We can make the list of all primes:

a(m,n+1) is the smallest prime of the form a(m,n)*2^k+1 (k>=0)

a(m+1,1) is the smallest prime not in the first m rows

Code:

2 3 7 29 59 1889 3779 7559
5 11 23 47 47*2^583+1
13 53 107 857 6857
17 137 1097 140417

The first row of this table is indeed A084435.

For the Riesel analog:

a(m,n+1) is the smallest prime of the form a(m,n)*2^k-1 (k>=1)

a(m+1,1) is the smallest prime not in the first m rows

Code:

2 3 5 19 37 73 9343
7 13 103 823 1685503
11 43 5503
17 67 2143