OFFSET
1,2
COMMENTS
Terms are arranged in order of increasing absolute value (if equal, the negative number comes first).
(5 - 4*n^2)^3 + (5 - 4*(n + 1)^2)^3 + 2*(2*n + 1)^6 = 128. A000290(2*n + 1) are terms of the sequence, i.e., there is an infinity of nontrivial solutions to the equation.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, D5.
EXAMPLE
1^3 + 5^3 + 2 * 1^3 = 128, 1 is a term.
(-11)^3 + (-31)^3 + 2 * (25)^3 = 128, 25 is a term.
MATHEMATICA
Clear[t]
t = {};
Do[y = (128 - x^3 - 2 z^3)^(1/3) /. (-1)^(1/3) -> -1; If[IntegerQ[y] && GCD[x, y, z] == 1, AppendTo[t, z]], {z, -4761, 4761}, {x, -11550, 11550}]
u = Union@t;
v = Table[(-1)^n*Floor[(n + 1)/2], {n, 0, 9523}];
Select[v, MemberQ[u, #] &]
CROSSREFS
KEYWORD
sign
AUTHOR
XU Pingya, Jul 12 2020
STATUS
approved