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A163827
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a(n)=6n^3+1, solution z in Diophantine equation x^3+y^3=z^3-2. It may be considered a Fermat near miss by 2.
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1
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7, 49, 163, 385, 751, 1297, 2059, 3073, 4375, 6001, 7987, 10369, 13183, 16465, 20251, 24577, 29479, 34993, 41155, 48001, 55567, 63889, 73003, 82945, 93751, 105457, 118099, 131713, 146335, 162001, 178747, 196609, 215623, 235825, 257251, 279937
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OFFSET
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1,1
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COMMENTS
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It is easy to check that with x=6n^2, y=6n^3-1, and this z=6n^3+1, it verifies the Diophantine equation x^3+y^3=z^3-2. Thus these are almost misses for Fermat equation.
For n>2, it seems to be the only solution of x^n+y^n=z^n-2 (or even that differ by 2 from FLT, see A050787 and A050791 for solutions that differ by 1). As 2 is not a cube, these solutions are not included in the theory for x^3+y^3=u^3+v^3.
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n)=6n^3+1.
a(1)=7, a(2)=49, a(3)=163, a(4)=385, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4) [From Harvey P. Dale, Dec 12 2011]
G.f.: (-x^3+9*x^2+21*x+7)/(x-1)^4 [From Harvey P. Dale, Dec 12 2011]
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EXAMPLE
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For n=1, a(1)=7 and 7^3-2(=341)=5^3+6^3.
For n=2, a(2)=49 and 49^3-2(=117647)=24^3+47^3.
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MATHEMATICA
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6*Range[40]^3+1 (* or *) LinearRecurrence[{4, -6, 4, -1}, {7, 49, 163, 385}, 40] (* From Harvey P. Dale, Dec 12 2011 *)
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CROSSREFS
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Cf. A050787, A050791.
Sequence in context: A044145 A152777 A003530 * A206989 A221962 A015953
Adjacent sequences: A163824 A163825 A163826 * A163828 A163829 A163830
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KEYWORD
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nonn
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Aug 05 2009
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STATUS
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approved
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