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Search: id:A165721
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| A165721 |
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Integers of the form k*(k+13)/12. |
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+0
1
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| 4, 14, 22, 25, 35, 55, 69, 74, 90, 120, 140, 147, 169, 209, 235, 244, 272, 322, 354, 365, 399, 459, 497, 510, 550, 620, 664, 679, 725, 805, 855, 872, 924, 1014, 1070, 1089, 1147, 1247, 1309, 1330, 1394, 1504, 1572, 1595, 1665, 1785, 1859, 1884, 1960, 2090
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OFFSET
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1,1
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COMMENT
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Integers of the form k+k*(k+1)/12 = k+A000217(k)/6 (see A069497). - R. J. Mathar, Sep 25 2009
Are all terms composite numbers?
Contribution from Zak Seidov (zakseidov(AT)yahoo.com), Sep 25 2009: (Start)
Integers of form n(13+n)/12, n=0,1,2,...
Each four terms of the sequence are composite numbers of forms:
{(4+3 m) (1+4 m), (2+3 m) (7+4 m), (2+m) (11+12 m), m (13+12 m)}, m=0,1,2,...
m=0: {4,14,22,25}; m=1: {35,55,69,74}; m=2: {90,120,140,147}, etc. (End)
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FORMULA
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a(n)= 3*a(n-1) -5*a(n-2) +7*a(n-3) -7*a(n-4) +5*a(n-5) -3*a(n-6) +a(n-7). - R. J. Mathar, Sep 25 2009
G.f.: x*(-4-2*x-x^3+x^5)/((x^2+1)^2*(x-1)^3). - R. J. Mathar, Sep 25 2009
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MATHEMATICA
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q=6; s=0; lst={}; Do[s+=((n+q)/q); If[IntegerQ[s], AppendTo[lst, s]], {n, 6!}]; lst
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CROSSREFS
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Cf. A165717, A165718, A165719, A165720.
Sequence in context: A051448 A075319 A030470 this_sequence A051806 A034051 A044437
Adjacent sequences: A165718 A165719 A165720 this_sequence A165722 A165723 A165724
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 24 2009
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EXTENSIONS
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Definition simplified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 25 2009
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