There are no such integers. Odd + odd = even, and adding odd to that makes it odd again. But 64 is even.
Put another way, let n be the smallest of the three integers. Then
n + (n + 2) + (n + 4) = 64
3n + 8 = 64
3n = 56
But 3 does not divide 56, so there is no integer solution for n.
