A064795 Home primes in base 2: primes reached when you start with n and (working in base 2) concatenate its prime factors (A048985); repeat until a prime is reached (or -1 if no prime is ever reached).

1, 10, 11, 11111, 101, 1011, 111, 10110011, 11101, 11111, 1011, 101011, 1101, 10111, 11101, 10111011100111, 10001, 101111, 10011, 11111011, 11111, 101011, 10111, 111110011, 111111111011, 111111111011, 1111111, 111111111011, 11101