A046299 2^a(n) contains 2^13=8192 as largest proper substring of form 2^n.

105, 269, 406, 463, 505, 513, 518, 536, 559, 570, 659, 821, 924, 948, 981, 993, 995, 1013, 1081, 1133, 1136, 1165, 1199, 1246, 1279, 1281, 1312, 1330, 1331, 1344, 1354, 1362, 1363, 1408, 1434, 1436, 1447, 1454, 1480, 1488, 1491, 1499, 1501, 1503, 1513