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A161884
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Smallest k such that n^4 = a_1^4+...+a_k^4 and all a_i are positive integers less than n.
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3
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16, 6, 16, 5, 6, 6, 16, 6, 5, 7, 6, 6, 6, 5, 16, 6, 6, 6, 5, 6, 7, 6, 6, 5, 6, 6, 6, 6, 5, 5, 16, 6, 6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 7, 5, 6, 6, 6, 6, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| It follows from Balasubramanian, Deshouillers, & Dress' result g(4) = 19 that a(n) <= 20. Deshouillers, Hennecart, & Landreau and Deshouillers, Kawada, & Wooley together give an effective proof that G(4) = 16, from which it can be determined by checking the 96 exceptions that a(n) <= 17. Probably a(n) <= 16. [Charles R Greathouse IV, Jul 31 2011]
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REFERENCES
| R. Balasubramanian, J.-M. Deshouillers, and F. Dress, "Problème de Waring pour les bicarrés I, II." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 303 (1986), pp. 85-88 and 161-163.
J.-M. Deshouillers, K. Kawada, and T. D. Wooley, "On sums of sixteen biquadrates", Mem. Soc. Math. Fr. 100 (2005), 120 pp.
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LINKS
| J.-M. Deshouillers, F. Hennecart and B. Landreau, Waring's problem for sixteen biquadrates , Journal de Théorie des Nombres de Bordeaux 12 (2000), pp. 411-422.
Jean-Charles Meyrignac, Computing minimal equal sums of like powers
Weisstein, Eric W., Diophantine Equation 4th Powers
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CROSSREFS
| Cf. A161882, A161883, A161885, A099591.
Sequence in context: A084527 A084517 A070568 * A166210 A141078 A057964
Adjacent sequences: A161881 A161882 A161883 * A161885 A161886 A161887
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KEYWORD
| nonn
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AUTHOR
| Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Jun 21 2009
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