Let q be a prime with primitive root 2. We show that (a) if (p(i)) for
i=1..q-2 is a sequence of primes such that p(i)=2p(i-1)+1 for all 1<=i<=q-2,
then q divides p(0)+1 or p(0) is 2, 3 or 5 and (b) if (p(i)) is a sequence of
primes such that p(i)=2p(i-1)-1 for all 1<=i<=q-2, then q divides p(0) or p(0)
is 2 or 3.