sum of first consecutive powers.

[Floor en Lyanne van Lamoen]

Sequence fans,

I just submitted a sequence (below) that I think is very short. But within
the limitations of my computer and my abilities, I didn't succeed to find
a(6). Any shots?

Remarkably there seem to be 3 different smallest solutions for n=5 - I
didn't reproduce them.

%I A113246
%S A113246 2,3,7,12,16,24
%N A113246 The smallest number such that 1^n +- 2^n +- ... +- a(n)^n = 0 has
a solution.
%e A113246 For n=2 we have 1^2 + 2^2 - 3^2 + 4^2 - 5^2 - 6^2 + 7^2 = 0 as
smallest solution, so a(2)=7.
%O A113246 0
%K A113246 ,more,nonn,

Kind regards,
Floor van Lamoen.