A099591 Numbers that are the sum of no fewer than 17 biquadrates (4th powers).

47, 62, 63, 77, 78, 79, 127, 142, 143, 157, 158, 159, 207, 222, 223, 237, 238, 239, 287, 302, 303, 317, 318, 319, 367, 382, 383, 397, 398, 399, 447, 462, 463, 477, 478, 479, 527, 542, 543, 557, 558, 559, 607, 622, 623, 687, 702, 703, 752, 767, 782, 783

Offset

1,1

Comments

There are 96 members in the sequence, the largest being 13792, see the Deshouillers et al. references.

Links

T. D. Noe, Table of n, a(n) for n = 1..96 (complete sequence)

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.

J.-M. Deshouillers, K. Kawada and T. D. Wooley, On Sums of Sixteen Biquadrates, Mém. Soc. Math. de France, Paris, 2005.

Eric Weisstein's World of Mathematics, Biquadratic Number

Eric Weisstein's World of Mathematics, Warings Problem

Example

62 is the sum of 17 4th powers and no fewer, so 62 is a member.
63 is the sum of 18 4th powers and no fewer, so 63 is a member, although it is not a member of A046048.

Mathematica

f[n_] := f[n] = (k = 0; While[k++; PowersRepresentations[n, k, 4] == {}]; k); Select[Range[800], f[#] >= 17 &] (* Jean-François Alcover, Sep 02 2011 *)

Crossrefs

Cf. A002377, A079611, A046048.

Sequence in context: A039355 A043178 A043958 * A046048 A163390 A332078

Adjacent sequences: A099588 A099589 A099590 * A099592 A099593 A099594

Keyword

nonn,fini,full,nice

Author

Ralf Stephan, Oct 25 2004

Extensions

a(25) changed from 368 to 367 by T. D. Noe, Sep 07 2006

Status

approved