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

1, 259, 518, 777, 3402, 3645, 3726, 7045, 7243, 12683, 16441, 13723, 13792, 21631, 20202, 23002, 24135, 27162, 28870, 28215, 33230, 39629, 36510, 41561, 43241, 29563, 47401, 41310, 47150, 47790, 56749, 43962, 48750, 62681, 65069, 50442

Offset: 1

Author

Martin Renner, Feb 09 2011

Keywords

• nonn

Comments

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

Examples

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

Links

• Eric Weisstein's World of Mathematics, Waring's Problem.

Crossrefs

Cf. A002377.

Programs

Mathematica

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]]-1]; Flatten[Table[Position[t,n,1,1],{n,mx}]]

Extensions

a(10)-a(36) from Alois P. Heinz, Feb 10 2011