Nearest partition numbers
Python 2, 179 bytes
Z=range(1,99)
R=Z+[1]
for i in Z:R[i]=sum(-(-1)**k*(3*k*k-k&lt;=i*2and R[i-k*(3*k-1)/2])for k in range(-i,i+1)if k)
f=lambda n:zip(*sorted((abs(n-R[i]),i)for i in Z))[1][:2-(n in R)]

Uses the recursive formula from Euler's pentagonal theorem.
Call with f(2484). Output is a tuple with one or two numbers.