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Search: id:A003325
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| A003325 |
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Numbers that are the sum of 2 positive cubes. |
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+0
37
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| 2, 9, 16, 28, 35, 54, 65, 72, 91, 126, 128, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 351, 370, 407, 432, 468, 513, 520, 539, 559, 576, 637, 686, 728, 730, 737, 756, 793, 854, 855, 945, 1001, 1008, 1024, 1027, 1064, 1072, 1125, 1216, 1241, 1332, 1339, 1343
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It is conjectured that this sequence and A052276 have infinitely many numbers in common, although only one example (128) is known.
A119976 is a subsequence; if m is a term then m+k^3 is a term of A003072 for all k>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 03 2006
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REFERENCES
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F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 (1998), 61-88.
Nils Bruin, On powers as sums of two cubes, in Algorithmic number theory (Leiden, 2000), 169-184, Lecture Notes in Comput. Sci., 1838, Springer, Berlin, 2000.
C. G. J. Jacobi, Gesammelte Werke, vol. 6, 1969, Chelsea, NY, p. 354.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
C. G. J. Jacobi, Gesammelte Werke.
D. Tournes, A Glance on Indian Mathematician Srinivasa Ramanujan(1887-1920). [Text in French]
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to sums of cubes
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FORMULA
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Comment from James Buddenhagen, Oct 16 2008: (i) N and N+1 are both the sum of two positive cubes if N=2*(2*n^2+4*n+1)*(4*n^4+16*n^3+23*n^2+14*n+4), n=1,2,.... (ii) For integer n >= 2, let N = 16*n^6-12*n^4+6*n^2-2, so N+1 = 16*n^6-12*n^4+6*n^2-1. Then the identities 16*n^6-12*n^4+6*n^2-2 = (2*n^2-n-1)^3 + (2*n^2+n-1)^3 16*n^6-12*n^4+6*n^2-1 = (2*n^2)^3 + (2*n^2-1)^3 show that N, N+1 are in the sequence.
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MATHEMATICA
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Union[Flatten[Table[Table[n^3 + m^3, {m, 1, n}], {n, 1, 15}]]] - Roger L. Bagula, Oct 16 2008
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PROGRAM
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(PARI) cubes=sum(n=1, 11, x^(n^3), O(x^1400)); print(cubes^2)
(PARI) isA003325(n) = for( k=1, sqrtn(n\2, 3), round(sqrtn(n-k^3, 3))^3+k^3==n & return(1)) [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 17 2008]
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CROSSREFS
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Cf. A003072, A001235, A011541, A003826.
Cf. A085323 (n such that a(n+1)=a(n)+1). [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 17 2008]
Sequence in context: A011193 A085960 A051386 this_sequence A101420 A097965 A075645
Adjacent sequences: A003322 A003323 A003324 this_sequence A003326 A003327 A003328
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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 (njas(AT)research.att.com).
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EXTENSIONS
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Error in formula line corrected by Zak Seidov, Jul 23 2009
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