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 A163827 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA 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] EXAMPLE 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. MATHEMATICA 6*Range[40]^3+1 (* or *) LinearRecurrence[{4, -6, 4, -1}, {7, 49, 163, 385}, 40] (* From Harvey P. Dale, Dec 12 2011 *) CROSSREFS Cf. A050787, A050791. Sequence in context: A044145 A152777 A003530 * A206989 A221962 A015953 Adjacent sequences:  A163824 A163825 A163826 * A163828 A163829 A163830 KEYWORD nonn AUTHOR Carlos Alves (cjsalves(AT)gmail.com), Aug 05 2009 STATUS approved

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