Smallest integer i stored as a float such that i+1=i
Standard “float” has a 24 bit mantissa (the highest bit doesn’t get stored because it is always 1). Therefore all integers that fit into 24 bits - all integers less than $2^{24}$ - can be represented exactly. 

From $2^{24}$ onward only even numbers can be stored. So you take N = $2^{24}$, and carefully check what n+1 is according to the rounding rules. 

BTW. It makes life a lot easier if you don't look at the exact bit representation of float, but just take it as "1 bit sign, 8 bit exponent, 23 bit mantissa + 1 implicit leading mantissa bit".