A004999 Sums of two nonnegative cubes.

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

Offset

1,3

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Kevin A. Broughan, Characterizing the sum of two cubes, J. Integer Seqs., Vol. 6, 2003.

Samuel S. Wagstaff, Jr., Equal Sums of Two Distinct Like Powers, J. Int. Seq., Vol. 25 (2022), Article 22.3.1.

Index entries for sequences related to sums of cubes

Mathematica

Union[(#[[1]]^3+#[[2]]^3)&/@Tuples[Range[0, 20], {2}]] (* Harvey P. Dale, Dec 04 2010 *)

Prog

(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) 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) 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)
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

Crossrefs

Subsequence of A045980; A003325 is a subsequence.

Cf. A000578, A004825, A010057

Sequence in context: A226825 A367984 A046679 * A105125 A230314 A220263

Adjacent sequences: A004996 A004997 A004998 * A005000 A005001 A005002

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Steven Finch

Status

approved