A046297 2^a(n) contains 2^11=2048 as largest proper substring of form 2^n.

103, 267, 279, 287, 404, 503, 511, 515, 657, 685, 745, 763, 883, 890, 922, 946, 973, 991, 1011, 1087, 1114, 1121, 1164, 1197, 1209, 1272, 1274, 1283, 1302, 1316, 1328, 1360, 1378, 1432, 1445, 1478, 1509, 1511, 1542, 1565, 1571, 1584, 1627, 1672, 1678