1281979*2^n-1 has a

Nash weight of 1789, so relatively low.

1281979

1 mod 3 so all primes of that sequence are only odd n-values.

k-values with 2 mod 3 can only produce primes with even n's, and k's divisible by 3 can produce primes with odd/even n-values.

1281979*2^n+1 has a low Nash weight of 847, so there should less primes for this sequence.

The

Liskovets-Gallot conjectures study the contribution of odd/even n-values of such seqs.

There exits k-values which never produce primes for any n-value like the Riesel problem.

PS: If your're done you can list the prime n-values in this thread and I can include those in the Wiki, both sides (Proth /Riesel) possible. Don't forget to give the search limits then.