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A161884 Smallest k such that n^4 = a_1^4+...+a_k^4 and all a_i are positive integers less than n. 6
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, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 6, 5, 6, 16, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
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]
REFERENCES
J.-M. Deshouillers, K. Kawada, and T. D. Wooley, "On sums of sixteen biquadrates", Mem. Soc. Math. Fr. 100 (2005), 120 pp.
LINKS
R. Balasubramanian, J.-M. Deshouillers, and F. Dress, Problème de Waring pour les bicarrés I, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 303 (1986), pp. 85-88.
R. Balasubramanian, J.-M. Deshouillers, and F. Dress, Problème de Waring pour les bicarrés II, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 303 (1986), pp. 161-163.
J.-M. Deshouillers, F. Hennecart and B. Landreau, Waring's Problem for sixteen biquadrates - numerical results, Journal de Théorie des Nombres de Bordeaux 12 (2000), pp. 411-422.
Manfred Scheucher, Sage Script
PROG
(PARI) a(n, verbose=0, m=4)={N=n^m; for(k=3, 99, forvec(v=vector(k-1, i, [1, n\sqrtn((k+1-i)*0.99999, m)]), ispower(N-sum(i=1, k-1, v[i]^m), m, &K)&&K>0&&!if(verbose, print1("/*"n" "v"*/"))&&return(k), 1))} \\ M. F. Hasler, Dec 17 2014
CROSSREFS
Sequence in context: A084527 A084517 A070568 * A166210 A141078 A298830
KEYWORD
nonn
AUTHOR
Dmitry Kamenetsky, Jun 21 2009
EXTENSIONS
a(51)-a(63) from M. F. Hasler, Dec 17 2014
a(64)-a(86) from Giovanni Resta, Aug 17 2015
STATUS
approved

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Last modified May 18 15:07 EDT 2024. Contains 372642 sequences. (Running on oeis4.)