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1999-12-11 03:00:00
2026-01-19 02:46:49
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A391782
Decimal expansion of Sum_{k>=1} eta(2*k) * Lucas(2*k) / 5^k, where eta is the Dirichlet eta function.
[ "1", "0", "5", "8", "0", "6", "0", "1", "1", "8", "9", "7", "8", "4", "3", "7", "3", "1", "3", "7", "5", "2", "7", "1", "6", "0", "8", "8", "6", "2", "3", "6", "7", "4", "9", "5", "6", "1", "5", "6", "1", "2", "1", "9", "3", "...
[ "nonn", "cons", "changed" ]
8
1
3
[ "A000032", "A005248", "A350760", "A391781", "A391782" ]
null
Amiram Eldar, Dec 20 2025
2026-01-17T17:22:47
oeisdata/seq/A391/A391782.seq
f20f959f69aafe7b274f0c8b32ddd172
A391783
Decimal expansion of Sum_{k>=1} (-1)^(k+1) * log(1 + 1/k) / k.
[ "5", "5", "2", "1", "2", "8", "3", "2", "2", "0", "8", "5", "4", "9", "2", "0", "7", "6", "5", "7", "7", "0", "1", "2", "1", "4", "7", "2", "0", "0", "8", "0", "8", "7", "0", "8", "9", "4", "3", "1", "0", "8", "3", "2", "0", "...
[ "nonn", "cons", "changed" ]
8
0
1
[ "A001008", "A001620", "A002805", "A058312", "A058313", "A131688", "A391783", "A391784" ]
null
Amiram Eldar, Dec 20 2025
2026-01-17T17:22:14
oeisdata/seq/A391/A391783.seq
05c5ff90344d94d97583276674c8024b
A391784
Decimal expansion of Sum_{k>=1} log(1 + 1/(k+1)) / k.
[ "8", "6", "0", "6", "2", "0", "1", "9", "2", "8", "5", "3", "1", "3", "8", "3", "6", "4", "0", "4", "3", "4", "9", "4", "9", "2", "0", "2", "7", "4", "5", "8", "7", "8", "2", "0", "1", "3", "6", "3", "9", "4", "4", "8", "6", "...
[ "nonn", "cons" ]
8
0
1
[ "A001008", "A001620", "A002805", "A006232", "A006233", "A058312", "A058313", "A391783", "A391784" ]
null
Amiram Eldar, Dec 20 2025
2025-12-20T03:38:44
oeisdata/seq/A391/A391784.seq
196f2cdbe01c12d586678e990c6e5b38
A391785
Decimal expansion of zeta(2) * Product_{p prime} (1 - 2/p^2 + 1/p^(2/5) - 1/p^(3/2) + 1/p^4).
[ "7", "6", "3", "3", "5", "6", "4", "3", "0", "2", "1", "6", "2", "2", "9", "5", "9", "0", "0", "9", "9", "9", "4", "4", "3", "9", "1", "6", "7", "3", "2", "0", "9", "1", "0", "7", "7", "4", "2", "4", "5", "8", "3", "6", "6", "...
[ "nonn", "cons" ]
9
0
1
[ "A013661", "A391785" ]
null
Amiram Eldar, Dec 20 2025
2025-12-20T10:16:06
oeisdata/seq/A391/A391785.seq
7c216230dc7c5c67f0da91db8a4068b8
A391787
a(n) is the least n-bit number k such that k has the maximum number of distinct (nonempty) substrings in the binary representation of k.
[ "0", "2", "4", "9", "19", "35", "70", "139", "278", "558", "1070", "2140", "4253", "8503", "17006", "34007", "68014", "136028", "272060", "534204", "1068408", "2133369", "4266362", "8532669", "17065338", "34130555", "68261103", "136522206", "273044399", "546...
[ "nonn", "base" ]
30
1
2
[ "A094913", "A141297", "A391787" ]
null
Ctibor O. Zizka, Dec 20 2025
2025-12-31T09:47:14
oeisdata/seq/A391/A391787.seq
010861b6a52144046ab4fd78283967b7
A391788
Array read by antidiagonals: A(n,k) = phi(n+k) with k >= 0 and A(0,0) = 0.
[ "0", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "4", "4", "4", "4", "4", "4", "2", "2", "2", "2", "2", "2", "2", "6", "6", "6", "6", "6", "6", "6", "6", "4", "4", "4", "4", "4", "4", "4", "4", "4", "...
[ "nonn", "easy", "tabl" ]
9
0
7
[ "A000010", "A002618", "A062570", "A391788", "A391789", "A391790" ]
null
Stefano Spezia, Dec 20 2025
2025-12-24T09:55:13
oeisdata/seq/A391/A391788.seq
b67330822248b3070967c90b0f1ae981
A391789
a(n) is the determinant of the n-th order Hankel matrix M(n) whose generic element is given by M(i,j) = phi(i+j) with i,j = 0, ..., n-1 and M(0,0) = 0.
[ "1", "0", "-1", "1", "-2", "-20", "-8", "256", "5920", "24320", "-385536", "380928", "109130240", "1048645632", "-26955161600", "266634035200", "3857663459328", "28245816836096", "-284017798938624", "-3430335521030144", "-27229528475172864", "4759106956244811776", "-16349...
[ "sign" ]
14
0
5
[ "A000010", "A368025", "A391788", "A391789", "A391790" ]
null
Stefano Spezia, Dec 20 2025
2025-12-24T09:55:08
oeisdata/seq/A391/A391789.seq
564d5e139a3418b596931f5fb6fd5877
A391790
a(n) is the permanent of the n-th order Hankel matrix M(n) whose generic element is given by M(i,j) = phi(i+j) with i,j = 0, ..., n-1 and M(0,0) = 0.
[ "1", "0", "1", "7", "154", "4860", "265048", "15959744", "1702784480", "174374326912", "25548068301056", "4392451231078400", "975899333856328192", "222438109032688009216", "67405846484696921661440", "20031561030571606152773632", "7508762497888891587398205440", "32611231980227966706...
[ "nonn" ]
13
0
4
[ "A000010", "A368026", "A391788", "A391789", "A391790" ]
null
Stefano Spezia, Dec 20 2025
2025-12-24T09:55:04
oeisdata/seq/A391/A391790.seq
ba9dd3a645457ec76879284c77bbb73a
A391791
a(n)/2^(n-1) is the expected win if one of two baskets is chosen randomly and the player optimally chooses the coins with values from 1 to n (see Comments for details).
[ "1", "5", "20", "65", "190", "530", "1407", "3585", "8942", "21819", "52204", "123190", "287044", "661329", "1509949", "3420580", "7688444", "17173896", "38143782", "84262365", "185278522", "405700861" ]
[ "nonn", "hard", "more", "changed" ]
16
1
2
[ "A391537", "A391538", "A391791", "A391792" ]
null
Ruediger Jehn, Dec 20 2025
2026-01-07T16:16:55
oeisdata/seq/A391/A391791.seq
b04b5e6b8052e592d7f96969d7f029ae
A391792
a(n)/3^(n-1) is the expected win if one of three baskets is chosen randomly and the player optimally chooses the coins with values from 1 to n (see Comments for details).
[ "1", "7", "40", "192", "837", "3423", "13478", "51396", "190809", "693595", "2477822", "8740848", "30419671", "104752091", "357748926", "1211285880", "4074000387", "13615817865" ]
[ "nonn", "hard", "more", "new" ]
6
1
2
[ "A391537", "A391538", "A391791", "A391792" ]
null
Ruediger Jehn, Dec 31 2025
2026-01-07T16:17:39
oeisdata/seq/A391/A391792.seq
5d345a6207eb6cc66bb569e101d0f93c
A391793
Multiplicative sequence a(n) with a(p^e) = ((e mod 5) * ((e mod 5) - 5) + 4) / 2 for prime p and e > 0.
[ "1", "0", "0", "-1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "0", "2", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0"...
[ "sign", "easy", "mult" ]
9
1
32
null
null
Werner Schulte, Dec 20 2025
2025-12-28T20:36:24
oeisdata/seq/A391/A391793.seq
c12c919bc11c60b954e9317cc304f2cc
A391795
Largest possible index of a topological sequence of three dimensional lattice points with depth n.
[ "1", "0", "2", "5", "7", "11", "17", "23", "31", "40", "47", "56" ]
[ "nonn", "more" ]
11
0
3
[ "A000219", "A000293", "A002836", "A207542", "A387672", "A391795" ]
null
John Tyler Rascoe, Dec 20 2025
2025-12-21T10:47:14
oeisdata/seq/A391/A391795.seq
703a73f28bc9e61c27786fcd2f788686
A391796
a(n) is the least k such that the residues mod 3 of the primes prime(k), prime(k+1), ... comprise a string of n 2's followed by 1.
[ "3", "9", "15", "54", "290", "987", "4530", "21481", "58554", "60967", "136457", "136456", "673393", "1254204", "1254203", "7709873", "21357254", "21357253", "25813465", "25813464", "39500858", "39500857", "947438661", "947438660", "947438659", "5703167679", "5703...
[ "nonn", "new" ]
17
1
1
[ "A390511", "A391796", "A391807", "A392104" ]
null
Clark Kimberling, Jan 05 2026
2026-01-17T12:56:04
oeisdata/seq/A391/A391796.seq
37517551777e80340e6ba270ee05ea96
A391797
Numbers k such that prime(2*k + 2) - prime(2*k) < prime(2*k + 1) - prime(2*k - 1).
[ "6", "8", "12", "16", "20", "24", "27", "28", "31", "34", "37", "40", "44", "46", "50", "51", "54", "56", "58", "61", "64", "65", "69", "70", "71", "73", "79", "81", "84", "85", "89", "90", "95", "97", "99", "100", "103", "104", "107", "1...
[ "nonn" ]
9
1
1
[ "A000027", "A000040", "A110854", "A391797", "A391798", "A391799", "A391800" ]
null
Clark Kimberling, Dec 23 2025
2025-12-30T15:33:13
oeisdata/seq/A391/A391797.seq
4ae705d268cba42f9c98c56c66c0137d
A391798
Numbers k such that prime(2*k + 2) - prime(2*k) = prime(2*k + 1) - prime(2*k - 1).
[ "2", "3", "5", "11", "13", "14", "15", "17", "19", "21", "22", "32", "36", "39", "41", "47", "52", "53", "63", "74", "75", "76", "77", "83", "86", "88", "91", "93", "96", "106", "118", "122", "124", "125", "128", "136", "137", "143", "151",...
[ "nonn" ]
10
1
1
[ "A000027", "A000040", "A022884", "A110854", "A391797", "A391798", "A391799", "A391800" ]
null
Clark Kimberling, Dec 23 2025
2026-01-01T23:31:00
oeisdata/seq/A391/A391798.seq
84738173393ec2c159871c52063f51c5
A391799
Numbers k such that prime(2*k + 2) - prime(2*k) > prime(2*k + 1) - prime(2*k - 1).
[ "1", "4", "7", "9", "10", "18", "23", "25", "26", "29", "30", "33", "35", "38", "42", "43", "45", "48", "49", "55", "57", "59", "60", "62", "66", "67", "68", "72", "78", "80", "82", "87", "92", "94", "98", "101", "102", "105", "108", "110...
[ "nonn" ]
6
1
2
[ "A000040", "A110854", "A391797", "A391798", "A391799", "A391800" ]
null
Clark Kimberling, Dec 29 2025
2026-01-04T19:51:35
oeisdata/seq/A391/A391799.seq
c41b1453aa990ef63d9793159a9fcde0
A391800
Primes indexed by A391797.
[ "13", "19", "37", "53", "71", "89", "103", "107", "127", "139", "157", "173", "193", "199", "229", "233", "251", "263", "271", "283", "311", "313", "347", "349", "353", "367", "401", "419", "433", "439", "461", "463", "499", "509", "523", "541", ...
[ "nonn" ]
4
1
1
[ "A000027", "A391797", "A391800", "A391801", "A391802" ]
null
Clark Kimberling, Dec 30 2025
2026-01-04T22:12:00
oeisdata/seq/A391/A391800.seq
f3ec5aa2f21f1ba662b5d3c904aaf7a5
A391801
Primes indexed by A391798.
[ "3", "5", "11", "31", "41", "43", "47", "59", "67", "73", "79", "131", "151", "167", "179", "211", "239", "241", "307", "373", "379", "383", "389", "431", "443", "457", "467", "487", "503", "577", "647", "673", "683", "691", "719", "769", "773"...
[ "nonn" ]
4
1
1
[ "A000027", "A391798", "A391800", "A391801", "A391802" ]
null
Clark Kimberling, Dec 30 2025
2026-01-04T22:12:23
oeisdata/seq/A391/A391801.seq
8599160baf936dd5863bfb9fc345e213
A391802
Primes indexed by A391799.
[ "2", "7", "17", "23", "29", "61", "83", "97", "101", "109", "113", "137", "149", "163", "181", "191", "197", "223", "227", "257", "269", "277", "281", "293", "317", "331", "337", "359", "397", "409", "421", "449", "479", "491", "521", "547", "5...
[ "nonn" ]
4
1
1
[ "A000027", "A391799", "A391800", "A391801", "A391802" ]
null
Clark Kimberling, Dec 30 2025
2026-01-04T22:12:44
oeisdata/seq/A391/A391802.seq
5237ee68ae3450bff052f696d6d4c136
A391803
a(n) = floor(Sum_{k=1..n} n/prime(k)).
[ "0", "1", "3", "4", "6", "8", "9", "11", "13", "15", "17", "19", "21", "22", "24", "26", "28", "30", "32", "34", "36", "38", "40", "43", "45", "47", "49", "51", "53", "55", "57", "59", "61", "63", "66", "68", "70", "72", "74", "76", "78...
[ "nonn", "new" ]
14
1
3
[ "A000040", "A046024", "A391803" ]
null
Clark Kimberling, Dec 31 2025
2026-01-05T15:00:48
oeisdata/seq/A391/A391803.seq
73273e61164cd50c539b125b3e1ac85b
A391804
a(n) = least prime greater than prime(n)*prime(n+1).
[ "7", "17", "37", "79", "149", "223", "331", "439", "673", "907", "1151", "1523", "1777", "2027", "2503", "3137", "3607", "4091", "4759", "5189", "5779", "6563", "7393", "8641", "9803", "10427", "11027", "11677", "12323", "14369", "16649", "17957", "190...
[ "nonn", "easy", "new" ]
9
1
1
[ "A000040", "A006094", "A151800", "A391804", "A391805" ]
null
Clark Kimberling, Jan 04 2026
2026-01-09T15:24:41
oeisdata/seq/A391/A391804.seq
a1cfaa8ae0520c4bd6e197cc77df7a3f
A391805
a(n) = greatest prime less than prime(n)*prime(n+1).
[ "5", "13", "31", "73", "139", "211", "317", "433", "661", "887", "1129", "1511", "1759", "2017", "2477", "3121", "3593", "4079", "4751", "5179", "5749", "6553", "7369", "8629", "9791", "10399", "11003", "11657", "12301", "14347", "16633", "17939", "190...
[ "nonn", "easy", "new" ]
10
1
1
[ "A000040", "A006094", "A391804", "A391805" ]
null
Clark Kimberling, Jan 04 2026
2026-01-09T15:24:05
oeisdata/seq/A391/A391805.seq
98a9f8bf0a344691ad954ff8f2cf4f4a
A391806
a(n) = least k such that the sum of the first k odd primes is divisible by n.
[ "1", "2", "1", "2", "3", "16", "6", "2", "13", "20", "44", "40", "4", "6", "3", "38", "33", "42", "25", "60", "60", "44", "24", "40", "7", "4", "100", "6", "89", "60", "13", "38", "44", "40", "60", "42", "27", "60", "5", "186", "157", ...
[ "nonn", "new" ]
11
1
2
[ "A053050", "A065091", "A071148", "A391806" ]
null
Clark Kimberling, Jan 05 2026
2026-01-17T16:13:48
oeisdata/seq/A391/A391806.seq
693b07b8bd726f0b7e20c4364c1ed2d1
A391807
a(n) is the least k such that the residues mod 3 of the primes prime(k), prime(k+1),... include a string of n 1's followed by 2.
[ "4", "11", "36", "273", "272", "271", "2209", "11199", "13718", "13717", "34369", "172147", "172146", "3094796", "3094795", "4308948", "12762142", "23902561", "72084958", "72084957", "72084956", "1052779162", "1052779161", "1857276774", "1857276773", "19398320447", ...
[ "nonn", "new" ]
20
1
1
[ "A039701", "A390511", "A391796", "A391807" ]
null
Clark Kimberling, Jan 05 2026
2026-01-18T23:45:46
oeisdata/seq/A391/A391807.seq
164d5388c37579117bfcf38039cf79dc
A391808
Number of topological sequences of three dimensional lattice points with depth n and the largest possible index.
[ "1", "0", "2", "1", "3", "9", "3", "10", "5", "1", "3", "9" ]
[ "nonn", "more" ]
7
0
3
[ "A000219", "A000293", "A002836", "A207542", "A387672", "A391808" ]
null
John Tyler Rascoe, Dec 20 2025
2025-12-28T19:53:03
oeisdata/seq/A391/A391808.seq
ff32c092b8938a69be9b961b307f4ab5
A391809
A Beatty sequence: floor(n*x) for n >= 1 where x = Sum_{n>=0} 1/2^floor(n*x).
[ "1", "3", "5", "6", "8", "10", "11", "13", "15", "16", "18", "20", "21", "23", "25", "26", "28", "30", "31", "33", "35", "36", "38", "40", "41", "43", "45", "46", "48", "50", "51", "53", "55", "57", "58", "60", "62", "63", "65", "67", "...
[ "nonn", "new" ]
22
1
2
[ "A329987", "A391809", "A391815" ]
null
Paul D. Hanna, Dec 31 2025
2026-01-05T09:59:56
oeisdata/seq/A391/A391809.seq
3fe2fac88a7598456e05100d466a5715
A391810
Irregular triangle, read by rows, where row n lists the coefficients of nonpositive powers of x in the doubly infinite series Sum_{k=-oo..oo} x^k * (1 - x^k)^(n+k) for n >= 1.
[ "-1", "1", "-1", "1", "-1", "1", "-1", "2", "-1", "-1", "1", "-2", "4", "-2", "-1", "1", "-3", "7", "-6", "2", "1", "0", "-2", "1", "-1", "1", "-4", "11", "-13", "6", "3", "0", "-6", "3", "-1", "1", "-5", "16", "-24", "16", "1", "2", ...
[ "sign", "tabf" ]
37
1
8
[ "A391810", "A391811" ]
null
Paul D. Hanna, Dec 21 2025
2025-12-28T09:57:11
oeisdata/seq/A391/A391810.seq
6b311d18bccda053e77a05184d7a77cb
A391811
a(n) equals half the sum of the squares of the terms in row n of irregular triangle A391810.
[ "1", "1", "4", "13", "53", "199", "674", "2313", "8731", "34453", "135151", "516056", "1929917", "7191767", "27150041", "104424657", "407094655", "1594363303", "6233521880", "24277356505", "94261319494", "365585759896", "1419238266986", "5523689999096", "2157387579183...
[ "nonn" ]
11
1
3
[ "A391810", "A391811" ]
null
Paul D. Hanna, Dec 21 2025
2025-12-28T09:56:55
oeisdata/seq/A391/A391811.seq
6209417e701a8e64eb2006720b195646
A391812
Decimal expansion of the constant x where each term in the simple continued fraction of x equals 2 minus the respective bit in the binary expansion of x, with an initial term of '1'.
[ "1", "3", "8", "6", "7", "5", "0", "5", "0", "6", "8", "3", "7", "5", "1", "7", "5", "6", "7", "9", "9", "4", "1", "6", "8", "2", "5", "7", "8", "0", "4", "5", "2", "2", "3", "3", "2", "4", "5", "1", "4", "0", "1", "5", "9", "...
[ "nonn", "cons" ]
13
1
2
[ "A391812", "A391813", "A391814" ]
null
Paul D. Hanna, Dec 30 2025
2025-12-30T11:19:38
oeisdata/seq/A391/A391812.seq
9368d19127278dd8eca9d788283ed056
A391813
Continued fraction of the constant x where a(n) = 2 - A391814(n+1) for n >= 0, and A391814 is the binary expansion of x starting with A391814(1) = 1.
[ "1", "2", "1", "1", "2", "2", "2", "1", "1", "2", "2", "2", "2", "2", "2", "1", "2", "2", "2", "2", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "2", "1", "2", "2", "1", "2", "1", "2", "2", "2", "2", "2", "1", "...
[ "nonn", "cofr", "new" ]
17
0
2
[ "A391812", "A391813", "A391814", "A391873" ]
null
Paul D. Hanna, Dec 30 2025
2026-01-05T10:02:22
oeisdata/seq/A391/A391813.seq
0025bba2765117d1ff48e5f4deed3a03
A391814
Binary expansion of the constant x where a(n) = 2 - A391813(n-1) for n >= 1, and A391813 is the continued fraction of x starting with A391813(0) = 1.
[ "1", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "...
[ "nonn", "base", "new" ]
15
1
null
[ "A391812", "A391813", "A391814", "A391872" ]
null
Paul D. Hanna, Dec 30 2025
2026-01-05T10:00:00
oeisdata/seq/A391/A391814.seq
f27c511264aff1510686661c35fd0364
A391815
Decimal expansion of the constant x that satisfies x = Sum_{n>=0} 1/2^floor(n*x).
[ "1", "6", "7", "7", "4", "1", "9", "3", "5", "4", "8", "3", "8", "7", "0", "9", "6", "7", "0", "2", "5", "6", "6", "2", "5", "6", "4", "7", "5", "7", "9", "6", "3", "3", "6", "3", "2", "6", "2", "7", "9", "7", "0", "6", "4", "...
[ "nonn", "cons", "new" ]
28
1
2
[ "A119809", "A119812", "A329986", "A391809", "A391815" ]
null
Paul D. Hanna, Dec 30 2025
2026-01-05T10:00:04
oeisdata/seq/A391/A391815.seq
e77419cadd91029c0c533c27d6a7956f
A391817
Number of topological sequences of three dimensional lattice points with index n and depth n - 2.
[ "1", "9", "25", "61", "125", "252", "472", "872", "1548" ]
[ "nonn", "more" ]
5
5
2
[ "A000219", "A000293", "A002836", "A207542", "A387672", "A391817" ]
null
John Tyler Rascoe, Dec 20 2025
2025-12-28T19:53:20
oeisdata/seq/A391/A391817.seq
1848c70192b5bbcf47c5a9709ede924a
A391818
Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from upper left corner to lower right corner, and no 1 having more than two 1's adjacent.
[ "1", "1", "1", "1", "3", "1", "1", "5", "5", "1", "1", "8", "17", "8", "1", "1", "13", "39", "39", "13", "1", "1", "20", "83", "132", "83", "20", "1", "1", "32", "175", "389", "389", "175", "32", "1", "1", "52", "375", "1095", "1561", ...
[ "nonn", "tabl" ]
11
1
5
[ "A000012", "A163684", "A163685", "A163686", "A163687", "A163688", "A163689", "A163690", "A163691", "A163692", "A163693", "A359573", "A391818", "A391819", "A391820", "A391822" ]
null
Andrew Howroyd, Dec 20 2025
2025-12-21T17:31:24
oeisdata/seq/A391/A391818.seq
623890a6959a6ac8c14e99a21da6781e
A391819
Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, all corners 1, and no 1 having more than two 1's adjacent.
[ "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "2", "5", "2", "1", "1", "4", "9", "9", "4", "1", "1", "6", "17", "13", "17", "6", "1", "1", "10", "39", "29", "29", "39", "10", "1", "1", "16", "95", "87", "73", "87", "95", ...
[ "nonn", "tabl" ]
9
1
8
[ "A000012", "A163732", "A163733", "A163734", "A163735", "A163736", "A163737", "A163738", "A163739", "A163740", "A163741", "A389687", "A391818", "A391819", "A391820", "A391822" ]
null
Andrew Howroyd, Dec 21 2025
2025-12-21T17:31:20
oeisdata/seq/A391/A391819.seq
d4f0c533decac8f98424af775ed160f8
A391820
Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected and no 1 having more than two 1's adjacent.
[ "1", "3", "3", "6", "13", "6", "10", "33", "33", "10", "15", "69", "108", "69", "15", "21", "131", "291", "291", "131", "21", "28", "235", "710", "1044", "710", "235", "28", "36", "407", "1635", "3408", "3408", "1635", "407", "36", "45", "689...
[ "nonn", "tabl" ]
6
1
2
[ "A360196", "A360199", "A391820", "A391821", "A391822" ]
null
Andrew Howroyd, Dec 21 2025
2025-12-21T17:31:16
oeisdata/seq/A391/A391820.seq
0e437fa6905896741bd5eadf1db8d014
A391821
Number of n X n binary arrays with all 1's connected and no 1 having more than two 1's adjacent.
[ "1", "13", "108", "1044", "15118", "338008", "11612695", "631125163", "56172850171", "8350747478181", "2075606259753276", "854387913414906842", "578644663866606223343", "646305755254714977651975", "1200822615271663184220885305" ]
[ "nonn" ]
5
1
2
[ "A059525", "A297664", "A360200", "A391820", "A391821" ]
null
Andrew Howroyd, Dec 21 2025
2025-12-21T20:02:14
oeisdata/seq/A391/A391821.seq
2f844029d3627924f7381b2cb49ed263
A391822
Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from top row to bottom row, and no 1 having more than two 1's adjacent.
[ "1", "3", "1", "6", "7", "1", "10", "21", "10", "1", "15", "49", "48", "16", "1", "21", "101", "163", "108", "26", "1", "28", "193", "463", "531", "236", "42", "1", "36", "351", "1186", "2119", "1611", "506", "68", "1", "45", "617", "2854",...
[ "nonn", "tabl" ]
5
1
2
[ "A000012", "A000217", "A163713", "A163714", "A163715", "A163716", "A163717", "A163718", "A163719", "A163720", "A163721", "A163722", "A163723", "A163724", "A163725", "A163726", "A163727", "A163728", "A163729", "A163730", "A163731", "A359574", "A391818", "A391819", "A39...
null
Andrew Howroyd, Dec 21 2025
2025-12-21T20:02:01
oeisdata/seq/A391/A391822.seq
11312609e55c603906b86cc32ff76671
A391823
Array read by antidiagonals: T(m,n) is the number of m X n binary arrays with all 1's connected, a path of 1's from top row to lower right corner, and no 1 having more than two 1's adjacent.
[ "1", "2", "1", "3", "5", "1", "4", "11", "7", "1", "5", "21", "28", "11", "1", "6", "38", "80", "63", "18", "1", "7", "66", "200", "259", "138", "29", "1", "8", "112", "469", "896", "775", "298", "47", "1", "9", "187", "1064", "2821", "...
[ "nonn", "tabl" ]
6
1
2
[ "A000012", "A000027", "A163694", "A163695", "A163696", "A163697", "A163698", "A163699", "A163700", "A163701", "A163702", "A163703", "A163704", "A163705", "A163706", "A163707", "A163708", "A163709", "A163710", "A163711", "A163712", "A391489", "A391818", "A391819", "A39...
null
Andrew Howroyd, Dec 22 2025
2025-12-22T22:07:05
oeisdata/seq/A391/A391823.seq
e76f50c150ffb1d66c514b147c39f309
A391824
Array read by antidiagonals: T(m,n) is the number of partitions of the vertices of the grid graph P_m X P_n into dominating sets.
[ "1", "2", "2", "2", "4", "2", "3", "13", "13", "3", "4", "35", "66", "35", "4", "6", "113", "397", "397", "113", "6", "9", "368", "2436", "4563", "2436", "368", "9", "14", "1182", "14785", "52595", "52595", "14785", "1182", "14", "22", "3838"...
[ "nonn", "tabl", "new" ]
9
1
2
[ "A001611", "A180771", "A207868", "A218354", "A230819", "A391824", "A391825", "A391826", "A391827" ]
null
Andrew Howroyd, Jan 10 2026
2026-01-10T20:11:58
oeisdata/seq/A391/A391824.seq
b310b4407aad8b76e24f8407613afe27
A391825
Number of partitions of the vertices of the n X n grid graph into dominating sets.
[ "1", "4", "66", "4563", "1168506", "1075501316", "3576191040553", "42884077247092791" ]
[ "nonn", "more", "new" ]
4
1
2
[ "A391824", "A391825" ]
null
Andrew Howroyd, Jan 10 2026
2026-01-10T20:11:46
oeisdata/seq/A391/A391825.seq
da26e5c9be57d81e57ee4b9fb00069ec
A391826
Number of partitions of the vertices of the n-ladder graph into dominating sets.
[ "2", "4", "13", "35", "113", "368", "1182", "3838", "12463", "40429", "131269", "426262", "1384198", "4495620", "14602111", "47431703", "154081177", "500554852", "1626190314", "5283311170", "17165381859", "55771348385", "181208069377", "588777467930", "1913070123762",...
[ "nonn", "new" ]
5
1
1
[ "A180762", "A230813", "A391824", "A391826", "A391827" ]
null
Andrew Howroyd, Jan 10 2026
2026-01-10T20:11:37
oeisdata/seq/A391/A391826.seq
ebd2812777d3ad7acf4c78d59005c813
A391827
Number of partitions of the vertices of the n X 3 grid graph into dominating sets.
[ "2", "13", "66", "397", "2436", "14785", "90660", "553739", "3388938", "20741171", "126964984", "777465223", "4761197556", "29162734671", "178641529684", "1094401625403", "6705058123466", "41082146261365", "251723814381242", "1542452107793101", "9451751484893444", "57919325...
[ "nonn", "new" ]
10
1
1
[ "A180763", "A230814", "A391824", "A391826", "A391827" ]
null
Andrew Howroyd, Jan 10 2026
2026-01-10T20:11:26
oeisdata/seq/A391/A391827.seq
63442230bd5d8c9ffbce1a66c6cace79
A391828
Numbers k such that the map k -> k' reaches a nonzero cycle, where k' is the arithmetic derivative.
[ "4", "27", "3125", "823543", "1647082", "2238771", "3358143", "3793738", "4425686", "4452758", "5682974", "6716282", "7251855", "8322027", "12974315", "14415850", "16650815", "18968665", "20182246", "21005098", "22838035", "24924635", "25650001", "25901246", "29126923...
[ "nonn", "new" ]
26
1
1
[ "A003415", "A051674", "A099309", "A348329", "A391828" ]
null
Michael Adams, Dec 20 2025
2026-01-07T15:29:53
oeisdata/seq/A391/A391828.seq
0c4ffc68da369dae3e13401015fcc377
A391829
a(n) = (1/4) * Sum_{k=0..n} (k+2) * binomial(2*k+2,2*n-2*k+1).
[ "1", "3", "9", "30", "91", "271", "801", "2330", "6710", "19172", "54386", "153362", "430257", "1201685", "3343079", "9268130", "25614741", "70595817", "194078465", "532337092", "1457119612", "3980884648", "10856936212", "29562266740", "80375490401", "218228740855",...
[ "nonn" ]
17
0
2
[ "A381421", "A391829", "A391832", "A391835" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T07:30:02
oeisdata/seq/A391/A391829.seq
7c416f80bd8a101526341b668e098e88
A391830
a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * binomial(2*k+2,2*n-4*k+1).
[ "1", "0", "3", "3", "6", "20", "16", "70", "85", "190", "399", "565", "1429", "2114", "4425", "8145", "13877", "28508", "47243", "92523", "165512", "297396", "562390", "982140", "1843714", "3292870", "5975118", "10938740", "19496065", "35751958", "63998039...
[ "nonn" ]
17
0
3
[ "A391830", "A391833", "A391836" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T06:26:37
oeisdata/seq/A391/A391830.seq
e4b3a5e3eb61c9ec2a947eb0fff2987f
A391831
a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * binomial(2*n-4*k+2,2*k+1).
[ "1", "3", "6", "13", "35", "91", "214", "491", "1151", "2711", "6290", "14427", "33010", "75444", "171786", "389500", "880533", "1986357", "4471290", "10042661", "22511404", "50374282", "112545858", "251073154", "559324988", "1244426930", "2765391188", "61384448...
[ "nonn" ]
17
0
2
[ "A391831", "A391834", "A391837" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T06:26:41
oeisdata/seq/A391/A391831.seq
5b7fea828df900e0bafe3531bea746d6
A391832
a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^k * binomial(2*k+2,2*n-2*k+1).
[ "1", "6", "30", "160", "824", "4112", "20240", "98432", "473648", "2260000", "10707872", "50428928", "236267264", "1101967872", "5119345152", "23699419136", "109371557120", "503331831296", "2310505584128", "10581929451520", "48363392444416", "220617599430656", "1004622677...
[ "nonn" ]
17
0
2
[ "A391829", "A391832", "A391835" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T07:30:05
oeisdata/seq/A391/A391832.seq
e21cec260922a65a000edc2d969fa21d
A391833
a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * 2^k * binomial(2*k+2,2*n-4*k+1).
[ "1", "0", "6", "6", "24", "80", "104", "560", "800", "2960", "6720", "15200", "46384", "90944", "273184", "601248", "1525760", "3863552", "8808192", "23230464", "53175296", "134251008", "323028992", "774392832", "1920513280", "4529858560", "11176308224", "266691...
[ "nonn" ]
17
0
3
[ "A391830", "A391833", "A391836" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T06:26:49
oeisdata/seq/A391/A391833.seq
19a9794f84b4d8fb33effd6b56f9520d
A391834
a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * 2^(n-2*k) * binomial(2*n-4*k+2,2*k+1).
[ "1", "6", "24", "86", "320", "1232", "4696", "17488", "64160", "233872", "848960", "3067200", "11026672", "39468576", "140761344", "500445344", "1774199808", "6273738240", "22132498176", "77912939008", "273744796672", "960083626496", "3361707657216", "11753105758208", ...
[ "nonn", "easy" ]
20
0
2
[ "A391831", "A391834", "A391837" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-02T15:47:23
oeisdata/seq/A391/A391834.seq
b3f0935f0e317add651fe4ddaa5bee3d
A391835
a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^(n-k) * binomial(2*k+2,2*n-2*k+1).
[ "1", "3", "12", "50", "179", "661", "2390", "8476", "29909", "104519", "362672", "1251478", "4295783", "14680713", "49976442", "169541536", "573390953", "1933856347", "6505983668", "21838288442", "73152323803", "244578237373", "816308965214", "2720178349156", "9051042...
[ "nonn" ]
17
0
2
[ "A391829", "A391832", "A391835" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T07:30:09
oeisdata/seq/A391/A391835.seq
fe8475352f5489995fb0be4270e291fa
A391836
a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * 2^(n-2*k) * binomial(2*k+2,2*n-4*k+1).
[ "1", "0", "3", "6", "6", "40", "34", "140", "295", "440", "1533", "2210", "5812", "12544", "22212", "58104", "103421", "233296", "499367", "957246", "2196050", "4265208", "9077206", "19147812", "38083843", "82195784", "165218433", "343559002", "715871584", "...
[ "nonn", "easy" ]
21
0
3
[ "A391830", "A391833", "A391836" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-02T15:47:18
oeisdata/seq/A391/A391836.seq
33c9d140d6cbe0cb42983155f62696f6
A391837
a(n) = (1/4) * Sum_{k=0..floor(n/3)} (n-2*k+2) * 2^k * binomial(2*n-4*k+2,2*k+1).
[ "1", "3", "6", "16", "55", "161", "412", "1086", "3013", "8199", "21602", "56748", "150163", "395885", "1034872", "2695210", "7014705", "18219971", "47176414", "121863960", "314305951", "809367049", "2080584852", "5340057974", "13687727069", "35041285439", "895992...
[ "nonn" ]
17
0
2
[ "A391831", "A391834", "A391837" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-03T07:29:59
oeisdata/seq/A391/A391837.seq
b9a5dd8e8c3bc82e9f6eaa2b4ad28f8a
A391839
a(n) is the least prime that can be written as (product + sum) of n distinct composite numbers.
[ "79", "383", "3491", "17317", "207409", "4976711", "46448719", "1088640103", "25082265727", "338610585739", "6270566400157", "147483721728181", "2781121609728199", "78219045273600227", "2294425328025600257", "70501432806604800289", "1803968969906847744313", "61225613524111196160347...
[ "nonn" ]
7
2
1
[ "A391772", "A391839" ]
null
Robert Israel, Dec 21 2025
2025-12-23T09:41:17
oeisdata/seq/A391/A391839.seq
fd57a9ab9a006387df77856aefb29928
A391840
Base 16 sum of digits of prime(n).
[ "2", "3", "5", "7", "11", "13", "2", "4", "8", "14", "16", "7", "11", "13", "17", "8", "14", "16", "7", "11", "13", "19", "8", "14", "7", "11", "13", "17", "19", "8", "22", "11", "17", "19", "14", "16", "22", "13", "17", "23", "14", "...
[ "nonn", "base" ]
21
1
1
[ "A007605", "A014499", "A053836", "A239690", "A239694", "A391840" ]
null
Kaloian Ivanov, Dec 21 2025
2025-12-30T13:31:44
oeisdata/seq/A391/A391840.seq
cd29de062451e0af1c6f5369712d8371
A391841
Positive integers k with exactly sqrt(tau(k)) square divisors.
[ "1", "8", "27", "125", "216", "343", "384", "640", "896", "1000", "1331", "1408", "1440", "1664", "2016", "2176", "2197", "2400", "2432", "2744", "2944", "3168", "3375", "3712", "3744", "3968", "4374", "4704", "4736", "4860", "4896", "4913", "5248", ...
[ "nonn" ]
7
1
2
[ "A000005", "A036436", "A046951", "A391841" ]
null
Felix Huber, Dec 30 2025
2026-01-04T20:49:38
oeisdata/seq/A391/A391841.seq
f99a963bec42615feee523293acdf6a9
A391842
Integers k such that d(k)*d(k+1) is a divisor of k*(k+1) where d(k) = A000005(k) is the number of divisors of k.
[ "1", "3", "7", "8", "11", "12", "15", "24", "32", "35", "36", "44", "63", "71", "72", "79", "95", "96", "116", "127", "128", "144", "159", "171", "179", "180", "239", "240", "243", "251", "287", "304", "324", "332", "335", "351", "360", "383"...
[ "nonn" ]
30
1
2
[ "A000005", "A002378", "A033950", "A092517", "A114617", "A391842" ]
null
Hoàn Toán, Dec 21 2025
2025-12-29T19:28:40
oeisdata/seq/A391/A391842.seq
d2d64316c67fd45bd931f4f930f05a7a
A391844
a(n) = 1 if the least prime not dividing the arithmetic derivative of n is equal to the least prime dividing n, otherwise 0. a(1) = 1 by convention.
[ "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "...
[ "nonn", "new" ]
7
1
null
[ "A003415", "A020639", "A053669", "A370124", "A391844", "A391845" ]
null
Antti Karttunen, Jan 16 2026
2026-01-16T13:17:12
oeisdata/seq/A391/A391844.seq
c259b0bdbd98ad8b8337e4f6aecb01c6
A391845
Numbers k such that the least prime not dividing the arithmetic derivative of k is equal to the least prime dividing k.
[ "1", "2", "6", "10", "14", "15", "18", "21", "22", "26", "30", "33", "34", "35", "38", "39", "42", "46", "50", "51", "54", "57", "58", "62", "65", "66", "69", "70", "74", "78", "82", "86", "87", "90", "93", "94", "95", "98", "102", "106",...
[ "nonn", "new" ]
14
1
2
[ "A003415", "A020639", "A048103", "A053669", "A080364", "A369650", "A370125", "A391844", "A391845", "A392592" ]
null
Antti Karttunen, Jan 16 2026
2026-01-17T16:41:03
oeisdata/seq/A391/A391845.seq
38f0d34f3b9ce8e01fa682c9810b2143
A391846
Numbers k such that 11*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "6", "8", "12", "15", "16", "17", "24", "27", "30", "31", "32", "33", "34", "48", "51", "54", "60", "62", "63", "64", "65", "66", "68", "96", "102", "108", "120", "124", "126", "127", "128", "129", "130", "132", "...
[ "nonn", "base" ]
13
1
3
[ "A048718", "A048720", "A115803", "A280500", "A391585", "A391740", "A391742", "A391744", "A391846", "A391847", "A391848", "A391850", "A391852", "A391854", "A391856", "A391858", "A391860", "A391925" ]
null
Antti Karttunen, Dec 21 2025
2025-12-29T07:32:42
oeisdata/seq/A391/A391846.seq
c55f7996164cd934363df181f274f7fb
A391847
Odd numbers k such that 11*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "15", "17", "27", "31", "33", "51", "63", "65", "127", "129", "195", "207", "219", "243", "255", "257", "273", "387", "403", "411", "415", "435", "499", "511", "513", "529", "545", "771", "783", "819", "831", "963", "975", "1011", "10...
[ "nonn", "base" ]
8
1
2
[ "A048720", "A280500", "A391584", "A391725", "A391741", "A391743", "A391745", "A391846", "A391847", "A391849", "A391851" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T14:41:40
oeisdata/seq/A391/A391847.seq
5fdfe82fffe86b9ccc2265d95d040ac7
A391848
Numbers k such that 13*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "8", "10", "12", "15", "16", "17", "20", "21", "24", "30", "31", "32", "33", "34", "40", "42", "45", "47", "48", "60", "61", "62", "63", "64", "65", "66", "68", "80", "84", "85", "90", "94", "95", "96"...
[ "nonn", "base" ]
12
1
3
[ "A048718", "A048720", "A115772", "A115805", "A280500", "A391585", "A391740", "A391742", "A391744", "A391846", "A391848", "A391849", "A391850", "A391925" ]
null
Antti Karttunen, Dec 21 2025
2025-12-29T07:32:45
oeisdata/seq/A391/A391848.seq
c18946ca0f316834d7598deecc9e1988
A391849
Odd numbers k such that 13*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "15", "17", "21", "31", "33", "45", "47", "61", "63", "65", "85", "95", "125", "127", "129", "165", "173", "175", "181", "189", "191", "195", "245", "253", "255", "257", "273", "341", "351", "381", "383", "387", "501", "509", "...
[ "nonn", "base" ]
6
1
2
[ "A048720", "A280500", "A391584", "A391725", "A391741", "A391743", "A391745", "A391847", "A391848", "A391849", "A391851" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T14:42:48
oeisdata/seq/A391/A391849.seq
450fec726bac4ddec69da9641437ae18
A391850
Numbers k such that 15*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "8", "10", "12", "15", "16", "17", "20", "21", "24", "30", "31", "32", "33", "34", "40", "42", "48", "51", "60", "62", "63", "64", "65", "66", "68", "80", "84", "85", "96", "102", "120", "124", "126", ...
[ "nonn", "base" ]
11
1
3
[ "A048718", "A048720", "A115774", "A115801", "A115807", "A280500", "A391585", "A391740", "A391742", "A391744", "A391846", "A391850", "A391851", "A391852", "A391854", "A391856", "A391858", "A391860", "A391925" ]
null
Antti Karttunen, Dec 21 2025
2025-12-29T07:32:53
oeisdata/seq/A391/A391850.seq
b760b8a64eb533ee8504d7272b7ab180
A391851
Odd numbers k such that 15*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "15", "17", "21", "31", "33", "51", "63", "65", "85", "127", "129", "195", "255", "257", "273", "341", "387", "511", "513", "529", "545", "645", "771", "819", "1023", "1025", "1041", "1057", "1089", "1285", "1365", "1539", "2047", ...
[ "nonn", "base" ]
6
1
2
[ "A048720", "A280500", "A391584", "A391725", "A391741", "A391743", "A391745", "A391847", "A391849", "A391850", "A391851" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T17:04:06
oeisdata/seq/A391/A391851.seq
268c8961c58ccb6ffcc88186a4161d04
A391852
Numbers k such that 17*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "18", "20", "22", "24", "26", "28", "30", "31", "32", "33", "36", "37", "40", "41", "44", "45", "48", "52", "56", "60", "62", "63", "64", "65", ...
[ "nonn", "base" ]
7
1
3
[ "A048720", "A115809", "A115847", "A280500", "A391852", "A391853" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T20:02:06
oeisdata/seq/A391/A391852.seq
920f2db2f2b2034ab37f748d605ec4ee
A391853
Odd numbers k such that 17*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "7", "9", "11", "13", "15", "31", "33", "37", "41", "45", "63", "65", "67", "73", "75", "97", "105", "127", "129", "131", "133", "135", "161", "165", "193", "195", "225", "255", "257", "259", "261", "263", "265", "267", "269", ...
[ "nonn", "base" ]
7
1
2
[ "A048720", "A280500", "A391725", "A391852", "A391853" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T20:02:10
oeisdata/seq/A391/A391853.seq
ddce0cc169aa87f1eee94db91c27ddc1
A391854
Numbers k such that 19*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "12", "14", "16", "20", "24", "28", "31", "32", "33", "40", "48", "56", "62", "63", "64", "65", "66", "80", "96", "112", "119", "124", "126", "127", "128", "129", "130", "132", "133", "16...
[ "nonn", "base" ]
9
1
3
[ "A048720", "A115805", "A115874", "A280500", "A391854", "A391855" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T20:02:17
oeisdata/seq/A391/A391854.seq
e5545e3ecb4d3c89e6c913ddbf9a8d92
A391855
Odd numbers k such that 19*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "7", "31", "33", "63", "65", "119", "127", "129", "133", "161", "195", "255", "257", "261", "321", "387", "455", "511", "513", "517", "641", "645", "771", "1023", "1025", "1029", "1057", "1281", "1285", "1539", "1799", "1823", "191...
[ "nonn", "base" ]
7
1
2
[ "A048720", "A280500", "A391725", "A391854", "A391855" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T20:01:57
oeisdata/seq/A391/A391855.seq
47c5905ee49d4aacaa533495a1b35ca3
A391856
Numbers k such that 21*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "8", "9", "10", "12", "16", "18", "20", "21", "24", "31", "32", "33", "36", "40", "42", "48", "62", "63", "64", "65", "66", "67", "72", "73", "80", "84", "85", "96", "97", "124", "126", "127", "128", "...
[ "nonn", "base" ]
13
1
3
[ "A048720", "A115422", "A115774", "A115809", "A280500", "A391856", "A391857", "A391925" ]
null
Antti Karttunen, Dec 21 2025
2025-12-26T16:03:01
oeisdata/seq/A391/A391856.seq
0b094267d471ee20c287a5e06d64112a
A391857
Odd numbers k such that 21*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "9", "21", "31", "33", "63", "65", "67", "73", "85", "97", "127", "129", "131", "193", "195", "255", "257", "259", "265", "289", "341", "385", "387", "511", "513", "515", "521", "577", "579", "585", "645", "769", "771", "777", ...
[ "nonn", "base" ]
8
1
2
[ "A048720", "A280500", "A391725", "A391856", "A391857" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T22:32:28
oeisdata/seq/A391/A391857.seq
11d3287558324923fabc47c1a6c92614
A391858
Numbers k such that 25*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "10", "12", "14", "16", "20", "24", "28", "31", "32", "33", "40", "48", "51", "56", "62", "63", "64", "65", "66", "80", "93", "95", "96", "102", "112", "124", "125", "126", "127", "128", "129",...
[ "nonn", "base" ]
17
1
3
[ "A048720", "A280500", "A391737", "A391738", "A391739", "A391744", "A391858", "A391859", "A391860", "A391925" ]
null
Antti Karttunen, Dec 21 2025
2025-12-23T15:04:18
oeisdata/seq/A391/A391858.seq
84eb8b25747e7d2158f1ee82cb4eaff9
A391859
Odd numbers k such that 25*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "7", "31", "33", "51", "63", "65", "93", "95", "125", "127", "129", "133", "161", "191", "253", "255", "257", "261", "321", "381", "383", "387", "509", "511", "513", "517", "641", "645", "765", "767", "771", "775", "819", "899", ...
[ "nonn", "base" ]
6
1
2
[ "A048720", "A280500", "A391725", "A391745", "A391858", "A391859", "A391861" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T22:31:55
oeisdata/seq/A391/A391859.seq
3aad8765619b9a5e77a2a5fb393a9f42
A391860
Numbers k such that 49*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "15", "16", "18", "20", "21", "24", "28", "30", "32", "36", "40", "42", "48", "56", "60", "63", "64", "65", "72", "73", "80", "84", "85", "96", "99", "112", "120", "126...
[ "nonn", "base" ]
7
1
3
[ "A048720", "A114384", "A280500", "A391744", "A391858", "A391860", "A391861" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T22:32:24
oeisdata/seq/A391/A391860.seq
c8bea68652de21c582a06a229ef9a165
A391861
Odd numbers k such that 49*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.
[ "1", "3", "5", "7", "9", "15", "21", "63", "65", "73", "85", "99", "127", "129", "189", "191", "253", "255", "257", "261", "321", "341", "383", "509", "511", "513", "517", "521", "577", "585", "641", "693", "701", "703", "757", "765", "767", ...
[ "nonn", "base" ]
7
1
2
[ "A048720", "A280500", "A391725", "A391745", "A391859", "A391860", "A391861" ]
null
Antti Karttunen, Dec 21 2025
2025-12-21T22:32:20
oeisdata/seq/A391/A391861.seq
174af854b368561565713d76b20631eb
A391862
Numbers k that are coprime to A276085(k), where A276085 is the primorial base log-function.
[ "1", "2", "3", "5", "7", "8", "9", "10", "11", "13", "14", "15", "17", "18", "19", "21", "22", "23", "24", "25", "26", "29", "31", "32", "33", "34", "35", "37", "39", "40", "41", "43", "46", "47", "49", "50", "51", "53", "54", "55", "56...
[ "nonn", "new" ]
8
1
2
[ "A276085", "A359794", "A369650", "A373361", "A391862", "A391863" ]
null
Antti Karttunen, Jan 16 2026
2026-01-16T19:12:40
oeisdata/seq/A391/A391862.seq
d2727537508e85fab20e4a12a877c7fc
A391863
Numbers k that are coprime to A276085(k) and that are not divisible by p^p for any prime p, where A276085 is the primorial base log-function.
[ "1", "2", "3", "5", "7", "9", "10", "11", "13", "14", "15", "17", "18", "19", "21", "22", "23", "25", "26", "29", "31", "33", "34", "35", "37", "39", "41", "43", "46", "47", "49", "50", "51", "53", "55", "57", "58", "59", "61", "62", "6...
[ "nonn", "new" ]
9
1
2
[ "A048103", "A276085", "A276086", "A324583", "A359550", "A373361", "A391862", "A391863", "A391866" ]
null
Antti Karttunen, Jan 16 2026
2026-01-16T19:12:17
oeisdata/seq/A391/A391863.seq
81d7295ce6a480f07dc543bf46d00398
A391864
Numbers k such that A003415(k) == A276085(k) (mod 2310), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.
[ "1", "2", "10", "15", "28", "161", "2189", "2308", "4618", "5005", "6924", "6927", "7917", "9684", "11024", "11540", "11548", "11555", "16331", "18478", "20772", "20788", "21147", "23098", "23105", "24660", "27717", "27718", "29861", "30028", "31065", "3...
[ "nonn", "new" ]
24
1
2
[ "A003415", "A276085", "A369650", "A391864", "A391865", "A391946", "A391947", "A392593", "A392598" ]
null
Antti Karttunen, Jan 16 2026
2026-01-18T15:40:34
oeisdata/seq/A391/A391864.seq
b30e612aee0a579a84cefb12be5ce5bf
A391865
Numbers k such that A003415(k) == A276085(k) (mod 5^5), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.
[ "1", "2", "10", "15", "28", "2681", "3828", "5005", "5239", "10906", "12768", "13656", "13761", "16119", "16591", "22616", "26318", "26831", "33881", "37105", "39477", "40806", "42638", "54940", "55228", "62883", "63957", "64331", "70119", "76882", "79199"...
[ "nonn", "new" ]
9
1
2
[ "A003415", "A276085", "A369650", "A377878", "A391864", "A391865" ]
null
Antti Karttunen, Jan 16 2026
2026-01-16T19:13:01
oeisdata/seq/A391/A391865.seq
8a893193239e91f655966459d12e03c4
A391866
Nonsquarefree numbers k that are not divisible by p^p for any prime p, and for which A276085(k) is a multiple of A003557(k), where A276085 is the primorial base log-function.
[ "150", "294", "578", "1050", "1083", "1650", "1694", "1950", "2535", "2550", "2625", "2850", "3234", "3450", "3630", "3822", "4350", "4650", "4998", "5145", "5550", "5586", "6150", "6375", "6450", "6762", "7050", "7942", "7950", "8526", "8850", "8918", ...
[ "nonn", "new" ]
10
1
1
[ "A003557", "A008966", "A276085", "A359550", "A371083", "A371086", "A391866", "A392592" ]
null
Antti Karttunen, Jan 16 2026
2026-01-17T16:41:07
oeisdata/seq/A391/A391866.seq
32b7d84e0f43f09d7152cbdc6b61e041
A391870
Records in A210693.
[ "4", "11", "18", "23", "48", "221", "2003", "2927", "4256", "10063", "19296", "23618", "57576", "70852", "125558", "181586", "211101", "593286", "742861", "1384104", "1938665", "2103883", "2341224", "2469308", "2757948", "3419961", "4763217", "8229111", "93441...
[ "nonn" ]
15
1
1
[ "A210693", "A391870", "A391871" ]
null
Paolo Xausa, Dec 21 2025
2025-12-23T03:06:15
oeisdata/seq/A391/A391870.seq
239a32ff97abf7ede91731b859a8cdb9
A391871
Indices of records in A210693.
[ "1", "2", "12", "21", "24", "27", "71", "407", "425", "447", "567", "1073", "1151", "1643", "2729", "3947", "5277", "5393", "9665", "14123", "17309", "21827", "28551", "30113", "33633", "42749", "45737", "50177", "75755", "83213", "126737", "145577", "...
[ "nonn" ]
19
1
2
[ "A210693", "A391870", "A391871" ]
null
Paolo Xausa, Dec 21 2025
2026-01-03T06:25:47
oeisdata/seq/A391/A391871.seq
3036b038eef5e42937b80aa782390af1
A391872
Decimal expansion of the constant x where the terms in the simple continued fraction expansion of x equal 2 plus the respective bits in the binary expansion of x, after the initial constant term of '1'.
[ "1", "4", "3", "4", "0", "5", "7", "5", "3", "6", "1", "6", "6", "2", "2", "9", "0", "9", "0", "1", "9", "9", "5", "8", "5", "3", "9", "2", "4", "8", "7", "9", "5", "1", "1", "3", "5", "9", "1", "7", "8", "5", "6", "0", "1", "...
[ "nonn", "cons" ]
15
1
2
[ "A391872", "A391873" ]
null
Paul D. Hanna, Dec 22 2025
2025-12-28T09:56:58
oeisdata/seq/A391/A391872.seq
155dc44f38cfd37819fb0cdc68cce1a3
A391873
Continued fraction expansion of the constant x in which each term equals 2 plus the respective bit in the binary expansion of x, after the initial constant term of '1'.
[ "1", "2", "3", "3", "2", "3", "3", "3", "3", "2", "2", "2", "3", "3", "3", "3", "2", "2", "3", "3", "2", "2", "3", "2", "3", "2", "2", "2", "2", "3", "2", "3", "2", "2", "3", "3", "2", "3", "2", "3", "2", "3", "2", "2", "3", "...
[ "nonn", "cofr", "cons", "easy" ]
15
0
2
[ "A391872", "A391873" ]
null
Paul D. Hanna, Dec 22 2025
2025-12-28T09:56:51
oeisdata/seq/A391/A391873.seq
a341b3454a411b1e4bb4865d5ff97c07
A391874
Nonsquare integers >= 2 for which the square of its largest prime factor equals the sum of the squares of its other prime factors, with multiplicity.
[ "240", "2240", "3402", "21504", "34650", "80262", "92664", "145350", "165000", "185130", "194922", "332640", "342342", "382200", "432630", "505197", "585728", "640458", "792918", "909558", "928200", "1395360", "1539384", "1584000", "1630200", "1706922", "1716858",...
[ "nonn", "changed" ]
28
1
1
[ "A385967", "A390574", "A391874" ]
null
Charles L. Hohn, Dec 21 2025
2026-01-12T12:17:57
oeisdata/seq/A391/A391874.seq
27fed3b21de2f934c6def8963fee4bd8
A391875
a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(2*k,2*(n-k)).
[ "1", "6", "30", "224", "1464", "8592", "48912", "270720", "1459248", "7709216", "40068000", "205378560", "1040357120", "5216715264", "25927942656", "127867834368", "626272781568", "3048584609280", "14758392452608", "71091792715776", "340910500030464", "1628080470994944", ...
[ "nonn", "easy" ]
20
0
2
[ "A108485", "A390700", "A391875" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-02T15:56:40
oeisdata/seq/A391/A391875.seq
829e542641423a22389a9bfd804e24a4
A391876
a(n) = Sum_{k=0..n} 2^(n-k) * binomial(k+2,2) * binomial(2*k,2*(n-k)).
[ "1", "3", "12", "82", "339", "1461", "6198", "24732", "97557", "377095", "1431792", "5370102", "19904711", "73046121", "265779354", "959669856", "3441865065", "12270185691", "43506695476", "153510593754", "539253893883", "1886647300701", "6576263406270", "22844885842020...
[ "nonn", "easy" ]
20
0
2
[ "A108480", "A390732", "A391876" ]
null
Seiichi Manyama, Dec 21 2025
2026-01-02T15:56:45
oeisdata/seq/A391/A391876.seq
db2ce1de87d7d94739f7fe7f727a2ee8
A391877
Number of directed Hamiltonian cycles in the complete 5-partite graph K_{n,n,n,n,n}.
[ "24", "112512", "8730457344", "3965523677282304", "6602585886478172160000", "30755963063492987269939200000", "335936272110882930782166948249600000", "7595808835329828456450518426001290035200000", "324050343201501938055429125845935244614775603200000", "2427896693981310120923718660456542234765474503...
[ "nonn" ]
12
1
1
[ "A010790", "A234365", "A378241", "A391877" ]
null
Medet Jumadildayev, Dec 21 2025
2025-12-28T21:16:13
oeisdata/seq/A391/A391877.seq
cd3c0a30edfb74618beaef19e970915a
A391880
Triangle T(n,k) read by rows, where the n-th row is the vector of n consecutive primes with minimum first element, such that the components of the sum of this vector and of this vector arranged in reverse order are all the same.
[ "2", "2", "3", "3", "5", "7", "5", "7", "11", "13", "18713", "18719", "18731", "18743", "18749", "5", "7", "11", "13", "17", "19", "683747", "683759", "683777", "683783", "683789", "683807", "683819", "17", "19", "23", "29", "31", "37", "41", "43...
[ "nonn", "tabl" ]
10
1
1
[ "A055382", "A175309", "A267028", "A391880", "A391881" ]
null
Hugo Pfoertner, Dec 22 2025
2025-12-22T10:40:23
oeisdata/seq/A391/A391880.seq
9a4eafe1de2f2ed9423a1885268adfa9
A391881
a(n) = T(n,1) + T(n,n), where T(n,k) is A391880.
[ "4", "5", "10", "18", "37462", "24", "1367566", "60", "196607854", "60", "120670499918", "330", "2339539498438", "16043622", "7891538081398078", "2142130380", "318135617703221314", "3227805300", "13839880244194493194", "3595191630030" ]
[ "nonn", "more", "hard" ]
5
1
1
[ "A175309", "A391880", "A391881" ]
null
Hugo Pfoertner, Dec 22 2025
2025-12-22T10:02:31
oeisdata/seq/A391/A391881.seq
737483e268c0d3e9cac19d132b45ab15
A391882
a(n) is the least k > 0 such that n! + k is an odd nonsquare semiprime (A046388).
[ "14", "14", "13", "9", "9", "3", "1", "5", "1", "5", "1", "3", "17", "1", "1", "7", "7", "3", "23", "1", "1", "11", "29", "3", "1", "1", "1", "37", "1", "41", "47", "19", "11", "11", "1", "7", "3", "41", "1", "13", "127", "47", "59"...
[ "nonn" ]
6
0
1
[ "A046388", "A131057", "A356207", "A391882" ]
null
Hugo Pfoertner, Dec 30 2025
2025-12-30T17:17:31
oeisdata/seq/A391/A391882.seq
d8ebbf913aabe41520a18649cb2a5315
A391883
a(n) = A000010(n) mod A048865(n).
[ "0", "0", "0", "0", "0", "1", "0", "0", "2", "1", "2", "2", "0", "3", "4", "1", "4", "2", "0", "4", "6", "1", "4", "5", "2", "5", "1", "1", "0", "6", "2", "7", "6", "3", "3", "8", "4", "6", "4", "2", "3", "8", "0", "10", "4", ...
[ "nonn", "look" ]
18
3
9
[ "A000010", "A048865", "A307712", "A391883" ]
null
Ctibor O. Zizka, Dec 22 2025
2025-12-29T05:59:05
oeisdata/seq/A391/A391883.seq
030cda256471efbbd977f11d546e2400
A391885
Numbers m such that the product m*(m+1) has a set of prime divisors, from greatest down to 2, that is missing exactly one prime divisor.
[ "4", "6", "21", "27", "44", "48", "49", "54", "55", "63", "65", "77", "90", "98", "99", "104", "120", "175", "195", "350", "363", "560", "594", "935", "1000", "1155", "1274", "2430", "2925", "4095", "4199", "4224", "5984", "10647", "10829", "1436...
[ "nonn", "fini", "full" ]
25
1
1
[ "A059957", "A252489", "A391449", "A391602", "A391885", "A391970" ]
null
Ken Clements, Dec 22 2025
2025-12-31T16:01:01
oeisdata/seq/A391/A391885.seq
9c083c8c60dc203e9b455c87ac3b3587
A391886
Array read by downward antidiagonals: A(n,k) = A(n-1,k) + (k+1)*A(n-1,k+1) + k*A(n-1,k-1) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = 1.
[ "1", "1", "2", "1", "4", "6", "1", "6", "18", "24", "1", "8", "38", "100", "124", "1", "10", "66", "272", "668", "792", "1", "12", "102", "588", "2236", "5264", "6056", "1", "14", "146", "1096", "5788", "20936", "47928", "53984", "1", "16", ...
[ "nonn", "tabl" ]
8
0
3
[ "A201158", "A391886" ]
null
Mikhail Kurkov, Dec 22 2025
2025-12-23T04:23:03
oeisdata/seq/A391/A391886.seq
a285e6d5465d88619b74f5c9e8179508
A391887
Alternately add and multiply the last two terms starting with 2, 1.
[ "2", "1", "3", "3", "6", "18", "24", "432", "456", "196992", "197448", "38895676416", "38895873864", "1512881323731695591424", "1512881323770591465288", "2288809899755012359448064967916189926490112", "2288809899755012359449577849239960517955400" ]
[ "nonn", "easy" ]
21
0
1
[ "A000032", "A000204", "A039941", "A077753", "A265496", "A391887" ]
null
Adolf Cusmariu, Dec 22 2025
2025-12-29T15:11:52
oeisdata/seq/A391/A391887.seq
f95ee24b67746d21dd842d7b91029c78
A391890
a(n) = Sum_{k=0..n} (k+1) * binomial(2*k+1,2*n-2*k+1).
[ "1", "6", "17", "58", "188", "570", "1715", "5074", "14787", "42676", "122104", "346804", "979013", "2749150", "7684437", "21393326", "59346996", "164112814", "452535543", "1244660906", "3415404295", "9352256360", "25559520752", "69730069352", "189923821833", "51651...
[ "nonn" ]
15
0
2
[ "A381421", "A391829", "A391890", "A391891" ]
null
Seiichi Manyama, Dec 22 2025
2026-01-01T15:17:01
oeisdata/seq/A391/A391890.seq
017c5e11bd2d18ddc7a973e615d9a10b
A391891
a(n) = Sum_{k=0..n} (k+1) * binomial(2*k+1,2*n-2*k).
[ "1", "2", "9", "34", "104", "326", "995", "2954", "8671", "25156", "72256", "205948", "583109", "1641570", "4598725", "12827750", "35646792", "98726370", "272611239", "750730314", "2062369787", "5653126280", "15464460608", "42225863096", "115102499721", "31326414157...
[ "nonn" ]
14
0
2
[ "A381421", "A391829", "A391890", "A391891" ]
null
Seiichi Manyama, Dec 22 2025
2026-01-01T15:16:11
oeisdata/seq/A391/A391891.seq
8d11b375af938927ba752da1e72b08df
A391892
a(n) = Sum_{k=0..n} (k+1) * 2^(n-k) * binomial(2*k+1,2*n-2*k+1).
[ "1", "6", "19", "88", "337", "1242", "4623", "16652", "59389", "209902", "734491", "2553024", "8819753", "30306498", "103669991", "353201460", "1199086357", "4057965398", "13694169715", "46095091816", "154799435457", "518763845034", "1735138977727", "5793377734748", "...
[ "nonn" ]
15
0
2
[ "A390732", "A391835", "A391892", "A391893" ]
null
Seiichi Manyama, Dec 22 2025
2026-01-01T06:51:36
oeisdata/seq/A391/A391892.seq
5730dd3f84095308393962ac90c7ec5f
A391893
a(n) = Sum_{k=0..n} (k+1) * 2^(n-k) * binomial(2*k+1,2*n-2*k).
[ "1", "2", "15", "64", "233", "926", "3411", "12380", "44605", "158074", "555687", "1938488", "6715217", "23135190", "79313403", "270741396", "920731749", "3120733874", "10545871951", "35542007920", "119494151033", "400860857358", "1342044618659", "4484767772876", "149...
[ "nonn" ]
14
0
2
[ "A390732", "A391835", "A391892", "A391893" ]
null
Seiichi Manyama, Dec 22 2025
2026-01-01T08:46:42
oeisdata/seq/A391/A391893.seq
a0c2cacd34d3db61500fb4305ef64c1e
A391894
a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(2*k+1,2*n-2*k+1).
[ "1", "12", "64", "344", "1852", "9504", "47616", "235072", "1145104", "5518400", "26364928", "125049984", "589461440", "2763899904", "12899926016", "59964819456", "277750014208", "1282419653632", "5904300064768", "27113852057600", "124223466028032", "567932306153472", "25...
[ "nonn" ]
15
0
2
[ "A390700", "A391832", "A391894", "A391895" ]
null
Seiichi Manyama, Dec 22 2025
2026-01-01T08:46:45
oeisdata/seq/A391/A391894.seq
5d2bb5b85fcac57ca2a87c0646eda35d