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A045980
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Numbers of the form x^3 + y^3 or x^3 - y^3.
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11
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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)
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OFFSET
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1,3
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 86.
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LINKS
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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
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EXAMPLE
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7 = (2)^3 + (-1)^3.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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