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A245035
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a(n) = (prime(n) - 7)^2 * (4*prime(n) - 1).
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2
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175, 176, 76, 0, 688, 1836, 6700, 10800, 23296, 55660, 70848, 132300, 188428, 221616, 299200, 446476, 635440, 708588, 961200, 1159168, 1267596, 1632960, 1911856, 2387020, 3134700, 3560908, 3787776, 4270000, 4525740, 5067436, 7300800, 8041648, 9244300
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OFFSET
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1,1
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COMMENTS
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The discriminant D of the Cardano Tartaglia equation x^3 + p*x + q = 0 is written -D = 27*q^2 + 4*p^3. Let q = p = prime(n) - 7 then -D = 27*(prime(n) - 7)^2 + 4*(prime(n) - 7)^3 = (prime(n)-7)^2 * ( 4*(prime(n) - 7) + 27 ) = (prime(n) - 7)^2 * (4* prime(n) - 4*7 + 27) = (7 - prime(n))^2 * (4* prime(n) - 1) = a(n).
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LINKS
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FORMULA
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a(n) = 27*(prime(n) - 7)^2 + 4*(prime(n) - 7)^3.
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EXAMPLE
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a(1) = (2 - 7)^2*(4*2 - 1) = 25*7 = 175.
a(4) = (7 - 7)^2*(4*7 - 1) = 0.
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MATHEMATICA
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PROG
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(Magma) [4*p^3-57*p^2+210*p-49: p in PrimesUpTo(200)]; // Bruno Berselli, Jul 31 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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