n-th prime has odd number of 1's in binary expansion and (n+1)st prime also has odd number of 1's.

Terms

a(0) =4a(1) =5a(2) =11a(3) =12a(4) =17a(5) =18a(6) =21a(7) =27a(8) =28a(9) =31a(10) =32a(11) =36a(12) =39a(13) =40a(14) =41a(15) =42a(16) =43a(17) =46a(18) =47a(19) =48a(20) =49a(21) =50a(22) =51a(23) =52a(24) =53a(25) =80a(26) =81a(27) =82a(28) =83a(29) =84