Integer pairs that generate only odd prime sums (as described in comment).

Terms

a(0) =1a(1) =2a(2) =6a(3) =11a(4) =12a(5) =17a(6) =30a(7) =41a(8) =72a(9) =101a(10) =156a(11) =546a(12) =1481a(13) =3917a(14) =11886a(15) =14627a(16) =27737a(17) =78696a(18) =118901a(19) =137436a(20) =1676610a(21) =12618762a(22) =111018431a(23) =574060031a(24) =47357739281a(25) =168920413410