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Search: id:A114557
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| A114557 |
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Sequence of cubics with two integer coefficients that give three real roots basaed on the square roots of a prime and negative two as a root. |
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+0
2
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| 2, 5, 4, 6, 8, 8, 12, 10, 20, 14, 24, 16, 32, 20, 36, 22, 44, 26, 56, 32, 60, 34, 72, 40, 80, 44, 84, 46, 92, 50, 104, 56, 116, 62, 120, 64, 132, 70, 140, 74, 144, 76, 156, 82, 164, 86, 176, 92, 192, 100, 200, 104, 204, 106, 212, 110, 216, 112, 224, 116, 252, 130, 260, 134
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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An earlier characteristic polynomial used in a vector Markov had this form of three real roots to a cubic equation. These form a special sequence of cubic equations with integer coefficients: b = Table[Expand[(x + 2)(x - (1 + Sqrt[Prime[n]]))*(x - (1 - Sqrt[Prime[n]]))], {n, 1, 50}]
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FORMULA
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Weierstrass elliptic form of a cubic: y^2 =4*x^3-g2[n]*x-g3[n] a(n) = {g3[n]/4,g2[n]/4}
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MATHEMATICA
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a = Flatten[Table[Abs[Coefficient[Expand[(x + 2)(x - (1 + Sqrt[Prime[n]]))*(x - (1 - Sqrt[Prime[n]]))], x, m]], {n, 1, 50}, {m, 0, 1}]]
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CROSSREFS
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Sequence in context: A163809 A075771 A132698 this_sequence A085347 A066337 A129491
Adjacent sequences: A114554 A114555 A114556 this_sequence A114558 A114559 A114560
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 15 2006
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