primes that never divide 2^k+1

[Maximilian Hasler]

Dear seqfans,
There is a series of sequences of primes which are almost the same:
primes which never divide 2^n+1, primes = {2,7} mod 8, and
primes such that x^(...) = 2 has a solution mod p :

A045315 A072936 A049564 A049584 A045382 A049560 etc etc
http://www.research.att.com/~njas/sequences/?q=7,23,31,47,71,73,79,89&fmt=1

some of them coincide for all terms that are listed, e.g.
http://www.research.att.com/~njas/sequences/?q=id:A049564|id:A072936
agree for all terms and there is no comment concerning that issue.
- BTW,  the ..64 one has offset =0, could be fixed at that occasion).
I think it would be useful to add cross references, comments on the differences
and/or  subsequence relations among them.
(I think those "x^(...) = 2 has a solution" are subsequences of
A072936 differing in only few terms, so it would be more interesting
to know what terms of A072936 are NOT in them)
Regards,
Maximilian
PS: and A014663 is essentially the same than A072936 ; b.t.w. the
comment should be amended to "ODD primes...", I'll send an EDIT for
that one.