I'm not sure if an example is necessarily the best route to take...
Regardless of small n, it's very difficult to take into account all negative primes of large magnitude and squares of equally large magnitude. Since the list of possibilities is infinite, I don't see a concrete way to say...
Homework Statement
Prove or disprove: If n is a positive integer, then n=p+a^2 where
a\in\mathbb{Z}
p is prime or p=1
Note that the interpretation of "prime" used here includes negative primes. So, an exhaustive list of possibilities for p is p=1,\pm2,\pm3,\pm5,\pm7,\pm11,\cdots...