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Search: id:A165718
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| A165718 |
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Integers of the form k*(k+7)/6. |
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+0
4
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| 3, 5, 10, 13, 20, 24, 33, 38, 49, 55, 68, 75, 90, 98, 115, 124, 143, 153, 174, 185, 208, 220, 245, 258, 285, 299, 328, 343, 374, 390, 423, 440, 475, 493, 530, 549, 588, 608, 649, 670, 713, 735, 780, 803, 850, 874, 923, 948, 999, 1025, 1078, 1105, 1160, 1188
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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)/6 = k+A000217(k)/3; for k see A007494, for A000217(k)/3 see A001318 - R. J. Mathar, Sep 25 2009
Only 3 terms are prime numbers (3,5,13). Are all the rest composite?
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FORMULA
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a(n)= a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5) - R. J. Mathar, Sep 25 2009
G.f.: x*(-3-2*x+x^2+x^3)/((1+x)^2 * (x-1)^3 ). - R. J. Mathar, Sep 25 2009
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EXAMPLE
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For k=1, 2,3,.. k*(k+7)/6 is 4/3, 3, 5, 22/3, 10, 13, 49/3, 20, 24, 85/3, 33,.., and the integer values out of these become the sequence.
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MATHEMATICA
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q=3; 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
Sequence in context: A007557 A034746 A080931 this_sequence A031878 A160792 A137395
Adjacent sequences: A165715 A165716 A165717 this_sequence A165719 A165720 A165721
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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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