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

1,2

Comments

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

Links

Table of n, a(n) for n=1..36.

Weisstein, Eric W.: MathWorld -- Waring's Problem.

Example

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)

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}]]

Crossrefs

Cf. A002377.

Sequence in context: A101521 A207060 A037987 * A082788 A043376 A038480

Adjacent sequences: A185670 A185671 A185672 * A185674 A185675 A185676

Keyword

nonn

Author

Martin Renner, Feb 09 2011

Extensions

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

Status

approved