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A336166 Values z of primitive solutions (x, y, z) to the Diophantine equation x^3 + y^3 + 2*z^3 = 2. 0
0, 1, -3, 4, 9, -12, 16, 25, -27, -35, 36, 37, -48, 49, -59, 64, -75, 81, 100, -108, 121, 144, -147, -159, 169, 172, -192, 196, 225, -227, -243, -255, 256, 261, -287, 289, -300, -311, 324, -335, 361, -363, 373, 400, -432, 441, 484, -507, 529, 568, 576, -588 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Terms are arranged in order of increasing absolute value (if equal, the negative number comes first).

Segre shows that 1-(9/2)*A000578(2n), (-3)*A000290(n), and A016754(n) are terms of the sequence.

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, D5.

LINKS

Table of n, a(n) for n=1..52.

Beniamino Segre, On the rational solutions of homogeneous cubic equations in four variables, Math. Notae, 11 (1951), 1-68.

EXAMPLE

(-5)^3 + (-11)^3 + 2 * 9^3 = 2, 9 is a term.

(25)^3 + (-23)^3 + 2 * (-12)^3 = 2, -12 is a term.

MATHEMATICA

t1 = Union[Plus@@@Tuples[Range[-11643, 11643]^3, 2]];

t2 = Table[2 - 2z^3, {z, -588, 588}];

t = Select[t1, MemberQ[t2, #] &];

u = ((2 - t)/2)^(1/3) /. (-1)^(1/3) -> (-1);

v = Table[(-1)^n*Floor[(n + 1)/2], {n, 0, 1176}];

Select[v, MemberQ[u, #] &]

CROSSREFS

Cf. A000290, A000578, A004825, A004826, A016754, A028387, A050791, A130472, A195006.

Sequence in context: A155564 A105137 A243185 * A230781 A025613 A097063

Adjacent sequences:  A336163 A336164 A336165 * A336167 A336168 A336169

KEYWORD

sign

AUTHOR

XU Pingya, Jul 10 2020

STATUS

approved

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Last modified June 13 03:22 EDT 2021. Contains 344980 sequences. (Running on oeis4.)