# A004999
## Sums of two nonnegative cubes.

### DATA
```text
0, 1, 2, 8, 9, 16, 27, 28, 35, 54, 64, 65, 72, 91, 125, 126, 128, 133, 152, 189, 216, 217, 224, 243, 250, 280, 341, 343, 344, 351, 370, 407, 432, 468, 512, 513, 520, 539, 559, 576, 637, 686, 728, 729, 730, 737, 756, 793, 854, 855, 945, 1000, 1001
```

### PYTHON IMPLEMENTATION
*No Python implementation recorded in the local database yet.*

### PROGRAMS
#### Mathematica
```mathematica
Union[(#[[1]]^3+#[[2]]^3)&/@Tuples[Range[0,20],{2}]] (* _Harvey P. Dale_, Dec 04 2010 *)
```

#### Other Programs
- **(PARI)** :
```pari
is(n)=my(k1=ceil((n-1/2)^(1/3)), k2=floor((4*n+1/2)^(1/3)), L); fordiv(n,d,if(d>=k1 && d<=k2 && denominator(L=(d^2-n/d)/3)==1 && issquare(d^2-4*L), return(1))); 0
list(lim)=my(v=List());for(x=0,(lim+.5)^(1/3),for(y=0,min(x,(lim-x^3)^(1/3)),listput(v,x^3+y^3))); vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Jun 12 2012
```
- **(PARI)** :
```pari
is(n)=my(L=sqrtnint(n-1,3)+1,U=sqrtnint(4*n,3));fordiv(n,m,if(L<=m&m<=U,my(ell=(m^2-n/m)/3);if(denominator(ell)==1&&issquare(m^2-4*ell),return(1))));0 \\ _Charles R Greathouse IV_, Apr 16 2013
```
- **(PARI)** :
```pari
T=thueinit('z^3+1);
is(n)=n==0 || #select(v->min(v[1],v[2])>=0, thue(T,n))>0 \\ _Charles R Greathouse IV_, Nov 29 2014
```
- **(Haskell)** :
```haskell
a004999 n = a004999_list !! (n-1)
a004999_list = filter c2 [1..] where
   c2 x = any (== 1) $ map (a010057 . fromInteger) $
                       takeWhile (>= 0) $ map (x -) $ tail a000578_list
-- _Reinhard Zumkeller_, Dec 20 2013
```

### LINKS
- T. D. Noe, [Table of n, a(n) for n = 1..1000](https://oeis.org/A004999/b004999.txt)
- Kevin A. Broughan, [Characterizing the sum of two cubes](http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Broughan/broughan25.html), J. Integer Seqs., Vol. 6, 2003.
- Samuel S. Wagstaff, Jr., [Equal Sums of Two Distinct Like Powers](https://cs.uwaterloo.ca/journals/JIS/VOL25/Wagstaff/wagstaff8.html), J. Int. Seq., Vol. 25 (2022), Article 22.3.1.
- [Index entries for sequences related to sums of cubes](https://oeis.org/index/Su#ssq)

### CROSSREFERENCES
- Subsequence of [A045980](A045980); [A003325](A003325) is a subsequence.
- Cf. [A000578](A000578), [A004825](A004825), [A010057](A010057), [A373972](A373972) (characteristic function).
- Indices of nonzero terms in [A025446](A025446).
- See also the official entry at <https://oeis.org/A004999>

### METADATA
- **OFFSET** : `1,3`
- **KEYWORDS** : `nonn,easy,nice`
- **AUTHOR** : [_N. J. A. Sloane_](https://oeis.org/wiki/User:N._J._A._Sloane), [_Steven Finch_](https://oeis.org/wiki/User:Steven_Finch)
- **IDENTIFICATION** : `#41 Jul 02 2024 07:23:35`