Sorry, Fibonacci.

Find the least positive integer $d$ for which there exists an infinite arithmetic progression satisfying the following properties:

1. Each term of the progression is a positive integer.
2. The common difference of the progression is $d$.
3. No term of the progression appears in the Fibonacci sequence.

Details and assumptions

The Fibonacci sequence is defined by $F_1 = 1, F_2 = 1$ and $F_{n+2} = F_{n+1} + F_{n}$ for $n \geq 1$.

The arithmetic progression has infinitely many terms.