A072667 Consider m such that prime(m) + prime(m+1) = prime(k) + 1 for some k; sequence gives initial primes prime(m).

3, 5, 7, 11, 13, 19, 29, 31, 41, 43, 61, 67, 73, 97, 113, 127, 151, 179, 191, 193, 199, 211, 223, 229, 239, 241, 271, 277, 281, 293, 307, 317, 337, 349, 367, 373, 379, 397, 401, 409, 419, 431, 439, 463, 487, 523, 541, 547, 577, 613, 619, 641, 643, 659, 683, 701, 709, 727