", "A066643", "A277690" ]
null
Clark Kimberling
2025-03-21T09:39:18
oeisdata/seq/A004/A004082.seq
d7be581f67acb9e09408493b6235cbe0
A004083
Numbers k such that cos(k-1) <= 0 and cos(k) > 0.
[ "5", "11", "18", "24", "30", "37", "43", "49", "55", "62", "68", "74", "81", "87", "93", "99", "106", "112", "118", "125", "131", "137", "143", "150", "156", "162", "169", "175", "181", "187", "194", "200", "206", "213", "219", "225", "231", "238", "244", "250", "257", "263", "269", "275", "282", "288", "294", "301", "307", "313", "319", "326", "332", "338", "345" ]
[ "nonn" ]
21
1
1
[ "A004083", "A145005" ]
null
Clark Kimberling
2021-04-23T01:23:21
oeisdata/seq/A004/A004083.seq
722e9c339bdc7ed062b5c695117ef3f7
A004084
a(n) = n-th positive integer k such that tan(k-1) <= 0 and tan(k) > 0.
[ "1", "4", "7", "10", "13", "16", "19", "22", "26", "29", "32", "35", "38", "41", "44", "48", "51", "54", "57", "60", "63", "66", "70", "73", "76", "79", "82", "85", "88", "92", "95", "98", "101", "104", "107", "110", "114", "117", "120", "123", "126", "129", "132", "136", "139", "142", "145", "148", "151", "154", "158", "161", "164", "167" ]
[ "nonn" ]
16
1
2
null
null
Clark Kimberling
2013-03-21T06:36:42
oeisdata/seq/A004/A004084.seq
5233c68fc8d2d10db39f5ea6a1615c55
A004085
Sum of digits of Euler totient function of n.
[ "1", "1", "2", "2", "4", "2", "6", "4", "6", "4", "1", "4", "3", "6", "8", "8", "7", "6", "9", "8", "3", "1", "4", "8", "2", "3", "9", "3", "10", "8", "3", "7", "2", "7", "6", "3", "9", "9", "6", "7", "4", "3", "6", "2", "6", "4", "10", "7", "6", "2", "5", "6", "7", "9", "4", "6", "9", "10", "13", "7", "6", "3", "9", "5", "12", "2", "12", "5", "8", "6", "7", "6", "9", "9", "4", "9", "6", "6", "15", "5", "9", "4", "10", "6", "10" ]
[ "nonn", "base" ]
24
1
3
[ "A000010", "A004085", "A007953", "A077651" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004085.seq
dca3ebefb2cae9628b86c6ec90736d27
A004086
Read n backwards (referred to as R(n) in many sequences).
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "1", "11", "21", "31", "41", "51", "61", "71", "81", "91", "2", "12", "22", "32", "42", "52", "62", "72", "82", "92", "3", "13", "23", "33", "43", "53", "63", "73", "83", "93", "4", "14", "24", "34", "44", "54", "64", "74", "84", "94", "5", "15", "25", "35", "45", "55", "65", "75", "85", "95", "6", "16", "26", "36", "46", "56", "66", "76", "86", "96", "7", "17", "27", "37", "47" ]
[ "nonn", "base", "nice", "look" ]
139
0
3
[ "A004086", "A004185", "A004186", "A009996", "A030101", "A030102", "A030103", "A030104", "A030105", "A030107", "A030108", "A073138", "A188649", "A221714" ]
null
N. J. A. Sloane
2023-10-29T06:37:15
oeisdata/seq/A004/A004086.seq
daf57ff29466a485bc0d8fa1106ce941
A004087
Primes written backwards.
[ "2", "3", "5", "7", "11", "31", "71", "91", "32", "92", "13", "73", "14", "34", "74", "35", "95", "16", "76", "17", "37", "97", "38", "98", "79", "101", "301", "701", "901", "311", "721", "131", "731", "931", "941", "151", "751", "361", "761", "371", "971", "181", "191", "391", "791", "991", "112", "322", "722", "922", "332", "932", "142", "152", "752", "362", "962", "172" ]
[ "nonn", "base", "look" ]
37
1
1
[ "A000040", "A004087" ]
null
N. J. A. Sloane
2022-06-24T20:14:26
oeisdata/seq/A004/A004087.seq
7ff1dbce2165d8e96e72637fbdf918bd
A004088
Sum of digits of number of partitions of n.
[ "1", "1", "2", "3", "5", "7", "2", "6", "4", "3", "6", "11", "14", "2", "9", "14", "6", "18", "16", "13", "15", "18", "3", "13", "18", "23", "15", "4", "19", "20", "15", "20", "24", "9", "7", "24", "31", "19", "14", "18", "24", "24", "20", "18", "25", "25", "24", "23", "24", "23", "16", "30", "33", "27", "28", "25", "26", "21", "17", "22", "38", "15", "16", "33", "22", "23", "17", "47", "33", "29", "42", "33", "37", "43", "29", "30", "38" ]
[ "nonn", "base" ]
8
0
3
[ "A000041", "A004088" ]
null
N. J. A. Sloane
2023-10-24T19:25:22
oeisdata/seq/A004/A004088.seq
bd996c66b014a37b4fac64e84824b0ee
A004089
Reverse digits of number of partitions of n.
[ "1", "1", "2", "3", "5", "7", "11", "51", "22", "3", "24", "65", "77", "101", "531", "671", "132", "792", "583", "94", "726", "297", "2001", "5521", "5751", "8591", "6342", "103", "8173", "5654", "4065", "2486", "9438", "34101", "1321", "38841", "77971", "73612", "51062", "58113", "83373", "38544", "47135", "16236", "57157", "43198", "855501", "457421", "372741", "525371" ]
[ "nonn", "base", "changed" ]
12
0
3
[ "A000041", "A004086", "A004089" ]
null
N. J. A. Sloane
2025-04-25T23:39:31
oeisdata/seq/A004/A004089.seq
2545657472520036251f8134fbc8cc9e
A004090
Sum of digits of Fibonacci numbers.
[ "0", "1", "1", "2", "3", "5", "8", "4", "3", "7", "10", "17", "9", "8", "17", "7", "24", "22", "19", "14", "24", "20", "17", "28", "27", "19", "19", "29", "21", "23", "17", "31", "30", "34", "37", "35", "27", "35", "44", "43", "24", "31", "46", "41", "33", "29", "35", "37", "54", "55", "46", "29", "48", "41", "53", "58", "48", "52", "73", "44", "54", "53", "62", "61", "51", "67", "73", "59" ]
[ "nonn", "base", "easy" ]
40
0
4
[ "A000045", "A004090", "A007953", "A030132", "A068500", "A246558", "A261587" ]
null
N. J. A. Sloane
2023-10-24T19:43:06
oeisdata/seq/A004/A004090.seq
11754dce503ee91dc627351205dbee58
A004091
Fibonacci numbers written backwards.
[ "0", "1", "1", "2", "3", "5", "8", "31", "12", "43", "55", "98", "441", "332", "773", "16", "789", "7951", "4852", "1814", "5676", "64901", "11771", "75682", "86364", "52057", "393121", "814691", "118713", "922415", "40238", "9626431", "9038712", "8754253", "7882075", "5647229", "25303941", "71875142", "96188093", "68954236", "551433201", "141085561", "692419762", "734494334", "337804107", "713094311", "3091136381", "3705121792" ]
[ "nonn", "base" ]
40
0
4
[ "A000045", "A004091", "A004170", "A014258" ]
null
N. J. A. Sloane
2024-06-21T12:34:30
oeisdata/seq/A004/A004091.seq
d320726cea4e7010ded6e7618cba22f9
A004092
Sum of digits of even numbers.
[ "0", "2", "4", "6", "8", "1", "3", "5", "7", "9", "2", "4", "6", "8", "10", "3", "5", "7", "9", "11", "4", "6", "8", "10", "12", "5", "7", "9", "11", "13", "6", "8", "10", "12", "14", "7", "9", "11", "13", "15", "8", "10", "12", "14", "16", "9", "11", "13", "15", "17", "1", "3", "5" ]
[ "nonn", "base", "easy" ]
22
0
2
[ "A004092", "A007953", "A169964" ]
null
N. J. A. Sloane, Dec 11 1996
2023-04-29T08:10:16
oeisdata/seq/A004/A004092.seq
643a43d04adfeda7e49dd3bf56c14b8a
A004093
Even numbers written backwards.
[ "0", "2", "4", "6", "8", "1", "21", "41", "61", "81", "2", "22", "42", "62", "82", "3", "23", "43", "63", "83", "4", "24", "44", "64", "84", "5", "25", "45", "65", "85", "6", "26", "46", "66", "86", "7", "27", "47", "67", "87", "8", "28", "48", "68", "88", "9", "29", "49", "69", "89", "1", "201", "401", "601", "801", "11", "211", "411", "611", "811", "21", "221", "421", "621", "821", "31" ]
[ "nonn", "base", "look" ]
25
0
2
[ "A004086", "A004093" ]
null
N. J. A. Sloane
2022-11-14T16:06:57
oeisdata/seq/A004/A004093.seq
bc8f4a4828777af86df807aec8d31bad
A004094
Powers of 2 written backwards.
[ "1", "2", "4", "8", "61", "23", "46", "821", "652", "215", "4201", "8402", "6904", "2918", "48361", "86723", "63556", "270131", "441262", "882425", "6758401", "2517902", "4034914", "8068838", "61277761", "23445533", "46880176", "827712431", "654534862", "219078635", "4281473701", "8463847412", "6927694924", "2954399858", "48196897171" ]
[ "nonn", "base", "easy" ]
50
0
2
[ "A000079", "A000244", "A004086", "A004094", "A004167", "A014963", "A028909", "A028910", "A036447", "A057615", "A057708", "A102382", "A102383", "A102384", "A102385", "A163632", "A263451", "A321539", "A321540", "A321541", "A321542" ]
null
N. J. A. Sloane
2025-01-07T02:01:00
oeisdata/seq/A004/A004094.seq
2aadc584f9d6074ff16aa637b0254c5c
A004095
Sum of digits of Catalan numbers.
[ "1", "1", "2", "5", "5", "6", "6", "15", "8", "20", "29", "34", "13", "22", "27", "45", "36", "42", "42", "42", "30", "39", "48", "45", "54", "54", "53", "56", "65", "49", "64", "73", "84", "39", "75", "73", "106", "79", "83", "95", "77", "90", "99", "90", "108", "99", "90", "135", "126", "117", "135", "126", "135", "132", "141" ]
[ "nonn", "base" ]
6
0
3
[ "A000108", "A004095" ]
null
N. J. A. Sloane
2023-10-24T19:31:13
oeisdata/seq/A004/A004095.seq
d4bf4abc8f1c8e0ddc22a56bbcc1f04f
A004096
Catalan numbers written backwards.
[ "1", "1", "2", "5", "41", "24", "231", "924", "341", "2684", "69761", "68785", "210802", "9247", "444762", "5484969", "7675353", "97446921", "7836774", "913627671", "240214656", "2076266442", "4636528419", "56316950343", "4237414099821", "2541046491684", "25127035376381", "40061905533596", "63057159747362" ]
[ "nonn", "base" ]
22
0
3
[ "A000108", "A004096" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004096.seq
19555c3676dcf48313acc95dcaa8f191
A004097
Sum of digits of Bell numbers.
[ "1", "1", "2", "5", "6", "7", "5", "22", "9", "15", "28", "33", "31", "37", "43", "50", "32", "63", "58", "50", "55", "78", "69", "64", "105", "94", "91", "118", "104", "101", "96", "121", "122", "139", "141", "102", "163", "150", "154", "172", "145", "164", "185", "186", "187", "194", "184", "153", "186", "172", "231", "211", "226", "196", "230", "266", "243", "247", "248", "280", "312", "285" ]
[ "nonn", "base" ]
12
0
3
[ "A000110", "A004097", "A007953" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004097.seq
44b7a9a776c6d61fbe2f47e80d45b964
A004098
Bell numbers written backwards.
[ "1", "1", "2", "5", "51", "25", "302", "778", "414", "74112", "579511", "75876", "7953124", "73444672", "223998091", "5458592831", "74124108401", "40896846828", "951608670286", "7505022472385", "27353285142715", "157651618968474", "3237448375176054", "64348055850025144", "982508492968859544" ]
[ "nonn", "base" ]
24
0
3
[ "A000110", "A004086", "A004098" ]
null
N. J. A. Sloane
2022-09-08T08:44:32
oeisdata/seq/A004/A004098.seq
1515167ce9dfcbbb260d56ff4c5e1ecc
A004099
Sum of digits of Euler numbers.
[ "1", "1", "1", "2", "5", "7", "7", "11", "17", "25", "13", "29", "29", "34", "46", "38", "41", "61", "61", "65", "62", "70", "85", "74", "83", "88", "91", "110", "113", "124", "106", "128", "170", "142", "157", "164", "128", "178", "172", "146", "176", "178", "178", "209", "206", "214", "247", "218", "263", "268", "235", "335", "284", "259", "295", "254", "278", "295", "283", "254", "308", "313" ]
[ "nonn", "base" ]
10
0
4
[ "A000111", "A004099", "A007953" ]
null
N. J. A. Sloane
2023-10-24T19:32:10
oeisdata/seq/A004/A004099.seq
9ceced35638fdfa5e5ee8965d1a60856
A004100
Number of labeled nonseparable bipartite graphs on n nodes.
[ "0", "1", "0", "3", "10", "355", "6986", "297619", "15077658", "1120452771", "111765799882", "15350524923547", "2875055248515242", "738416821509929731", "260316039943139322858", "126430202628042630866787", "84814075550928212558332858", "78847417416749666369637926851" ]
[ "nonn", "nice", "easy" ]
36
1
4
[ "A001832", "A004100", "A013922" ]
[ "M2878" ]
N. J. A. Sloane
2019-09-04T08:06:22
oeisdata/seq/A004/A004100.seq
a648e9e0cb14ad5f3249279ed07276ba