[andrewla]

Straightforward to pose as a decision problem -- you're given a sequence of {0,1} representing a base-2 input (N), output a string of {0, 1} such that there are N 1's. You could make it "N 1s followed by N 0s" to avoid being too trivial, but even in the original formulation there are plenty of "wrong" answers for each value of N, and determining whether a witness is correct requires O(2^b) time, where b is the number of bits in N.

[bubblyworld]

That's not a decision problem either. You need to cast it in the form of determining membership in some set of strings (the "language"). In this case the natural choice of language is the set of all strings of the form "{encoding of n}{1111....1 n times}", which is decidable in O(log(n)+n) steps, i.e. linear time.