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1999-12-11 03:00:00
2025-04-28 00:58:08
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A007601
Positions where A007600 increases.
[ "1", "2", "3", "4", "5", "7", "10", "13", "19", "28", "37", "55", "82", "109", "163", "244", "325", "487", "730", "973", "1459", "2188", "2917", "4375", "6562", "8749", "13123", "19684", "26245", "39367", "59050", "78733", "118099", "177148", "236197", "354295", "531442", "708589", "1062883", "1594324", "2125765", "3188647" ]
[ "nonn", "easy" ]
19
1
2
null
[ "M0525" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007601.seq
3c0e590e0f2de1b16cb5de33077997c6
A007602
Numbers that are divisible by the product of their digits.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "12", "15", "24", "36", "111", "112", "115", "128", "132", "135", "144", "175", "212", "216", "224", "312", "315", "384", "432", "612", "624", "672", "735", "816", "1111", "1112", "1113", "1115", "1116", "1131", "1176", "1184", "1197", "1212", "1296", "1311", "1332", "1344", "1416", "1575", "1715", "2112", "2144" ]
[ "nonn", "base", "easy" ]
113
1
2
[ "A001103", "A002796", "A005349", "A007602", "A034709", "A034838", "A055471", "A286590", "A288069" ]
[ "M0482" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2024-03-25T06:36:22
oeisdata/seq/A007/A007602.seq
1e83d863dfed41a978c93456a9d287f1
A007603
Power-sum numbers: let n = a_1 a_2 ... a_k be a k-digit number; n is a power-sum number if there are exponents e_1 ... e_m such that n = Sum_{i=1..m} Sum_{j=1..k} a_j^e_i.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "18", "20", "21", "23", "24", "27", "30", "36", "40", "42", "45", "48", "50", "54", "60", "63", "70", "72", "80", "81", "84", "90", "100", "102", "104", "108", "110", "111", "112", "113", "114", "115", "116", "117", "120", "122", "126", "130", "131", "132", "133", "134", "135", "136", "140", "144", "150", "151", "152", "153", "154", "156", "160", "162", "170", "171", "172", "173", "174", "178", "180", "182" ]
[ "nonn", "easy", "nice", "base" ]
23
1
2
[ "A005349", "A007603", "A034087", "A034088", "A169665", "A169666" ]
[ "M0480" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2021-09-04T13:30:01
oeisdata/seq/A007/A007603.seq
0eb56c9849cb220058f3ad4c9595fa37
A007604
a(n) = a(n-1) + a(n-1-(number of odd terms so far)).
[ "1", "2", "3", "4", "6", "9", "12", "16", "22", "31", "40", "52", "68", "90", "121", "152", "192", "244", "312", "402", "523", "644", "796", "988", "1232", "1544", "1946", "2469", "2992", "3636", "4432", "5420", "6652", "8196", "10142", "12611", "15080", "18072", "21708", "26140", "31560", "38212", "46408", "56550", "69161", "81772", "96852" ]
[ "nonn", "nice", "easy" ]
30
1
2
[ "A003056", "A006336", "A007604", "A046936" ]
[ "M0567" ]
N. J. A. Sloane, Robert G. Wilson v
2023-03-15T07:56:17
oeisdata/seq/A007/A007604.seq
e4cd3418058600369d479264616c8ea7
A007605
Sum of digits of n-th prime.
[ "2", "3", "5", "7", "2", "4", "8", "10", "5", "11", "4", "10", "5", "7", "11", "8", "14", "7", "13", "8", "10", "16", "11", "17", "16", "2", "4", "8", "10", "5", "10", "5", "11", "13", "14", "7", "13", "10", "14", "11", "17", "10", "11", "13", "17", "19", "4", "7", "11", "13", "8", "14", "7", "8", "14", "11", "17", "10", "16", "11", "13", "14", "10", "5", "7", "11", "7", "13", "14", "16", "11", "17", "16", "13", "19", "14", "20", "19", "5" ]
[ "nonn", "base", "easy" ]
75
1
1
[ "A000040", "A007605", "A007953", "A038194", "A065073", "A067180", "A067523", "A068395", "A133223", "A376714", "A380192" ]
[ "M0633" ]
N. J. A. Sloane, Mira Bernstein, and Robert G. Wilson v
2025-02-05T21:46:22
oeisdata/seq/A007/A007605.seq
7b3eb00a13e9e1349cd486c754b6a29e
A007606
Take 1, skip 2, take 3, etc.
[ "1", "4", "5", "6", "11", "12", "13", "14", "15", "22", "23", "24", "25", "26", "27", "28", "37", "38", "39", "40", "41", "42", "43", "44", "45", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "79", "80", "81", "82", "83", "84", "85", "86", "87", "88", "89", "90", "91", "106", "107", "108", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "120", "137", "138" ]
[ "nonn", "tabf", "nice", "easy" ]
51
1
2
[ "A000384", "A004201", "A005917", "A007606", "A007607", "A007950", "A007951", "A007952", "A048859", "A084849", "A096376" ]
[ "M3241" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2023-02-10T19:19:10
oeisdata/seq/A007/A007606.seq
0310fdbcaebfc070c1bcf87c97788c21
A007607
Skip 1, take 2, skip 3, etc.
[ "2", "3", "7", "8", "9", "10", "16", "17", "18", "19", "20", "21", "29", "30", "31", "32", "33", "34", "35", "36", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "92", "93", "94", "95", "96", "97", "98", "99", "100", "101", "102", "103", "104", "105", "121", "122", "123", "124", "125", "126", "127", "128", "129", "130" ]
[ "nonn", "easy", "tabf" ]
72
1
1
[ "A004202", "A007606", "A007607", "A014105", "A063656", "A063657", "A064801", "A130883", "A317297", "A360418" ]
[ "M0821" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2023-02-10T12:54:13
oeisdata/seq/A007/A007607.seq
09d7a1a2c0365af18d65b8e495083f1d
A007608
Nonnegative integers in base -4.
[ "0", "1", "2", "3", "130", "131", "132", "133", "120", "121", "122", "123", "110", "111", "112", "113", "100", "101", "102", "103", "230", "231", "232", "233", "220", "221", "222", "223", "210", "211", "212", "213", "200", "201", "202", "203", "330", "331", "332", "333", "320", "321", "322", "323", "310", "311", "312", "313", "300", "301", "302", "303", "13030" ]
[ "base", "nice", "easy", "nonn" ]
54
0
3
[ "A007090", "A007608", "A039723", "A039724", "A066323", "A073785", "A073786", "A073787", "A073788", "A073789", "A073790", "A212526", "A212556" ]
[ "M0926" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007608.seq
31ff4ee0cc3c31611b6de710d00bce18
A007609
Values taken by the sigma function A000203, listed with multiplicity and in ascending order.
[ "1", "3", "4", "6", "7", "8", "12", "12", "13", "14", "15", "18", "18", "20", "24", "24", "24", "28", "30", "31", "31", "32", "32", "36", "38", "39", "40", "42", "42", "42", "44", "48", "48", "48", "54", "54", "56", "56", "57", "60", "60", "60", "62", "63", "68", "72", "72", "72", "72", "72", "74", "78", "80", "80", "84", "84", "84", "90", "90", "90", "91", "93", "96", "96", "96", "96", "98", "98" ]
[ "nonn", "easy", "nice" ]
43
1
2
[ "A000203", "A002191", "A007368", "A007609", "A085790" ]
null
Walter Nissen
2020-04-15T02:23:56
oeisdata/seq/A007/A007609.seq
1c57d986f1bb45ec67a7aba1543424ff
A007610
Sum of n consecutive primes starting at a(n) is prime (or 0 if impossible).
[ "2", "2", "5", "2", "5", "2", "17", "0", "3", "0", "5", "2", "29", "2", "3", "0", "3", "0", "11", "0", "7", "0", "7", "0", "5", "0", "7", "0", "13", "0", "13", "0", "7", "0", "5", "0", "5", "0", "13", "0", "7", "0", "7", "0", "7", "0", "7", "0", "11", "0", "17", "0", "3", "0", "3", "0", "97", "0", "29", "2", "3", "0", "13", "2", "3", "0", "19", "0", "19", "0", "3", "0", "5", "0", "3", "0", "23", "0", "7", "0", "11", "0", "53", "0", "31", "0", "89", "0", "53", "0", "19", "0", "11", "0", "3", "2" ]
[ "nonn", "nice", "easy" ]
27
1
1
[ "A007610", "A013916", "A071149" ]
[ "M0343" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2021-12-22T00:12:06
oeisdata/seq/A007/A007610.seq
174be719bb10fa7c7b37fbdd99065882
A007611
a(n) = n! + 2^n.
[ "2", "3", "6", "14", "40", "152", "784", "5168", "40576", "363392", "3629824", "39918848", "479005696", "6227028992", "87178307584", "1307674400768", "20922789953536", "355687428227072", "6402373705990144", "121645100409356288", "2432902008177688576" ]
[ "nonn", "easy" ]
55
0
1
[ "A000079", "A000142", "A007611" ]
[ "M0807" ]
N. J. A. Sloane, Robert G. Wilson v
2023-04-09T07:53:48
oeisdata/seq/A007/A007611.seq
6ac0f2e3dd3db4607df7e38fab1df4cf
A007612
a(n+1) = a(n) + digital root (A010888) of a(n).
[ "1", "2", "4", "8", "16", "23", "28", "29", "31", "35", "43", "50", "55", "56", "58", "62", "70", "77", "82", "83", "85", "89", "97", "104", "109", "110", "112", "116", "124", "131", "136", "137", "139", "143", "151", "158", "163", "164", "166", "170", "178", "185", "190", "191", "193", "197", "205", "212", "217", "218", "220", "224", "232", "239", "244", "245", "247", "251" ]
[ "nonn", "base", "easy", "nice" ]
54
1
2
[ "A004207", "A007612", "A010888", "A029898", "A064806" ]
[ "M1114" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007612.seq
66a472ae811bdd208c091d7a719a2743
A007613
a(n) = (8^n + 2*(-1)^n)/3.
[ "1", "2", "22", "170", "1366", "10922", "87382", "699050", "5592406", "44739242", "357913942", "2863311530", "22906492246", "183251937962", "1466015503702", "11728124029610", "93824992236886", "750599937895082", "6004799503160662", "48038396025285290", "384307168202282326", "3074457345618258602" ]
[ "nonn", "easy" ]
52
0
2
[ "A001045", "A006566", "A007613", "A078008", "A082311", "A139459" ]
[ "M2129" ]
N. J. A. Sloane, Robert G. Wilson v
2024-11-10T20:42:20
oeisdata/seq/A007/A007613.seq
5d3c8f60f5026aa8e888fd9225b128eb
A007614
All values attained by the phi(n) function, in ascending order.
[ "1", "1", "2", "2", "2", "4", "4", "4", "4", "6", "6", "6", "6", "8", "8", "8", "8", "8", "10", "10", "12", "12", "12", "12", "12", "12", "16", "16", "16", "16", "16", "16", "18", "18", "18", "18", "20", "20", "20", "20", "20", "22", "22", "24", "24", "24", "24", "24", "24", "24", "24", "24", "24", "28", "28", "30", "30", "32", "32", "32", "32", "32", "32", "32", "36", "36", "36", "36", "36", "36", "36", "36" ]
[ "nonn", "easy", "nice" ]
40
1
3
[ "A000010", "A002110", "A002202", "A007614", "A032447", "A058277" ]
null
Walter Nissen
2024-11-15T05:24:30
oeisdata/seq/A007/A007614.seq
4a461afdbb96f2897741224e10d61cbb
A007615
Primes with unique period length (the periods are given in A007498).
[ "3", "11", "37", "101", "333667", "9091", "9901", "909091", "1111111111111111111", "11111111111111111111111", "99990001", "999999000001", "909090909090909091", "900900900900990990990991", "9999999900000001", "909090909090909090909090909091", "900900900900900900900900900900990990990990990990990990990991" ]
[ "nonn", "nice", "easy", "base" ]
42
1
1
[ "A002371", "A006530", "A006883", "A007498", "A007615", "A007732", "A019328", "A040017", "A048595", "A051626", "A061075" ]
[ "M2890" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2024-01-03T23:46:24
oeisdata/seq/A007/A007615.seq
326b75a90556e8212b0d715c01bd781b
A007616
Palindromic reflectable primes.
[ "3", "11", "101", "131", "181", "313", "383", "10301", "11311", "13331", "13831", "18181", "30103", "30803", "31013", "38083", "38183", "1003001", "1008001", "1180811", "1183811", "1300031", "1303031", "1311131", "1333331", "1338331", "1831381", "1880881", "1881881", "1883881", "3001003", "3083803", "3103013", "3181813", "3310133" ]
[ "nonn", "base" ]
32
1
1
[ "A002385", "A007616" ]
[ "M2911" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2023-04-03T10:36:09
oeisdata/seq/A007/A007616.seq
66c30474a2edcc57a3db10e701f2a582
A007617
Values not in range of Euler phi function.
[ "3", "5", "7", "9", "11", "13", "14", "15", "17", "19", "21", "23", "25", "26", "27", "29", "31", "33", "34", "35", "37", "38", "39", "41", "43", "45", "47", "49", "50", "51", "53", "55", "57", "59", "61", "62", "63", "65", "67", "68", "69", "71", "73", "74", "75", "76", "77", "79", "81", "83", "85", "86", "87", "89", "90", "91", "93", "94", "95", "97", "98", "99", "101", "103", "105", "107" ]
[ "nonn" ]
75
1
1
[ "A000010", "A002202", "A005277", "A007617", "A083534", "A180639", "A264739" ]
null
Walter Nissen
2023-11-17T11:49:47
oeisdata/seq/A007/A007617.seq
359292694601360e6a88cdd38c9b5d1d
A007618
a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5.
[ "5", "10", "11", "13", "17", "25", "32", "37", "47", "58", "71", "79", "95", "109", "119", "130", "134", "142", "149", "163", "173", "184", "197", "214", "221", "226", "236", "247", "260", "268", "284", "298", "317", "328", "341", "349", "365", "379", "398", "418", "431", "439", "455", "469", "488", "508", "521", "529", "545", "559", "578", "598", "620", "628", "644" ]
[ "nonn", "base", "easy" ]
33
1
1
[ "A006507", "A007618", "A016052", "A016096" ]
[ "M3792" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2022-03-29T08:32:43
oeisdata/seq/A007/A007618.seq
5f6177845bfc3e70dc1dfec5f4b50fe3
A007619
Wilson quotients: ((p-1)! + 1)/p where p is the n-th prime.
[ "1", "1", "5", "103", "329891", "36846277", "1230752346353", "336967037143579", "48869596859895986087", "10513391193507374500051862069", "8556543864909388988268015483871", "10053873697024357228864849950022572972973", "19900372762143847179161250477954046201756097561", "32674560877973951128910293168477013254334511627907" ]
[ "nonn", "changed" ]
77
1
3
[ "A005450", "A005451", "A007540", "A007619", "A050299", "A157249", "A157250", "A163212", "A225672", "A225906", "A261779", "A292691" ]
[ "M4023" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2025-04-25T04:27:21
oeisdata/seq/A007/A007619.seq
eae9b9119d3c6b1fd87cdba93b341ae5
A007620
Numbers m such that every k <= m is a sum of proper divisors of m (for m>1).
[ "1", "6", "12", "18", "20", "24", "28", "30", "36", "40", "42", "48", "54", "56", "60", "66", "72", "78", "80", "84", "88", "90", "96", "100", "104", "108", "112", "120", "126", "132", "140", "144", "150", "156", "160", "162", "168", "176", "180", "192", "196", "198", "200", "204", "208", "210", "216", "220", "224", "228", "234", "240", "252", "260", "264", "270", "272", "276", "280", "288", "294", "300", "304", "306" ]
[ "nonn", "nice", "easy" ]
41
1
2
[ "A000079", "A005153", "A007620", "A027751" ]
[ "M4095" ]
N. J. A. Sloane, Robert G. Wilson v
2023-07-06T09:05:10
oeisdata/seq/A007/A007620.seq
640f991459fe79b029a5ca3c6d39a788
A007621
Impractical numbers: even abundant numbers (A173490) that are not practical(2) (A007620).
[ "70", "102", "114", "138", "174", "186", "222", "246", "258", "282", "318", "350", "354", "366", "372", "402", "426", "438", "444", "474", "490", "492", "498", "516", "534", "550", "564", "572", "582", "606", "618", "636", "642", "650", "654", "678", "708", "732", "738", "748", "762", "770", "774", "786", "804", "822", "834", "836", "846", "852", "876", "894" ]
[ "nonn" ]
20
1
1
[ "A007620", "A007621", "A035480", "A173490" ]
[ "M5337" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2017-06-22T10:58:50
oeisdata/seq/A007/A007621.seq
c6ec81c079c4aea2066317a01d7d9459
A007622
Consider Leibniz's harmonic triangle (A003506) and look at the non-boundary terms. Sequence gives numbers appearing in denominators, sorted.
[ "6", "12", "20", "30", "42", "56", "60", "72", "90", "105", "110", "132", "140", "156", "168", "182", "210", "240", "252", "272", "280", "306", "342", "360", "380", "420", "462", "495", "504", "506", "552", "600", "630", "650", "660", "702", "756", "812", "840", "858", "870", "930", "992", "1056", "1092", "1122", "1190", "1260", "1320", "1332" ]
[ "nonn" ]
32
1
1
null
[ "M4096" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007622.seq
67b8b6019b5d14656a6313fd81dd99f1
A007623
Integers written in factorial base.
[ "0", "1", "10", "11", "20", "21", "100", "101", "110", "111", "120", "121", "200", "201", "210", "211", "220", "221", "300", "301", "310", "311", "320", "321", "1000", "1001", "1010", "1011", "1020", "1021", "1100", "1101", "1110", "1111", "1120", "1121", "1200", "1201", "1210", "1211", "1220", "1221", "1300", "1301", "1310", "1311", "1320", "1321", "2000", "2001", "2010" ]
[ "base", "nonn", "nice", "easy" ]
123
0
3
[ "A000142", "A007623", "A034968", "A049345", "A055089", "A055881", "A060112", "A060130", "A060495", "A064039", "A099563" ]
[ "M4678" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2024-10-21T11:59:15
oeisdata/seq/A007/A007623.seq
cc86316ca1cfd717712792dcb6aa7a70
A007624
Numbers m such that the product of proper divisors of m = m^k, k>1.
[ "12", "18", "20", "24", "28", "30", "32", "40", "42", "44", "45", "48", "50", "52", "54", "56", "60", "63", "66", "68", "70", "72", "75", "76", "78", "80", "84", "88", "90", "92", "96", "98", "99", "102", "104", "105", "108", "110", "112", "114", "116", "117", "120", "124", "126", "128", "130", "132", "135", "136", "138", "140", "147", "148", "150", "152", "153", "154" ]
[ "nonn", "easy" ]
26
1
1
[ "A000005", "A007624", "A007956" ]
[ "M4824" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2019-11-20T11:55:05
oeisdata/seq/A007/A007624.seq
eebec6c35f1a0c1cd09c7a56a8738844
A007625
Number of M-sequences from multicomplexes on at most 6 variables with no monomial of degree more than n-1.
[ "1", "2", "8", "64", "904", "20926", "753994", "40412530", "3099627142", "329518779600", "47292630585258", "8962444327321130", "2200336508719464304", "688212546598963025056", "270220456234745707986648" ]
[ "nonn" ]
4
-1
2
[ "A003659", "A007625", "A011819", "A011820" ]
null
N. J. A. Sloane.
2012-03-30T16:45:13
oeisdata/seq/A007/A007625.seq
78fccf557bb714879c594789a99dfc77
A007626
Sum of divisors of superabundant numbers (A004394).
[ "1", "3", "7", "12", "28", "60", "91", "124", "168", "360", "546", "744", "1170", "2418", "2880", "4368", "5952", "9360", "19344", "39312", "59520", "99944", "112320", "232128", "471744", "714240", "1199328", "1451520", "2437344", "2926080", "3249792", "6604416", "9999360" ]
[ "nonn", "easy", "nice" ]
27
1
2
[ "A000203", "A002093", "A002192", "A004394", "A007626", "A034885", "A051444" ]
null
Walter Nissen
2022-10-04T18:32:51
oeisdata/seq/A007/A007626.seq
acfedfbe249b34fb2415688f1785c6dc
A007627
Primitive modest numbers.
[ "13", "19", "23", "29", "49", "59", "79", "89", "103", "109", "111", "133", "199", "203", "209", "211", "233", "299", "311", "409", "411", "433", "499", "509", "511", "533", "599", "611", "709", "711", "733", "799", "809", "811", "833", "899", "911", "1003", "1009", "1011", "1027", "1033", "1037", "1099", "1111" ]
[ "nonn", "easy", "base" ]
32
1
1
[ "A007627", "A054986", "A055018" ]
[ "M4888" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2017-12-20T23:29:39
oeisdata/seq/A007/A007627.seq
fbea1262cebeddf950c76f884bde66da
A007628
Reflectable emirps.
[ "13", "31", "113", "311", "1031", "1033", "1103", "1181", "1301", "1381", "1811", "1831", "3011", "3083", "3301", "3803", "10333", "11003", "11083", "11833", "18013", "18133", "18803", "30011", "30881", "31033", "31081", "31183", "33013", "33181", "33301", "33811", "38011", "38113" ]
[ "nonn", "base", "nice", "easy" ]
20
1
1
[ "A003684", "A004086", "A006567", "A007628", "A010051", "A046732", "A048051", "A048052", "A048053", "A048054", "A048895", "A125308" ]
[ "M4892" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2023-04-03T10:36:09
oeisdata/seq/A007/A007628.seq
5dfe51f72c217805d8727f321e5b24d7
A007629
Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers).
[ "14", "19", "28", "47", "61", "75", "197", "742", "1104", "1537", "2208", "2580", "3684", "4788", "7385", "7647", "7909", "31331", "34285", "34348", "55604", "62662", "86935", "93993", "120284", "129106", "147640", "156146", "174680", "183186", "298320", "355419", "694280", "925993", "1084051", "7913837", "11436171", "33445755", "44121607" ]
[ "nonn", "base", "nice" ]
100
1
1
[ "A006576", "A007629", "A048970", "A050235", "A130010", "A162724", "A186830", "A187713", "A188195", "A188200", "A188201", "A188380", "A188381", "A274769", "A274770", "A281915", "A281916", "A281917", "A281918", "A281919", "A281920", "A281921" ]
[ "M4922" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007629.seq
7a9555ef225e84774547ddac99139291
A007630
Duplicate of A002562.
[ "46", "92", "341", "1787", "9233", "45752", "285053", "1846955" ]
[ "dead" ]
21
9
1
null
[ "M5288" ]
null
2025-02-14T23:11:28
oeisdata/seq/A007/A007630.seq
d967745f4e968409996bf9113e8fc448
A007631
Number of solutions to non-attacking reflecting queens problem.
[ "1", "1", "0", "0", "2", "4", "0", "2", "10", "32", "38", "140", "496", "1186", "3178", "16792", "82038", "289566", "1139874", "5914118", "33800010", "142337180", "721286448", "4384569864" ]
[ "nonn", "nice", "more" ]
53
0
5
[ "A000170", "A002968", "A007631", "A051223", "A051224", "A272363" ]
[ "M0929" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2018-10-07T17:15:14
oeisdata/seq/A007/A007631.seq
8e6bfde749be546544519c619e6c782b
A007632
Numbers that are palindromic in bases 2 and 10.
[ "0", "1", "3", "5", "7", "9", "33", "99", "313", "585", "717", "7447", "9009", "15351", "32223", "39993", "53235", "53835", "73737", "585585", "1758571", "1934391", "1979791", "3129213", "5071705", "5259525", "5841485", "13500531", "719848917", "910373019", "939474939", "1290880921", "7451111547" ]
[ "base", "nonn", "nice" ]
90
1
3
[ "A007632", "A007633", "A029731", "A029804", "A029961", "A029962", "A029963", "A029964", "A029965", "A029966", "A029967", "A029968", "A029969", "A029970", "A097855", "A099165", "A120764" ]
[ "M2406" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2022-09-13T13:05:04
oeisdata/seq/A007/A007632.seq
fa599f400151dda9b83d9ad51663780a
A007633
Palindromic in bases 3 and 10.
[ "0", "1", "2", "4", "8", "121", "151", "212", "242", "484", "656", "757", "29092", "48884", "74647", "75457", "76267", "92929", "93739", "848848", "1521251", "2985892", "4022204", "4219124", "4251524", "4287824", "5737375", "7875787", "7949497", "27711772", "83155138", "112969211", "123464321" ]
[ "nonn", "base" ]
58
1
3
[ "A007632", "A007633", "A029731", "A029804", "A029961", "A029962", "A029963", "A029964", "A029965", "A029966", "A029967", "A029968", "A029969", "A029970", "A097855", "A099165" ]
[ "M1164" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2023-10-30T00:47:45
oeisdata/seq/A007/A007633.seq
1b7d1d9c198bba56323bfe2aaa563f5f
A007634
Numbers k such that k^2 + k + 41 is composite.
[ "40", "41", "44", "49", "56", "65", "76", "81", "82", "84", "87", "89", "91", "96", "102", "104", "109", "117", "121", "122", "123", "126", "127", "130", "136", "138", "140", "143", "147", "155", "159", "161", "162", "163", "164", "170", "172", "173", "178", "184", "185", "186", "187", "190", "201", "204", "205", "207", "208", "209", "213", "215", "216", "217" ]
[ "nonn", "easy" ]
47
1
1
[ "A002837", "A007634", "A055390", "A201998" ]
[ "M5269" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2023-07-26T09:14:38
oeisdata/seq/A007/A007634.seq
b3a819be4bf322ae8f40f92c866337f4
A007635
Primes of form n^2 + n + 17.
[ "17", "19", "23", "29", "37", "47", "59", "73", "89", "107", "127", "149", "173", "199", "227", "257", "359", "397", "479", "523", "569", "617", "719", "773", "829", "887", "947", "1009", "1277", "1423", "1499", "1657", "1823", "1997", "2087", "2179", "2273", "2467", "2879", "3209", "3323", "3557", "3677", "3923", "4049", "4177", "4987", "5273" ]
[ "nonn", "easy" ]
63
1
1
[ "A005846", "A007635", "A028823", "A048059", "A160548" ]
[ "M5069" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007635.seq
2b35d796fce55adb26f21b6cd2433e1a
A007636
Numbers k such that k^2 + k + 17 is composite.
[ "16", "17", "20", "25", "32", "33", "34", "36", "39", "41", "43", "48", "50", "51", "52", "54", "55", "58", "61", "65", "66", "67", "68", "69", "71", "74", "77", "78", "80", "83", "84", "85", "88", "89", "90", "93", "94", "96", "97", "99", "100", "101", "102", "105", "106", "107", "111", "112", "115", "116", "117", "118", "119", "122", "124", "126", "131", "134", "135", "136", "137" ]
[ "nonn", "easy" ]
22
1
1
null
[ "M4996" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2022-09-08T08:44:35
oeisdata/seq/A007/A007636.seq
e5d90ff81c5547208867456aded666b2
A007637
Primes of form 3*k^2 - 3*k + 23.
[ "23", "29", "41", "59", "83", "113", "149", "191", "239", "293", "353", "419", "491", "569", "653", "743", "839", "941", "1049", "1163", "1283", "1409", "1823", "1973", "2129", "2459", "2633", "2999", "3191", "3389", "3593", "3803", "4019", "4241", "4703", "4943", "5189", "5441", "6791", "7079", "7673", "8291", "8609" ]
[ "nonn", "easy", "changed" ]
32
1
1
[ "A007637", "A007638" ]
[ "M5130" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2025-04-18T08:53:45
oeisdata/seq/A007/A007637.seq
a950e0d7f3c47d9326df536d5fbe023f
A007638
Numbers k such that 3*k^2 - 3*k + 23 is composite.
[ "23", "24", "28", "31", "39", "44", "45", "46", "47", "50", "52", "56", "57", "60", "63", "67", "69", "70", "71", "79", "80", "85", "86", "88", "89", "90", "92", "93", "96", "97", "102", "107", "108", "112", "115", "116", "118", "119", "121", "122", "123", "126", "128", "131", "134", "137", "138", "139", "143", "144", "145", "147", "148", "151", "153", "156", "157", "161", "162" ]
[ "nonn", "easy" ]
23
1
1
null
[ "M5129" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2022-09-08T08:44:35
oeisdata/seq/A007/A007638.seq
626423f1f375bfb878fd57a6672f7aab
A007639
Primes of form 2n^2 - 2n + 19.
[ "19", "23", "31", "43", "59", "79", "103", "131", "163", "199", "239", "283", "331", "383", "439", "499", "563", "631", "859", "1031", "1123", "1319", "1423", "1531", "1759", "1879", "2003", "2131", "2399", "2539", "2683", "3299", "3463", "3631", "3803", "4159", "4723", "4919", "5119", "5323", "5531", "5743", "6863", "7583", "8599" ]
[ "nonn", "easy" ]
28
1
1
[ "A007639", "A139827" ]
[ "M5070" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2022-09-08T08:44:35
oeisdata/seq/A007/A007639.seq
e6785ee9edcf895840cb5226fbbb17bd
A007640
Numbers k such that 2*k^2 - 2*k + 19 is composite.
[ "19", "20", "22", "25", "29", "34", "38", "39", "40", "45", "47", "48", "55", "56", "57", "58", "60", "61", "63", "64", "65", "68", "71", "74", "76", "77", "78", "82", "83", "85", "90", "91", "93", "94", "95", "96", "97", "102", "104", "107", "110", "112", "113", "114", "115", "117", "119", "122", "123", "124", "126", "127", "129", "130", "131", "133", "134", "135", "137", "139" ]
[ "nonn" ]
19
1
1
null
[ "M5068" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2022-09-08T08:44:35
oeisdata/seq/A007/A007640.seq
4562e8158f6ea5fe44466d544405e15b
A007641
Primes of the form 2*k^2 + 29.
[ "29", "31", "37", "47", "61", "79", "101", "127", "157", "191", "229", "271", "317", "367", "421", "479", "541", "607", "677", "751", "829", "911", "997", "1087", "1181", "1279", "1381", "1487", "1597", "1951", "2207", "2341", "2621", "2767", "2917", "3229", "3391", "3557", "3727", "4079", "4261", "4447", "4637", "4831", "5231", "5437" ]
[ "nonn", "easy" ]
45
1
1
[ "A005846", "A007641", "A050265", "A352800" ]
[ "M5219" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007641.seq
0691c7d0d35b3f41652c8062487632fa
A007642
Numbers k such that 2*k^2 +29 is composite.
[ "29", "30", "32", "35", "39", "44", "50", "57", "58", "61", "63", "65", "72", "74", "76", "84", "87", "88", "89", "91", "92", "94", "95", "97", "99", "102", "107", "109", "113", "116", "118", "120", "122", "123", "125", "126", "127", "134", "138", "144", "145", "146", "147", "148", "149", "150", "153", "154", "156", "157", "163", "164", "165", "166", "169", "174", "175", "179", "180", "182", "183", "185", "187" ]
[ "nonn" ]
17
1
1
null
[ "M5205" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2022-04-15T11:22:46
oeisdata/seq/A007/A007642.seq
9b858174058c5c4c1c993660226b5c8b
A007643
Primes not of form | 3^x - 2^y |.
[ "41", "43", "53", "59", "67", "71", "83", "89", "97", "103", "107", "109", "113", "131", "137", "149", "151", "157", "163", "167", "173", "181", "191", "193", "197", "199", "223", "233", "251", "257", "263", "271", "277", "281", "283", "293", "307", "311", "313", "317", "331", "337", "347", "349", "353", "359", "367", "373", "379", "383", "389" ]
[ "nonn" ]
21
1
1
[ "A004051", "A007643", "A007644", "A103146" ]
[ "M5274" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2019-10-13T11:20:48
oeisdata/seq/A007/A007643.seq
e17ca1347fa326fae494e7265775f815
A007644
Primes not of form | 3^a +- 2^b | where a, b are nonnegative integers.
[ "53", "71", "103", "107", "109", "149", "151", "157", "163", "167", "173", "181", "191", "193", "197", "199", "223", "233", "263", "271", "277", "281", "293", "311", "313", "317", "331", "347", "349", "353", "359", "367", "373", "379", "383", "389", "397", "401", "409", "419", "421", "433", "439", "443", "449", "457", "461", "463", "467", "479", "487", "491" ]
[ "nonn" ]
30
1
1
[ "A004051", "A007643", "A007644", "A103146" ]
[ "M5307" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2020-02-16T01:17:06
oeisdata/seq/A007/A007644.seq
d1e304c7878e04924fcfd39684efbb59
A007645
Generalized cuban primes: primes of the form x^2 + xy + y^2; or primes of the form x^2 + 3*y^2; or primes == 0 or 1 (mod 3).
[ "3", "7", "13", "19", "31", "37", "43", "61", "67", "73", "79", "97", "103", "109", "127", "139", "151", "157", "163", "181", "193", "199", "211", "223", "229", "241", "271", "277", "283", "307", "313", "331", "337", "349", "367", "373", "379", "397", "409", "421", "433", "439", "457", "463", "487", "499", "523", "541", "547", "571", "577", "601", "607", "613" ]
[ "nonn", "easy" ]
113
1
1
[ "A000040", "A001479", "A001480", "A002407", "A002648", "A003136", "A003627", "A007645", "A034017", "A045331", "A201477" ]
[ "M2637" ]
N. J. A. Sloane, Mira Bernstein and Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007645.seq
e9c65be63a29a9cacdf75ca83694af60
A007646
Numbers k such that k*4^k + 1 is prime.
[ "1", "3", "7", "33", "67", "223", "663", "912", "1383", "3777", "3972", "10669", "48375" ]
[ "hard", "nonn" ]
17
1
2
null
[ "M2699" ]
N. J. A. Sloane
2019-04-08T03:07:11
oeisdata/seq/A007/A007646.seq
74d43465432ca0290a5b872a36f8a515
A007647
Numbers k such that k*10^k + 1 is prime.
[ "1", "3", "9", "21", "363", "2161", "4839", "49521", "105994", "207777" ]
[ "hard", "nonn" ]
20
1
2
[ "A004023", "A007647" ]
[ "M2783" ]
N. J. A. Sloane
2024-03-22T19:38:18
oeisdata/seq/A007/A007647.seq
3c862c22188aca34e67a33f65c9b8a5b
A007648
n*18^n + 1 is a prime.
[ "1", "3", "21", "23", "842", "1683", "3401", "16839", "49963", "60239", "150940", "155928" ]
[ "nonn", "hard" ]
22
1
2
null
[ "M3079" ]
N. J. A. Sloane.
2016-04-10T15:16:26
oeisdata/seq/A007/A007648.seq
3f24accfc4d66ce89831dba695962161
A007649
Number of set-like molecular species of degree n.
[ "1", "1", "2", "3", "7", "9", "20", "26", "54", "74", "137", "184", "356", "473", "841", "1154", "2034", "2742", "4740", "6405", "10874", "14794", "24515", "33246", "54955", "74380", "120501", "163828", "263144", "356621", "567330", "768854", "1212354", "1644335", "2567636", "3478873", "5403223", "7314662", "11265825", "15258443", "23363143", "31608055", "48113280", "65063640", "98501538", "133168305", "200503864" ]
[ "nonn" ]
33
0
3
[ "A000638", "A007649", "A007650" ]
[ "M0824" ]
Simon Plouffe
2024-12-31T06:32:40
oeisdata/seq/A007/A007649.seq
f68eebe8d149b83a03ad4b2dc2795840
A007650
Number of set-like atomic species of degree n.
[ "0", "1", "1", "1", "3", "1", "6", "1", "10", "4", "12", "1", "33", "1", "29", "13", "64", "1", "100", "1", "156", "30", "187", "1", "443", "10", "476", "78", "877", "1", "1326", "1", "2098", "188", "2745", "36", "5203", "1", "6408", "477", "11084", "1", "15687", "1", "24709", "1241", "33249", "1", "57432", "27", "74529", "2746", "120984", "1", "168668", "194", "264075", "6409", "356624", "1", "579893", "1", "768857", "14898", "1214452", "483", "1669060", "1" ]
[ "nonn" ]
35
0
5
[ "A005226", "A007649", "A007650" ]
[ "M2227" ]
Simon Plouffe
2024-12-31T06:32:21
oeisdata/seq/A007/A007650.seq
09aa97850ae294cd4007d60d9c1dc652
A007651
Describe the previous term! (method B - initial term is 1).
[ "1", "11", "12", "1121", "122111", "112213", "12221131", "1123123111", "12213111213113", "11221131132111311231", "12221231123121133112213111", "1123112131122131112112321222113113", "1221311221113112221131132112213121112312311231" ]
[ "nonn", "base", "easy", "nice" ]
31
1
2
[ "A005150", "A007651", "A022470", "A022499", "A022500", "A022505" ]
[ "M4768" ]
N. J. A. Sloane
2022-09-18T12:10:54
oeisdata/seq/A007/A007651.seq
18090b8c996e5a9017394c7e8fd281fa
A007652
Final digit of prime(n).
[ "2", "3", "5", "7", "1", "3", "7", "9", "3", "9", "1", "7", "1", "3", "7", "3", "9", "1", "7", "1", "3", "9", "3", "9", "7", "1", "3", "7", "9", "3", "7", "1", "7", "9", "9", "1", "7", "3", "7", "3", "9", "1", "1", "3", "7", "9", "1", "3", "7", "9", "3", "9", "1", "1", "7", "3", "9", "1", "7", "1", "3", "3", "7", "1", "3", "7", "1", "7", "7", "9", "3", "9", "7", "3", "9", "3", "9", "7", "1", "9", "9", "1", "1", "3", "9", "3", "9", "7", "1", "3", "7", "9", "7", "1", "9", "3", "9", "1", "3", "1", "7", "7", "3", "9", "1" ]
[ "nonn", "base", "easy" ]
61
1
1
[ "A000040", "A007652", "A010879", "A038194", "A039701", "A039706", "A039709", "A039715", "A110923", "A290450" ]
[ "M0632" ]
N. J. A. Sloane, Simon Plouffe
2024-12-12T09:29:00
oeisdata/seq/A007/A007652.seq
2b309559e42dc3fb264598119a426538
A007653
Coefficients of L-series for elliptic curve "37a1": y^2 + y = x^3 - x.
[ "1", "-2", "-3", "2", "-2", "6", "-1", "0", "6", "4", "-5", "-6", "-2", "2", "6", "-4", "0", "-12", "0", "-4", "3", "10", "2", "0", "-1", "4", "-9", "-2", "6", "-12", "-4", "8", "15", "0", "2", "12", "-1", "0", "6", "0", "-9", "-6", "2", "-10", "-12", "-4", "-9", "12", "-6", "2", "0", "-4", "1", "18", "10", "0", "0", "-12", "8", "12", "-8", "8", "-6", "-8", "4", "-30", "8", "0", "-6", "-4", "9", "0", "-1", "2", "3", "0", "5", "-12", "4", "8", "9", "18", "-15", "6", "0", "-4", "-18", "0", "4", "24", "2", "4", "12", "18", "0" ]
[ "sign", "easy", "mult" ]
37
1
2
[ "A000748", "A007653", "A045866", "A045867" ]
[ "M0419" ]
N. J. A. Sloane
2023-08-02T11:45:59
oeisdata/seq/A007/A007653.seq
22ffd51306d12f8921093c3d0df115d8
A007654
Numbers k such that the standard deviation of 1,...,k is an integer.
[ "0", "3", "48", "675", "9408", "131043", "1825200", "25421763", "354079488", "4931691075", "68689595568", "956722646883", "13325427460800", "185599261804323", "2585064237799728", "36005300067391875", "501489136705686528", "6984842613812219523", "97286307456665386800", "1355023461779503195683" ]
[ "easy", "nonn" ]
74
1
2
[ "A001075", "A001353", "A007654", "A007655", "A011944", "A055793", "A098301" ]
[ "M3154" ]
N. J. A. Sloane
2023-03-16T08:14:54
oeisdata/seq/A007/A007654.seq
7c357f0b578eb35f7daae7056f93848c
A007655
Standard deviation of A007654.
[ "0", "1", "14", "195", "2716", "37829", "526890", "7338631", "102213944", "1423656585", "19828978246", "276182038859", "3846719565780", "53577891882061", "746243766783074", "10393834843080975", "144767444036350576", "2016350381665827089", "28084137899285228670", "391161580208327374291", "5448177985017298011404" ]
[ "nonn", "easy" ]
143
1
3
[ "A000027", "A000217", "A001090", "A001109", "A001353", "A001570", "A003500", "A004189", "A004191", "A007655", "A011922", "A011943", "A011945", "A028230", "A029547", "A029548", "A046184", "A049310", "A049660", "A053120", "A055793", "A067900", "A075843", "A077412", "A077421", "A077423", "A078987", "A097309", "A097311", "A097313", "A097316", "A098301", "A101950", "A103974", "A144128", "A323182" ]
[ "M4948" ]
N. J. A. Sloane
2024-02-28T06:33:03
oeisdata/seq/A007/A007655.seq
7b3bf5373686467bc3d439905940542e
A007656
Mass number of the most abundant isotope of the element with atomic number Z = n.
[ "1", "4", "7", "9", "11", "12", "14", "16", "19", "20", "23", "24", "27", "28", "31", "32", "35", "40", "39", "40", "45", "48", "51", "52", "55", "56", "59", "58", "63", "64", "69", "74", "75", "80", "79", "84", "85", "88", "89", "90", "93", "98", "98", "102", "103", "106", "107", "114", "115", "120", "121", "130", "127", "132", "133", "138", "139", "140", "141", "142", "145", "152", "153", "158", "159", "164", "165", "168", "169", "174", "175", "180", "181", "184", "187", "192", "193", "195", "197", "202", "205", "208", "209", "209", "210", "222", "223", "226", "227", "232", "231", "238", "237", "244", "243", "247", "247", "251", "252", "257", "258", "259", "260", "261", "262", "263", "264", "265", "266", "269", "272", "277", "286", "289", "289", "293", "294", "294" ]
[ "nonn", "fini" ]
63
1
2
[ "A007656", "A058317", "A121818", "A179301" ]
[ "M3296" ]
N. J. A. Sloane
2024-05-07T13:25:32
oeisdata/seq/A007/A007656.seq
ad9becfa5b6445a13bc31a2095314fb4
A007657
Maximal coefficient in (x + x^2 + x^4 + x^8 + ...)^n.
[ "1", "2", "6", "36", "270", "2520", "28560", "361200", "5481000", "88565400", "1654052400", "32885455680", "721400359680", "17024709461760", "429108154675200", "11721695953968000", "333806974560259200", "10358856500289897600", "331148326165228091520", "11429645706428485536000", "407641141014720316704000" ]
[ "nonn" ]
17
1
2
null
[ "M1705" ]
N. J. A. Sloane.
2018-12-06T14:45:07
oeisdata/seq/A007/A007657.seq
3a7836ae2b6a1e04761bf9961527739c
A007658
Numbers k such that (3^k + 1)/4 is prime.
[ "3", "5", "7", "13", "23", "43", "281", "359", "487", "577", "1579", "1663", "1741", "3191", "9209", "11257", "12743", "13093", "17027", "26633", "104243", "134227", "152287", "700897", "1205459", "1896463", "2533963", "2674381", "7034611" ]
[ "hard", "nonn", "more" ]
72
1
1
null
[ "M2420" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007658.seq
81d32496efefe37c89dba1d76b37bb7f
A007659
Primes p such that Ramanujan number tau(p) is divisible by p.
[ "2", "3", "5", "7", "2411", "7758337633" ]
[ "hard", "nonn", "more" ]
39
1
1
[ "A000594", "A007332", "A007659", "A063938" ]
[ "M0681" ]
N. J. A. Sloane, Robert G. Wilson v
2025-01-07T02:38:34
oeisdata/seq/A007/A007659.seq
47a1863e6a00040e7f2ef2c8392c9af1
A007660
a(n) = a(n-1)*a(n-2) + 1 with a(0) = a(1) = 0.
[ "0", "0", "1", "1", "2", "3", "7", "22", "155", "3411", "528706", "1803416167", "953476947989903", "1719515742866809222961802", "1639518622529236077952144318816050685207", "2819178082162327154499022366029959843954512194276761760087463015" ]
[ "nonn", "easy" ]
65
0
5
[ "A007660", "A250309", "A253853", "A258113" ]
[ "M0853" ]
N. J. A. Sloane, Robert G. Wilson v
2025-01-09T09:35:59
oeisdata/seq/A007/A007660.seq
181ab885533b50d458d9fb9189fe2b95
A007661
Triple factorial numbers a(n) = n!!!, defined by a(n) = n*a(n-3), a(0) = a(1) = 1, a(2) = 2. Sometimes written n!3.
[ "1", "1", "2", "3", "4", "10", "18", "28", "80", "162", "280", "880", "1944", "3640", "12320", "29160", "58240", "209440", "524880", "1106560", "4188800", "11022480", "24344320", "96342400", "264539520", "608608000", "2504902400", "7142567040", "17041024000", "72642169600", "214277011200", "528271744000", "2324549427200" ]
[ "nonn", "easy", "nice" ]
75
0
3
[ "A000142", "A000165", "A001147", "A001813", "A006882", "A007559", "A007661", "A007662", "A007696", "A008544", "A008545", "A008585", "A016777", "A016789", "A032031", "A047053", "A085157", "A085158", "A161474", "A288055" ]
[ "M0596" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2025-03-19T08:24:36
oeisdata/seq/A007/A007661.seq
e86d3e8b5e85b568af4e63f9ccfbe5ef
A007662
Quadruple factorial numbers n!!!!: a(n) = n*a(n-4).
[ "1", "1", "2", "3", "4", "5", "12", "21", "32", "45", "120", "231", "384", "585", "1680", "3465", "6144", "9945", "30240", "65835", "122880", "208845", "665280", "1514205", "2949120", "5221125", "17297280", "40883535", "82575360", "151412625", "518918400", "1267389585", "2642411520", "4996616625" ]
[ "nonn" ]
37
0
3
[ "A000142", "A001813", "A006882", "A007661", "A007662", "A007696", "A008545", "A047053", "A288091" ]
[ "M0534" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
2025-02-16T08:32:31
oeisdata/seq/A007/A007662.seq
572fb2e6b21389b65f22d8db369dd03c
A007663
Fermat quotients: (2^(p-1)-1)/p, where p=prime(n).
[ "1", "3", "9", "93", "315", "3855", "13797", "182361", "9256395", "34636833", "1857283155", "26817356775", "102280151421", "1497207322929", "84973577874915", "4885260612740877", "18900352534538475", "1101298153654301589", "16628050996019877513", "64689951820132126215", "3825714619033636628817" ]
[ "nonn", "easy", "nice" ]
104
2
2
[ "A001045", "A001917", "A002322", "A007663", "A096060" ]
[ "M2828" ]
N. J. A. Sloane, Sep 19 1994
2024-12-29T16:10:46
oeisdata/seq/A007/A007663.seq
f0bdb41c36ee874771f73bc2935d7a3c
A007664
Reve's puzzle: number of moves needed to solve the Towers of Hanoi puzzle with 4 pegs and n disks, according to the Frame-Stewart algorithm.
[ "0", "1", "3", "5", "9", "13", "17", "25", "33", "41", "49", "65", "81", "97", "113", "129", "161", "193", "225", "257", "289", "321", "385", "449", "513", "577", "641", "705", "769", "897", "1025", "1153", "1281", "1409", "1537", "1665", "1793", "2049", "2305", "2561", "2817", "3073", "3329", "3585", "3841", "4097", "4609", "5121", "5633" ]
[ "nonn", "nice" ]
104
0
3
[ "A000225", "A003056", "A007664", "A007665", "A137688", "A182058" ]
[ "M2449" ]
N. J. A. Sloane, Mira Bernstein and Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007664.seq
938b4b791999f9a75c859a83aee20a50
A007665
Tower of Hanoi with 5 pegs.
[ "1", "3", "5", "7", "11", "15", "19", "23", "27", "31", "39", "47", "55", "63", "71", "79", "87", "95", "103", "111", "127", "143", "159", "175", "191", "207", "223", "239", "255", "271", "287", "303", "319", "335", "351", "383", "415", "447", "479", "511", "543", "575", "607", "639", "671", "703", "735", "767", "799" ]
[ "nonn" ]
42
1
2
[ "A007664", "A007665", "A056556", "A182058" ]
[ "M2414" ]
N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007665.seq
1d43225907492dbd3fd81ffc8a46e4d9
A007666
a(n) = smallest number k such that k^n is the sum of n positive n-th powers, or 0 if no solution exists.
[ "1", "5", "6", "353", "72" ]
[ "nonn", "hard", "nice", "more" ]
50
1
2
[ "A003294", "A007666", "A061988", "A063922" ]
[ "M3753" ]
N. J. A. Sloane, Robert G. Wilson v
2017-07-23T04:04:23
oeisdata/seq/A007/A007666.seq
859934cf2db75837ab7f389a0eaf39d5
A007667
The sum of both two and three consecutive squares.
[ "5", "365", "35645", "3492725", "342251285", "33537133085", "3286296790925", "322023548377445", "31555021444198565", "3092070077983081805", "302991312620897818205", "29690056566770003102165" ]
[ "nonn", "easy" ]
55
1
1
[ "A003154", "A006061", "A007667", "A031138", "A054320" ]
[ "M4037" ]
N. J. A. Sloane, Robert G. Wilson v
2024-12-10T17:11:53
oeisdata/seq/A007/A007667.seq
e572cfc7e05e0887a2fce31b2acdbe7c
A007668
Numbers k such that phi(k) divides sigma(k) and sigma(k)/k > sigma(m)/m for all m < k.
[ "1", "2", "6", "12", "840", "332640" ]
[ "nonn" ]
16
1
2
[ "A004394", "A007668", "A020492" ]
null
Walter Nissen
2024-05-22T10:20:44
oeisdata/seq/A007/A007668.seq
974552b0578cc009781aab4948209481
A007669
Duplicate of A034343.
[ "1", "2", "4", "8", "16", "36", "80", "194", "506", "1449", "4631", "17106", "74820", "404283", "2815595" ]
[ "dead" ]
13
1
2
null
[ "M1135" ]
null
2017-11-27T23:08:19
oeisdata/seq/A007/A007669.seq
22ba91b22ccaadc85ea5ea9eb33601ce
A007670
Numbers n such that 2^n - 2^((n + 1)/2) + 1 is prime.
[ "3", "7", "47", "73", "79", "113", "151", "167", "239", "241", "353", "367", "457", "1367", "3041", "27529", "49207", "160423", "364289", "991961", "1203793", "1667321", "4792057" ]
[ "nonn", "hard", "more" ]
28
1
1
[ "A006598", "A007670" ]
[ "M2703" ]
N. J. A. Sloane, Robert G. Wilson v
2020-06-17T02:23:36
oeisdata/seq/A007/A007670.seq
13374f26f7c1b82b1eea8b8fd5988f10
A007671
Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.
[ "1", "3", "5", "11", "19", "29", "157", "163", "283", "379", "997", "10141", "14699", "77291", "85237", "106693", "203789", "3704053" ]
[ "nonn", "hard", "more" ]
28
1
2
[ "A007671", "A057429" ]
[ "M2481" ]
N. J. A. Sloane, Robert G. Wilson v
2024-07-21T21:50:29
oeisdata/seq/A007/A007671.seq
c453117d01541b2315a92f887c0f20a8
A007672
a(n) = A002034(n)!/n.
[ "1", "1", "2", "6", "24", "1", "720", "3", "80", "12", "3628800", "2", "479001600", "360", "8", "45", "20922789888000", "40", "6402373705728000", "6", "240", "1814400", "1124000727777607680000", "1", "145152", "239500800", "13440", "180", "304888344611713860501504000000" ]
[ "nonn", "nice" ]
21
1
3
null
[ "M1669" ]
N. J. A. Sloane, Robert G. Wilson v
2017-05-09T10:41:24
oeisdata/seq/A007/A007672.seq
f4a73ba762792abb02a3df7878a05abb
A007673
Number of coins needed for ApSimon's mints problem.
[ "1", "2", "4", "8", "15", "28", "51", "90" ]
[ "hard", "nonn", "more", "nice" ]
42
1
2
null
[ "M1109" ]
N. J. A. Sloane, Robert G. Wilson v, Aug 01 1994
2015-12-12T04:26:39
oeisdata/seq/A007/A007673.seq
99da897d0c285120b5171aa953f992a6
A007674
Numbers m such that m and m+1 are squarefree.
[ "1", "2", "5", "6", "10", "13", "14", "21", "22", "29", "30", "33", "34", "37", "38", "41", "42", "46", "57", "58", "61", "65", "66", "69", "70", "73", "77", "78", "82", "85", "86", "93", "94", "101", "102", "105", "106", "109", "110", "113", "114", "118", "122", "129", "130", "133", "137", "138", "141", "142", "145" ]
[ "nonn", "easy" ]
49
1
2
[ "A005117", "A007674", "A013929", "A172186", "A172187" ]
[ "M1322" ]
N. J. A. Sloane, Robert G. Wilson v
2024-03-22T19:25:27
oeisdata/seq/A007/A007674.seq
855e22f4da382349609a8e93962c3800
A007675
Numbers m such that m, m+1 and m+2 are squarefree.
[ "1", "5", "13", "21", "29", "33", "37", "41", "57", "65", "69", "77", "85", "93", "101", "105", "109", "113", "129", "137", "141", "157", "165", "177", "181", "185", "193", "201", "209", "213", "217", "221", "229", "237", "253", "257", "265", "281", "285", "301", "309", "317", "321", "329", "345", "353", "357", "365", "381", "389", "393", "397", "401", "409", "417", "429", "433", "437", "445", "453" ]
[ "nonn", "easy", "nice" ]
99
1
2
[ "A005117", "A007531", "A007674", "A007675", "A008966", "A013929", "A016813", "A056911" ]
[ "M3824" ]
N. J. A. Sloane, Robert G. Wilson v
2024-07-16T12:51:39
oeisdata/seq/A007/A007675.seq
a8145b9e949f50d1781b9909973ad73c
A007676
Numerators of convergents to e.
[ "2", "3", "8", "11", "19", "87", "106", "193", "1264", "1457", "2721", "23225", "25946", "49171", "517656", "566827", "1084483", "13580623", "14665106", "28245729", "410105312", "438351041", "848456353", "14013652689", "14862109042", "28875761731", "534625820200", "563501581931", "1098127402131", "22526049624551" ]
[ "nonn", "easy", "nice", "frac" ]
67
0
1
[ "A003417", "A007676", "A007677" ]
[ "M0869" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007676.seq
c143fce89a739f0359e1d8bbcf6b3530
A007677
Denominators of convergents to e.
[ "1", "1", "3", "4", "7", "32", "39", "71", "465", "536", "1001", "8544", "9545", "18089", "190435", "208524", "398959", "4996032", "5394991", "10391023", "150869313", "161260336", "312129649", "5155334720", "5467464369", "10622799089", "196677847971", "207300647060", "403978495031", "8286870547680", "8690849042711" ]
[ "nonn", "easy", "nice", "frac" ]
63
0
3
[ "A003417", "A007676", "A007677" ]
[ "M2343" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007677.seq
9eb646867775dc0aa29c0bcb7b4991e1
A007678
Number of regions in regular n-gon with all diagonals drawn.
[ "0", "0", "1", "4", "11", "24", "50", "80", "154", "220", "375", "444", "781", "952", "1456", "1696", "2500", "2466", "4029", "4500", "6175", "6820", "9086", "9024", "12926", "13988", "17875", "19180", "24129", "21480", "31900", "33856", "41416", "43792", "52921", "52956", "66675", "69996", "82954", "86800", "102050", "97734", "124271", "129404", "149941" ]
[ "nonn", "nice" ]
155
1
4
[ "A001006", "A006522", "A006533", "A006561", "A006600", "A007569", "A007678", "A054726", "A062361", "A135565", "A187781", "A331450", "A331451", "A333654", "A335614", "A335646", "A337330" ]
[ "M3411" ]
N. J. A. Sloane, Bjorn Poonen (poonen(AT)math.princeton.edu)
2025-02-16T08:32:31
oeisdata/seq/A007/A007678.seq
12ddacb3863e15634ccdead106aef14b
A007679
If n mod 4 = 0 then 2^(n-1)+1 elif n mod 4 = 2 then 2^(n-1)-1 else 2^(n-1).
[ "1", "1", "4", "9", "16", "31", "64", "129", "256", "511", "1024", "2049", "4096", "8191", "16384", "32769", "65536", "131071", "262144", "524289", "1048576", "2097151", "4194304", "8388609", "16777216", "33554431", "67108864", "134217729", "268435456", "536870911" ]
[ "nonn", "easy", "changed" ]
37
1
3
null
[ "M3359" ]
N. J. A. Sloane, R. K. Guy, Simon Plouffe
2025-04-22T12:07:00
oeisdata/seq/A007/A007679.seq
347932f0eacc3d99c39c04435d15a052
A007680
a(n) = (2n+1)*n!.
[ "1", "3", "10", "42", "216", "1320", "9360", "75600", "685440", "6894720", "76204800", "918086400", "11975040000", "168129561600", "2528170444800", "40537905408000", "690452066304000", "12449059983360000", "236887827111936000", "4744158915944448000", "99748982335242240000" ]
[ "nonn", "easy" ]
111
0
2
[ "A007680", "A019704", "A099288", "A167546", "A167556" ]
[ "M2861" ]
N. J. A. Sloane
2025-04-02T05:16:18
oeisdata/seq/A007/A007680.seq
c1274a5713c0ca9c93faff15d4f02629
A007681
a(n) = (2*n+1)^2*n!.
[ "1", "9", "50", "294", "1944", "14520", "121680", "1134000", "11652480", "130999680", "1600300800", "21115987200", "299376000000", "4539498163200", "73316942899200", "1256675067648000", "22784918188032000", "435717099417600000" ]
[ "nonn" ]
21
0
2
null
[ "M4632" ]
N. J. A. Sloane
2023-03-26T10:27:28
oeisdata/seq/A007/A007681.seq
ce4cbbcabb76a9e6e64ac808ddc31c35
A007682
a(n) = -Sum_{k = 0..n-1} (n+k)!a(k)/(2k)!.
[ "1", "-1", "1", "1", "-1", "-17", "-107", "-415", "1231", "56671", "924365", "11322001", "97495687", "-78466897", "-31987213451", "-1073614991039", "-26754505127713", "-558657850929473", "-9259584394031075", "-70982644052430799", "3334438016903221111", "240585292388924690959", "10679411902033402697861" ]
[ "sign", "easy", "nice" ]
18
0
6
null
[ "M5044" ]
N. J. A. Sloane
2018-01-10T03:11:52
oeisdata/seq/A007/A007682.seq
4019ca3a61c41da534a7af437954cbf0
A007683
a(1) = 1; a(n) = -Sum_{k = 1..n-1} (n+k)!a(k)/(2k)!.
[ "1", "-3", "3", "9", "21", "-33", "-1173", "-13515", "-113739", "-532209", "6284379", "264830061", "5897799141", "104393462439", "1459983940203", "10308316834293", "-308010522508395", "-19576840707893409", "-726806556195360069", "-22261372611370303875", "-591210850189999983099" ]
[ "sign" ]
14
1
2
[ "A007683", "A067000" ]
[ "M2289" ]
N. J. A. Sloane
2018-01-10T03:12:00
oeisdata/seq/A007/A007683.seq
9d24753e1bd6c6d959c223b2884a27e5
A007684
Prime(n)*...*prime(a(n)) is the least product of consecutive primes that is non-deficient.
[ "2", "6", "11", "21", "35", "51", "73", "98", "130", "167", "204", "249", "296", "347", "406", "471", "538", "608", "686", "768", "855", "950", "1050", "1156", "1266", "1377", "1495", "1621", "1755", "1898", "2049", "2194", "2347", "2504", "2670", "2837", "3013", "3194", "3380", "3573", "3771", "3974", "4187", "4401", "4625", "4856" ]
[ "nonn" ]
45
1
1
[ "A002110", "A005100", "A005101", "A005231", "A007684", "A007686", "A007702", "A007707", "A064001", "A112640" ]
null
Walter Nissen
2022-07-16T14:20:31
oeisdata/seq/A007/A007684.seq
b68ca648128c05e5c1b8f120f6fa2b2e
A007685
a(n) = Product_{k=1..n} binomial(2*k,k).
[ "1", "2", "12", "240", "16800", "4233600", "3911846400", "13425456844800", "172785629592576000", "8400837310791045120000", "1552105098192510332190720000", "1094904603628138948657963991040000", "2960792853328653706847125274154762240000", "30794022150329995743434211126374020153344000000" ]
[ "nonn", "easy" ]
45
0
2
[ "A000984", "A001142", "A007685", "A112332", "A203471", "A268196", "A296589", "A296590", "A338550" ]
[ "M2047" ]
N. J. A. Sloane
2024-10-25T14:27:49
oeisdata/seq/A007/A007685.seq
c8cd453608b942419efb63558355a093
A007686
Prime(n)*...*a(n) is the least product of consecutive primes which is non-deficient.
[ "3", "13", "31", "73", "149", "233", "367", "521", "733", "991", "1249", "1579", "1949", "2341", "2791", "3343", "3881", "4481", "5147", "5849", "6619", "7499", "8387", "9341", "10321", "11411", "12517", "13709", "15013", "16363", "17881", "19381", "20873", "22369", "24007", "25763", "27611", "29399", "31357" ]
[ "nonn" ]
36
1
1
[ "A005100", "A007684", "A007686", "A007702", "A007708" ]
null
Walter Nissen
2025-03-18T07:08:46
oeisdata/seq/A007/A007686.seq
695bf40b296b1da3483ed84f2f0d54c0
A007687
Number of 4-colorings of cyclic group of order n.
[ "3", "10", "21", "44", "83", "218", "271", "692", "865", "2622", "2813", "9220", "9735", "35214", "35911", "135564", "136899", "533290", "535081" ]
[ "nonn", "more", "hard" ]
32
1
1
[ "A007687", "A007688" ]
[ "M2833" ]
N. J. A. Sloane
2024-09-26T23:37:25
oeisdata/seq/A007/A007687.seq
2ba1035688efebae2da988060799ac40
A007688
Number of 5-colorings of cyclic group of order n.
[ "4", "16", "52", "144", "420", "816", "1732", "3508", "7060", "18640" ]
[ "nonn", "more" ]
18
1
1
[ "A007687", "A007688" ]
[ "M3514" ]
N. J. A. Sloane
2022-08-26T19:55:36
oeisdata/seq/A007/A007688.seq
fa0634e34be1bed1706d95d1f68ba36a
A007689
a(n) = 2^n + 3^n.
[ "2", "5", "13", "35", "97", "275", "793", "2315", "6817", "20195", "60073", "179195", "535537", "1602515", "4799353", "14381675", "43112257", "129271235", "387682633", "1162785755", "3487832977", "10462450355", "31385253913", "94151567435", "282446313697", "847322163875" ]
[ "nonn", "easy", "nice" ]
83
0
1
[ "A000051", "A000079", "A000244", "A001550", "A007689", "A063376", "A063481", "A074600", "A074624", "A082101", "A096951" ]
[ "M1444" ]
N. J. A. Sloane, Robert G. Wilson v
2023-03-13T05:54:22
oeisdata/seq/A007/A007689.seq
cf15ba28c6b81f5512a20ab89c7bb1e8
A007690
Number of partitions of n in which no part occurs just once.
[ "1", "0", "1", "1", "2", "1", "4", "2", "6", "5", "9", "7", "16", "11", "22", "20", "33", "28", "51", "42", "71", "66", "100", "92", "147", "131", "199", "193", "275", "263", "385", "364", "516", "511", "694", "686", "946", "925", "1246", "1260", "1650", "1663", "2194", "2202", "2857", "2928", "3721", "3813", "4866", "4967", "6257", "6487", "8051", "8342", "10369" ]
[ "nonn" ]
57
0
5
[ "A000041", "A007690", "A055922", "A055923", "A100405", "A114917", "A114918", "A160974", "A160990", "A183558", "A183568" ]
[ "M0167" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A007/A007690.seq
afe62dff43c78e914594a86f09054eb3
A007691
Multiply-perfect numbers: n divides sigma(n).
[ "1", "6", "28", "120", "496", "672", "8128", "30240", "32760", "523776", "2178540", "23569920", "33550336", "45532800", "142990848", "459818240", "1379454720", "1476304896", "8589869056", "14182439040", "31998395520", "43861478400", "51001180160", "66433720320", "137438691328", "153003540480", "403031236608" ]
[ "nonn", "nice" ]
145
1
2
[ "A000203", "A000396", "A005153", "A005820", "A007358", "A007539", "A007691", "A009194", "A011775", "A017666", "A019278", "A019294", "A027687", "A046060", "A046061", "A046762", "A046763", "A046764", "A046985", "A046986", "A046987", "A047728", "A054024", "A054027", "A054030", "A055715", "A056006", "A065997", "A066135", "A066289", "A066961", "A069926", "A071707", "A076231", "A076233", "A076234", "A081756", "A082901", "A083865", "A088843", "A088844", "A088845", "A088846", "A089748", "A091443", "A093034", "A094467", "A094701", "A098203", "A098204", "A102783", "A114887", "A134639", "A134665", "A134740", "A145551", "A166069", "A166070", "A173438", "A175200", "A189000", "A194771", "A214842", "A219545", "A225110", "A226476", "A227302", "A227306", "A227470", "A229110", "A237719", "A245774", "A245775", "A245782", "A246454", "A259307", "A260508", "A262432", "A263928", "A272008", "A282775", "A295078", "A300906", "A306667", "A307740", "A307741", "A308423", "A318996", "A320024", "A323652", "A323653", "A325021", "A325022", "A325023", "A325024", "A325025", "A325026", "A325637", "A325639", "A326194", "A327158", "A330532", "A330533", "A330746", "A331724", "A332318", "A332319", "A335830", "A336702", "A336745", "A336849", "A340864", "A341045", "A341524", "A341608", "A342658", "A342659", "A342660" ]
[ "M4182" ]
N. J. A. Sloane, Robert G. Wilson v
2025-03-12T10:38:11
oeisdata/seq/A007/A007691.seq
b1b107a8152c4d60c0f5ce0c62a1c714
A007692
Numbers that are the sum of 2 nonzero squares in 2 or more ways.
[ "50", "65", "85", "125", "130", "145", "170", "185", "200", "205", "221", "250", "260", "265", "290", "305", "325", "338", "340", "365", "370", "377", "410", "425", "442", "445", "450", "481", "485", "493", "500", "505", "520", "530", "533", "545", "565", "578", "580", "585", "610", "625", "629", "650", "680", "685", "689", "697", "725", "730", "740", "745", "754", "765" ]
[ "nonn", "easy" ]
47
1
1
[ "A000404", "A001481", "A004431", "A007692", "A018825", "A025284", "A025285", "A118882" ]
[ "M5299" ]
N. J. A. Sloane.
2020-08-29T09:00:35
oeisdata/seq/A007/A007692.seq
96228c0a4ccc7afe75eb3da924dd2c3d
A007693
Primes p such that 6*p + 1 is also prime.
[ "2", "3", "5", "7", "11", "13", "17", "23", "37", "47", "61", "73", "83", "101", "103", "107", "131", "137", "151", "173", "181", "233", "241", "257", "263", "271", "277", "283", "293", "311", "313", "331", "347", "367", "373", "397", "443", "461", "467", "503", "557", "577", "593", "601", "607", "641", "653", "661", "683", "727", "751", "761", "773", "787", "797", "853" ]
[ "nonn", "easy" ]
54
1
1
[ "A002476", "A007693", "A016921", "A023256", "A024899", "A051644", "A091178" ]
[ "M0656" ]
N. J. A. Sloane and Robert G. Wilson v
2025-03-27T05:20:57
oeisdata/seq/A007/A007693.seq
b68aeb590a331e17b4428d538294095e
A007694
Numbers k such that phi(k) divides k.
[ "1", "2", "4", "6", "8", "12", "16", "18", "24", "32", "36", "48", "54", "64", "72", "96", "108", "128", "144", "162", "192", "216", "256", "288", "324", "384", "432", "486", "512", "576", "648", "768", "864", "972", "1024", "1152", "1296", "1458", "1536", "1728", "1944", "2048", "2304", "2592", "2916", "3072", "3456", "3888", "4096", "4374", "4608", "5184", "5832", "6144", "6912", "7776", "8192", "8748", "9216" ]
[ "nonn", "nice", "easy" ]
108
1
2
[ "A000010", "A001221", "A003557", "A003586", "A007694", "A007947", "A023200", "A033950", "A049237", "A068997", "A235353" ]
[ "M0992" ]
N. J. A. Sloane, Robert G. Wilson v
2024-08-03T07:10:11
oeisdata/seq/A007/A007694.seq
8c55c8547cc431dcea9fe025289f0e3d
A007695
Cardinalities of Sperner families on 1,...,n.
[ "2", "3", "5", "10", "26", "96", "553", "5461", "100709", "3718354", "289725509", "49513793526", "19089032278261", "16951604697397302", "35231087224279091310", "173550485517380958360611", "2047581288200721764035942914" ]
[ "nonn", "nice" ]
28
0
1
[ "A001405", "A007695", "A011828", "A011833" ]
[ "M2466" ]
N. J. A. Sloane, Don Knuth
2023-11-29T11:41:41
oeisdata/seq/A007/A007695.seq
eb7af91acc1a9bd7324954637712758b
A007696
Quartic (or 4-fold) factorial numbers: a(n) = Product_{k = 0..n-1} (4*k + 1).
[ "1", "1", "5", "45", "585", "9945", "208845", "5221125", "151412625", "4996616625", "184874815125", "7579867420125", "341094033905625", "16713607661375625", "885821206052908125", "50491808745015763125", "3080000333445961550625", "200200021673987500790625", "13813801495505137554553125" ]
[ "nonn", "easy" ]
138
0
3
[ "A001147", "A001813", "A004981", "A007559", "A007696", "A008545", "A034255", "A047053", "A049029", "A051142", "A264781" ]
[ "M4001" ]
N. J. A. Sloane
2025-03-07T09:36:58
oeisdata/seq/A007/A007696.seq
140038f61a1746cc9709ba58b3577c51
A007697
Smallest odd number expressible in at least n ways as p+2*m^2 where p is 1 or a prime and m >= 0.
[ "1", "3", "13", "19", "55", "61", "139", "139", "181", "181", "391", "439", "559", "619", "619", "829", "859", "1069", "1081", "1459", "1489", "1609", "1741", "1951", "2029", "2341", "2341", "3331", "3331", "3331", "3961", "4189", "4189", "4261", "4801", "4801", "5911", "5911", "5911", "6319", "6319", "6319", "8251", "8251", "8251", "8251", "8251" ]
[ "nonn", "nice", "easy" ]
42
1
2
[ "A007697", "A016067", "A046921" ]
[ "M2292" ]
N. J. A. Sloane
2023-08-05T06:26:29
oeisdata/seq/A007/A007697.seq
da72c4e718da796be8900f4cd8aad2fc
A007698
a(n) = 22*a(n-1) - 3*a(n-2) + 18*a(n-3) - 11*a(n-4). Deviates from A007699 at the 1403rd term.
[ "10", "219", "4796", "105030", "2300104", "50371117", "1103102046", "24157378203", "529034393290", "11585586272312", "253718493496142", "5556306986017175", "121680319386464850", "2664737596978110299", "58356408797678883616" ]
[ "nonn", "easy" ]
47
1
1
[ "A007698", "A007699" ]
[ "M4746" ]
N. J. A. Sloane and J. H. Conway
2025-01-05T19:51:34
oeisdata/seq/A007/A007698.seq
f6f75dc50e6dd52e11a6c55f4b1f4a71
A007699
Pisot sequence E(10,219): a(n) = nearest integer to a(n-1)^2 / a(n-2), starting 10, 219, ... Deviates from A007698 at 1403rd term.
[ "10", "219", "4796", "105030", "2300104", "50371117", "1103102046", "24157378203", "529034393290", "11585586272312", "253718493496142", "5556306986017175", "121680319386464850", "2664737596978110299", "58356408797678883616", "1277975907130111287030", "27987027523701766535844" ]
[ "nonn" ]
65
1
1
[ "A007698", "A007699", "A008776" ]
[ "M4747" ]
N. J. A. Sloane and J. H. Conway
2022-01-01T14:05:42
oeisdata/seq/A007/A007699.seq
afde9bd0e01294c115156fe8eb8ba651
A007700
Numbers n such that n, 2n+1, and 4n+3 all prime.
[ "2", "5", "11", "41", "89", "179", "359", "509", "719", "1019", "1031", "1229", "1409", "1451", "1481", "1511", "1811", "1889", "1901", "1931", "2459", "2699", "2819", "3449", "3491", "3539", "3821", "3911", "5081", "5399", "5441", "5849", "6101", "6131", "6449", "7079", "7151", "7349", "7901", "8969", "9221", "10589", "10691", "10709", "11171" ]
[ "nonn" ]
68
1
1
[ "A005384", "A005385", "A005602", "A007700", "A023213", "A023272", "A023302", "A023330", "A057331" ]
[ "M1406" ]
N. J. A. Sloane, Simon Plouffe
2022-09-12T07:59:10
oeisdata/seq/A007/A007700.seq
f04f2f5d217550ce7c1c0d2a6248c33d