This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A099591 Numbers that are the sum of no fewer than 17 biquadrates (4th powers). 10

%I

%S 47,62,63,77,78,79,127,142,143,157,158,159,207,222,223,237,238,239,

%T 287,302,303,317,318,319,367,382,383,397,398,399,447,462,463,477,478,

%U 479,527,542,543,557,558,559,607,622,623,687,702,703,752,767,782,783

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

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

%H T. D. Noe, <a href="/A099591/b099591.txt">Table of n, a(n) for n = 1..96</a> (complete sequence)

%H J.-M. Deshouillers, F. Hennecart and B. Landreau, <a href="http://www.math.ethz.ch/EMIS/journals/JTNB/2000-2/Dhl.ps">Waring's Problem for sixteen biquadrates - numerical results</a>, Journal de Théorie des Nombres de Bordeaux 12 (2000), pp. 411-422.

%H J.-M. Deshouillers, K. Kawada and T. D. Wooley, <a href="https://doi.org/10.24033/msmf.413">On Sums of Sixteen Biquadrates</a>, Mém. Soc. Math. de France, Paris, 2005.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Warings Problem</a>

%e 62 is the sum of 17 4th powers and no fewer, so 62 is a member.

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

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

%Y Cf. A002377, A079611, A046048.

%K nonn,fini,full,nice

%O 1,1

%A _Ralf Stephan_, Oct 25 2004

%E a(25) changed from 368 to 367 by _T. D. Noe_, Sep 07 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)