A046298 2^a(n) contains 2^12=4096 as largest proper substring of form 2^n.

104, 268, 346, 405, 455, 462, 504, 512, 658, 726, 820, 884, 923, 947, 974, 992, 994, 1012, 1122, 1123, 1132, 1198, 1251, 1278, 1280, 1329, 1356, 1361, 1379, 1411, 1433, 1435, 1446, 1453, 1479, 1498, 1502, 1512, 1543, 1544, 1552, 1572, 1585, 1628, 1665