A020894 Nonnegative numbers that are sums of two nonzero cubes.

0, 2, 7, 9, 16, 19, 26, 28, 35, 37, 54, 56, 61, 63, 65, 72, 91, 98, 117, 124, 126, 127, 128, 133, 152, 169, 189, 208, 215, 217, 218, 224, 243, 250, 271, 279, 280, 296, 316, 331, 335, 341, 342, 344, 351, 370, 386, 387, 397, 407, 432, 448, 468, 469

Offset

1,2

Comments

From Michael B. Porter, Oct 16 2009: (Start)

When calculating terms, there is no need to search beyond a value x defined by x^3 - (x-1)^3 = n. The positive solution is given by x = 1/2 + (sqrt(12n-3))/6.

There are no cubes in this sequence, but the numbers before and after a cube are all included. (End)

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]

Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]

Example

From Michael B. Porter, Oct 16 2009: (Start)
7 is in the sequence because 2^3 + (-1)^3 = 7
8 is not in the sequence because the only solutions to x^3 + y^3 = 8 have either x=0 or y=0. (End)

Mathematica

Reap[For[n = 0, n < 500, n++, fi = FindInstance[x > 0 && y != 0 && n == x^3 + y^3, {x, y}, Integers, 1]; If[fi =!= {}, Print[n, " = ", Hold[x^3 + y^3] /. fi[[1]]]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 05 2016 *)

Prog

(PARI) isA020894(n) = {r=0; x=1.0/2+sqrt(12*n-3.0)/6; for(i=1, floor(x), if(ispower(n-i^3, 3) & (n != i^3), r++)); r>0}; \\ Michael B. Porter, Oct 16 2009
(PARI) T=thueinit('z^3+1);
is(n)=n==0 || #select(v->v[1] && v[2], thue(T, n))>0 \\ Charles R Greathouse IV, Nov 29 2014

Crossrefs

Cf. A045980 [From Michael B. Porter, Oct 16 2009]

Sequence in context: A098017 A225675 A185869 * A165995 A287575 A267212

Adjacent sequences: A020891 A020892 A020893 * A020895 A020896 A020897

Keyword

nonn

Author

Steven Finch

Extensions

Definition and offset edited by N. J. A. Sloane, Dec 01 2009

Status

approved