A153740 Smallest non-twin prime > n-th and (n+1)-th twin primes.

23, 37, 47, 67, 79, 113, 157, 211, 233, 251, 277, 293, 317, 353, 439, 467, 541, 577, 607, 631, 647, 673, 839, 863, 887, 1039, 1069, 1097, 1163, 1237, 1283, 1297, 1307, 1327, 1433, 1459, 1493, 1613, 1627, 1693, 1709, 1733, 1801, 1889, 1973, 2003, 2039, 2099