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 A045980 Numbers of the form x^3 + y^3 or x^3 - y^3. 12
 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 COMMENTS Sums of two integer cubes. - Charles R Greathouse IV, Mar 30 2022 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. M. Kim, Diophantine equations in two variables Index entries for sequences related to sums of cubes 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 \\ Charles R Greathouse IV, Jun 12 2012 (PARI) list(lim)={ my(v=List(), x3, t); for(x=0, sqrtnint(lim\=1, 3), x3=x^3; for(y=0, min(sqrtnint(lim-x3, 3), x), listput(v, x3+y^3) ) ); for(x=2, t=sqrtint(lim\3), x3=x^3; for(y=sqrtnint(max(0, x3-lim-1), 3)+1, x-1, listput(v, x3-y^3) ) ); t=(t+1)^3-t^3; if(t<=lim, listput(v, t)); Set(v); } \\ Charles R Greathouse IV, Jun 12 2012, updated Jan 13 2022 (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 A004999 and A003325 are subsequences. Cf. A222304, A222305, A222306, A027750, A010052. Sequence in context: A037455 A020675 A317303 * A104339 A199004 A168064 Adjacent sequences: A045977 A045978 A045979 * A045981 A045982 A045983 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane STATUS approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)