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 A045980 Numbers of the form x^3 + y^3 or x^3 - y^3. 11
 0, 1, 2, 7, 8, 9, 16, 19, 26, 27, 28, 35, 37, 54, 56, 61, 63, 64, 65, 72, 91, 98, 117, 124, 125, 126, 127, 128, 133, 152, 169, 189, 208, 215, 216, 217, 218, 224, 243, 250, 271, 279, 280, 296, 316, 331, 335, 341, 342, 343, 344, 351, 370, 386, 387, 397, 407, 432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 86. 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. EXAMPLE 7 = (2)^3 + (-1)^3. MATHEMATICA Union[Select[Sort[Flatten[Table[{j^3-i^3, j^3+i^3}, {i, 0, 20}, {j, i, 20}]]], #<20^3-19^3&]] With[{nn=20}, Take[Union[Select[Flatten[{Total[#], #[[1]]-#[[2]]}&/@(Tuples[ Range[0, nn], 2]^3)], #>-1&]], 3*nn]] (* Harvey P. Dale, Jun 22 2014 *) PROG (PARI) is(n)=fordiv(n, d, my(L=(d^2-n/d)/3); if(denominator(L)==1 && issquare(d^2-4*L), return(1))); 0 list(lim)={     my(v=List(), X, t);     for(x=0, (lim+1/2)^(1/3),         X=x^3;         for(y=0, min(x, (lim+1/2-X)^(1/3)),             listput(v, X+y^3)         )     );     for(x=2, t=sqrtint(lim\3),         X=x^3;         for(y=ceil((max(1, X-lim))^(1/3)), x-1,             listput(v, X-y^3)         )     );     t=(t+1)^3-t^3;     if(t<=lim, listput(v, t));     vecsort(Vec(v), , 8) }; \\ Charles R Greathouse IV, Jun 12 2012 (PARI) is(n)=#thue(thueinit(z^3+1), n) \\ Ralf Stephan, Oct 18 2013 (Haskell) a045980 n = a045980_list !! (n-1) a045980_list = 0 : filter f [1..] where    f x = g \$ takeWhile ((<= 4 * x) . (^ 3)) \$ a027750_row x where      g [] = False      g (d:ds) = r == 0 && a010052 (d ^ 2 - 4 * y) == 1 || g ds        where (y, r) = divMod (d ^ 2 - div x d) 3 -- Reinhard Zumkeller, Dec 20 2013 CROSSREFS Cf. A222304, A222305, A222306, A027750, A010052, A004999, A003325. Sequence in context: A037455 A020675 A317303 * A104339 A199004 A168064 Adjacent sequences:  A045977 A045978 A045979 * A045981 A045982 A045983 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)