
COMMENTS

Intersection of A156560 and A050522.
By comparing A059608 and A001770, the next term, if it exists, is larger than 2^350028.  Giovanni Resta, Mar 06 2014
Lesser prime of Mersenne prime pair of order k and of the form (2^m  (2k  1), (2k  1)*2^m  1}:
for order k = 1: 3, 7, 31, 127, 8191, 131071, ... (Mersenne primes A000668)
for order k = 2: 5, 13, 61, ...
for order k = 3: 11, 251, 1019, 4091, 655531, 4294967291, ... (this sequence)
for order k = 4:
for order k = 5: 2097143, ...
for order k = 6: 3, ...
for order k = 7:
for order k = 8: 17, 1009, 16369, ...
for order k = 9: 47, 65519, 1048559, 68719476719, ...
for order k = 10: 13, 2097133, ...
for order k = 11: 107, 8171, ...
for order k = 12: 41, 233, 4073, ...
for order k = 13: 487, ...
for order k = 14: 5, 229, 997, ...
for order k = 15: 97, ...
