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%I #22 Apr 14 2019 14:05:18
%S 0,2,7,9,16,19,26,28,35,37,54,56,61,63,65,72,91,98,117,124,126,127,
%T 128,133,152,169,189,208,215,217,218,224,243,250,271,279,280,296,316,
%U 331,335,341,342,344,351,370,386,387,397,407,432,448,468,469
%N Nonnegative numbers that are sums of two nonzero cubes.
%C From _Michael B. Porter_, Oct 16 2009: (Start)
%C 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.
%C There are no cubes in this sequence, but the numbers before and after a cube are all included. (End)
%H Charles R Greathouse IV, <a href="/A020894/b020894.txt">Table of n, a(n) for n = 1..10000</a>
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/csolve/fermat.pdf">On a Generalized Fermat-Wiles Equation</a> [broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010602030546/http://www.mathsoft.com/asolve/fermat/fermat.html">On a Generalized Fermat-Wiles Equation</a> [From the Wayback Machine]
%e From _Michael B. Porter_, Oct 16 2009: (Start)
%e 7 is in the sequence because 2^3 + (-1)^3 = 7
%e 8 is not in the sequence because the only solutions to x^3 + y^3 = 8 have either x=0 or y=0. (End)
%t 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 *)
%o (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
%o (PARI) T=thueinit('z^3+1);
%o is(n)=n==0 || #select(v->v[1] && v[2], thue(T, n))>0 \\ _Charles R Greathouse IV_, Nov 29 2014
%Y Cf. A045980 [From _Michael B. Porter_, Oct 16 2009]
%K nonn
%O 1,2
%A _Steven Finch_
%E Definition and offset edited by _N. J. A. Sloane_, Dec 01 2009
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