A027705 Primes with odd number of 1's in binary expansion such that next prime has even number of 1's.

2, 13, 19, 41, 47, 67, 79, 97, 109, 137, 157, 193, 251, 271, 283, 307, 313, 331, 367, 379, 397, 443, 457, 463, 499, 521, 541, 569, 587, 617, 641, 661, 677, 733, 743, 769, 787, 809, 829, 859, 877, 883, 929, 971, 1009, 1021, 1039, 1051, 1087, 1109, 1129, 1171, 1213, 1231, 1259, 1279, 1291