2^k - 2m+1 = prime: (Was: Sum Of Primes Is Power Of Primes: Question)

[Maximilian Hasler]

David,
I agree with you, the %N A096502 should be changed to
"..., 0 if no such x exists."
did you/ do you intend to submit your comment ?

If not, I'd like to add some PARI code which should work at least up to 1871/2.
Do you know a solution for 2^k-1871 ?
It seems difficult to find a prime already here.
Obviously, we must have k = 2 or k=14 (mod 36).
Moreover, k=2+36m won't give a prime for m in 3+5Z (11 divides), 4+11Z
(23 divides), 7+11Z (89 divides), 11+34Z (103 divides),...
and for k=14+36m we can exclude m in 1+5Z (11 divides), 0+11Z (23
divides), 7+35Z (71 divides), 3+11Z (89 divides), 5+34Z (103 divides),
5Z (631 divides),...

But maybe this has already been analyzed and a solution is known ?

Regards,
Maximilian