Semi-sums (average) of two (not necessarily distinct) Mersenne primes (A000668).

Terms

a(0) =3a(1) =5a(2) =7a(3) =17a(4) =19a(5) =31a(6) =65a(7) =67a(8) =79a(9) =127a(10) =4097a(11) =4099a(12) =4111a(13) =4159a(14) =8191a(15) =65537a(16) =65539a(17) =65551a(18) =65599a(19) =69631a(20) =131071a(21) =262145a(22) =262147a(23) =262159a(24) =262207a(25) =266239a(26) =327679a(27) =524287a(28) =1073741825a(29) =1073741827