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

Author

N. J. A. Sloane, Steven Finch

Keywords

• nonn
• easy
• nice

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

Crossrefs

Subsequence of A045980; A003325 is a subsequence.

Cf. A000578, A004825, A010057, A373972 (characteristic function).

Indices of nonzero terms in A025446.

Programs

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

Mathematica

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

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