by direct evaluation N=2 divides 3^2-3=6 and N=3 divides 3^3-3=24. By Fermat's little theorem, all larger primes also satisfy N divides 3^N-3. Thus no primes are solutions so N must be composite.
The term Pseudoprime describes any composite number N that divides A^(N-1) with N coprime to A, which is only trivially different from N dividing A^N-A. Then what we seek is for N to be a pseudoprime of base 2 but not base 3.
Then the OEIS has already done the hard work:
A001567: Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers.
The very first number in A001567 is 341 and it is not in A005935, then that means N=341 is the minimum value of a positive integer N such that N divides 2^N-2, but N does NOT divide 3^N - 3.
Quick solution
