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

Terms

a(0) =1a(1) =6a(2) =8a(3) =13a(4) =15a(5) =19a(6) =22a(7) =25a(8) =29a(9) =33a(10) =37a(11) =44a(12) =54a(13) =58a(14) =61a(15) =63a(16) =65a(17) =67a(18) =73a(19) =75a(20) =78a(21) =86a(22) =88a(23) =90a(24) =95a(25) =98a(26) =100a(27) =104a(28) =107a(29) =113