A001474 w such that w^3+x^3+y^3+z^3=0, w>|x|>|y|>|z|, is soluble.

6, 9, 12, 16, 19, 20, 25, 27, 28, 29, 34, 39, 40, 41, 44, 46, 51, 53, 54, 55, 58, 60, 67, 69, 70, 71, 72, 75, 76, 80, 81, 82, 84, 85, 87, 88, 89, 90, 93, 94, 96, 97, 98, 99, 102, 103, 105, 108, 109, 110, 111, 113, 115, 116, 120, 121, 122, 123, 126, 127, 129, 132, 134, 137, 139

Offset

1,1

References

J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780, see p. 799.

H. W. Richmond, On integers which satisfy ..., Trans. Camb. Phil. Soc., 22 (1920), 389-403, see p. 402.

Links

Table of n, a(n) for n=1..65.

Mathematica

sol[w_] := Reap[ Do[ If[ GCD[w, x, y, z] == 1 && w > Abs[x] > Abs[y] > Abs[z] && w^3 + x^3 + y^3 + z^3 == 0, Print[{w, x, y, z}]; Sow[{w, x, y, z}]; Break[]], {x, -w+1, -1}, {y, x+1, -1}, {z, y+1, -y-1}]][[2]]; Select[ Range[140], sol[#] =!= {} & ] (* Jean-François Alcover, Feb 24 2012 *)

Crossrefs

Cf. A001235.

Sequence in context: A343043 A343047 A023040 * A084806 A020938 A136360

Adjacent sequences: A001471 A001472 A001473 * A001475 A001476 A001477

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

Status

approved