Values of gcd(k!+1,2^k+1) not equal to 1 taking k in increasing order.

Terms

a(0) =2a(1) =11a(2) =19a(3) =43a(4) =67a(5) =131a(6) =163a(7) =179a(8) =227a(9) =347a(10) =419a(11) =443a(12) =491a(13) =523a(14) =563a(15) =571a(16) =619a(17) =683a(18) =691a(19) =739a(20) =787a(21) =947a(22) =1019a(23) =1051a(24) =1091a(25) =1123a(26) =1187a(27) =1291a(28) =1451a(29) =1499