PROG
(MAGMAMagma) [6*n^3+1 : n in [1..50]]; // Wesley Ivan Hurt, Jan 09 2017
The OEIS is supported by the many generous donors to the OEIS Foundation.
(MAGMAMagma) [6*n^3+1 : n in [1..50]]; // Wesley Ivan Hurt, Jan 09 2017
proposed
approved
editing
proposed
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.
It is easy to check that with x = 6n^2, y = 6n^3 - 1, and this z = 6n^3 + 1, it satisfies the Diophantine equation x^3 + y^3 = z^3 - 2. Thus these are near-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.
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.
proposed
editing
editing
proposed
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.
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]
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.
A163827:=n->6*n^3+1: seq(A163827(n), n=1..50); # Wesley Ivan Hurt, Jan 09 2017
(MAGMA) [6*n^3+1 : n in [1..50]]; // Wesley Ivan Hurt, Jan 09 2017
approved
editing
editing
approved
<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
approved
editing
editing
approved