A005988 x^3 + n*y^3 = 1 is solvable. (Formerly M1732)

2, 7, 9, 17, 19, 20, 26, 28, 37, 43, 63, 65, 91, 124, 126, 182, 215, 217, 254, 342, 344, 422, 511, 513, 614, 635, 651, 728, 730, 813, 999, 1001, 1330, 1332, 1521, 1588, 1657, 1727, 1729, 1801, 1876, 1953, 2196, 2198, 2743, 2745, 3155, 3374, 3376

Offset

1,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. C. Williams and C. R. Zarnke, Computation of the solutions of the Diophantine equation x^3+dy^3=1, Proc. Conf. Numerical Maths., Winnipeg (1971), 671-676.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..135

István Gaál, László Remete, Solving binomial Thue equations, arXiv:1810.01819 [math.NT], 2018. See 4.1 Solutions for n = 3 p. 6.

H. C. Williams and C. R. Zarnke, Computation of the solutions of the Diophantine equation x^3+dy^3=1, Proc. Conf. Numerical Maths., Winnipeg (1971), 671-676. (Annotated scanned copy)

H. C. Williams and R. Holte, Computation of the solution of x^3 + D y^3 = 1, Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 778-785.

Mathematica

m = 400; s = {}; Do[If[x*y < 0, r = Reduce[ n > 0 && x^3 + n*y^3 == 1, n, Integers]; If[r =!= False, AppendTo[s, n /. ToRules[r]]]], {x, -m, m}, {y, -m, m}]; Union[s] [[1 ;; 38]] (* Jean-François Alcover, Jun 08 2011 *)

Crossrefs

Cf. A055735, A259453.

Sequence in context: A042345 A041973 A042807 * A199537 A079326 A055673

Adjacent sequences: A005985 A005986 A005987 * A005989 A005990 A005991

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 17 2016

Status

approved