6. Consider c, a 3-colouring of the set of natural numbers defined by 0 if 9|n c(n) 1 if 9 n and n is even 2 if 9 Xn and n is odd Determine the size of the longest c-monochromatic sequence a₁ <a₂ < < a with the property that for each i = [2, k], a; - a¡-1 is a prime number.

Fig: 1