[johntb86]

It needs to be a decision problem (or easily recast as a decision problem). "given a number as input, output as many 1's as that number" doesn't have a yes or no answer. You could try to ask a related question like "given a number as input and a list of 1s, are there as many 1s as the number?" but that has a very large input.

[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.