
COMMENTS

Intersection of A057732 and A002253.  Joerg Arndt, Mar 04 2014
By checking primality of 2^n+3 for values n in A002253, it follows a(7) > 7033641.  Giovanni Resta, Mar 08 2014
Exponents of second Fermat prime pairs.  JuriStepan Gerasimov, Mar 08 2014
From JuriStepan Gerasimov, Mar 04 2014: (Start)
If prime pair {2^n + (2k+1), (2k+1)*2^n + 1} is called a Fermat prime pair, then numbers n such that 2^n + (2k + 1) and (2k + 1)*2^n + 1 are both prime:
for k = 0: 0, 1, 2, 4, 8, 16, ... the exponents first Fermat prime pairs;
for k = 1: 1, 2, 6, 12, 18, 30, ... the exponents second Fermat prime pairs;
for k = 2: 1, 3, ... the exponents third Fermat prime pairs;
for k = 3: 2, 4, 6, 20, 174, ... the exponents fourth Fermat prime pairs;
for k = 4: 1, 2, 3, 6, 7, ... the exponents fifth Fermat prime pairs;
for k = 5: 1, 3, 5, 7, ... the exponents sixth Fermat prime pairs;
for k = 6: 2, 8, 20, ... the exponents seventh Fermat prime pairs;
for k = 7: 1, 2, 4, 10, 12, ... the exponents eighth Fermat prime pairs;
for k = 8:
for k = 9: 6, ... the exponents tenth Fermat prime pairs;
for k = 10: 1, 4, 5, 7, 16, ... the exponents eleventh Fermat prime pairs;
for k = 11:
for k = 12: 2, 4, 6, 10, 20, 22, ...the exponents thirteenth Fermat prime pairs;
for k = 13: 2, 4, 16, 40, 44, ... the exponents fourteenth Fermat prime pairs;
for k = 14: 1, 3, 5, 27, 43, ... the exponents fifteenth Fermat prime pairs.
Semiprimes of the form (2^m+2k+1)*((2k+1)*2^m+1): 4, 9, 25, 35, 77, 91, 209, 289, 319, 481, 527, 533, 901, 989, ...
(End)
