A027708 n-th prime has odd number of 1's in binary expansion and (n+1)st prime also has odd number of 1's.

4, 5, 11, 12, 17, 18, 21, 27, 28, 31, 32, 36, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51, 52, 53, 80, 81, 82, 83, 84, 85, 93, 94, 102, 103, 106, 110, 111, 112, 115, 118, 119, 120, 126, 127, 128, 129, 134, 135, 143, 144, 156, 157, 160, 161, 162, 163, 167, 168, 171