A050423 Numbers for which in base 2 the least number of digits that can be removed to leave a palindrome (possibly beginning with 0) is 4.

232, 240, 368, 424, 432, 440, 452, 456, 468, 472, 482, 484, 488, 496, 542, 543, 558, 559, 688, 720, 752, 816, 868, 872, 888, 900, 920, 932, 962, 970, 972, 978, 980, 984, 994, 996, 1000, 1008, 1052, 1054, 1055, 1068, 1070, 1071, 1078, 1079