A004999 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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, A373972 (characteristic function).

Indices of nonzero terms in A025446.