Now since a(n+1) = an^2 - an + 1 and after a1, the next terms are odd... so terms will be of the type odd^2 - odd + 1 odd^2 is always odd... and odd^2 + 1 will become even. then even - odd = odd always....
so there won't be any distinct pair with GCD = 6... 2 will be the only even number in the sequence.