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 A185673 Least number k having n representations as the sum of the minimal number of biquadrates A002377(k). 1

%I #26 Mar 31 2012 10:24:16

%S 1,259,518,777,3402,3645,3726,7045,7243,12683,16441,13723,13792,21631,

%T 20202,23002,24135,27162,28870,28215,33230,39629,36510,41561,43241,

%U 29563,47401,41310,47150,47790,56749,43962,48750,62681,65069,50442

%N Least number k having n representations as the sum of the minimal number of biquadrates A002377(k).

%C This sequence is not monotonically increasing: a(21)=33230 > a(26)=29563.

%H Weisstein, Eric W.: <a href="http://mathworld.wolfram.com/WaringsProblem.html">MathWorld -- Waring's Problem.</a>

%e a(1) = 1 since 1 = 1^4 (1 way with minimal representation)

%e a(2) = 259 since 259 = 1^4 + 1^4 + 1^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4 (2 ways with minimal representation)

%e a(3) = 518 since 518 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 (3 ways with minimal representation)

%t t=Table[r=PowersRepresentations[n,19,4]; Sort[Tally[19-Count[#,0]&/@r]][[1,2]], {n,800}]; u=Union[t]; c=Complement[Range[Max[u]],u]; If[c=={}, mx=u[[-1]], mx=c[]-1]; Flatten[Table[Position[t,n,1,1],{n,mx}]]

%Y Cf. A002377.

%K nonn

%O 1,2

%A _Martin Renner_, Feb 09 2011

%E a(10)-a(36) from _Alois P. Heinz_, Feb 10 2011

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Last modified December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)