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frugal n.  and  Ulam n.

First numbers that belong to both sets:

243, 1536, 1792, 2809, 3481, 6889, 8192, 10112, 11776, 11881, 12482, 16121, 18750, 19375, 19683, 20169, 20480, 20736, 21870, 24367, 25000, 28431, 30527, 34263, 36015, 36875, 45625, 47045, 49664, 63423, 65625, 71875, 72361, 78961, 81920, 100842, 101250, 101306, 101375, 102303, 102912, 103058, 103518, 103625, 106496, 107359, 108578, 110464, 111747, 112023, 114875, 115591, 118459, 118528, 119021, 120409, 121079, 121257, 121875, 122567, 123776, 123823, 125440, 126603, 127253, 131463, 134017, 134865, 138752, 140697, 141376, 145408, 147456, 148125, 150417, 155277, 159375, 160000, 160137, 166698, 167042, 169984, 173312, 174243, 175616, 177957, 181781, 188498, 190333, 192000, 192080, 192256, 194045, 194375, 196249, 196830, 199017, 203877, 206875, 207616, 208737, 210125, 212625, 214528, 215625, 219904, 220549, 224512, 226816, 229147, 229888, 233125, 233147, 237917, 240128, 240443, 241115, 242501, 243187, 251419, 253125, 253472, 253477, 254464, 255507, 256907, 257337, 260389, 261709, 261711, 261875, 268279, 271663, 273371, 274625, 276875, 278258, 281603, 282747, 288125, 290871, 301077, 307501, 311469, 315657, 315904, 320031, 321734, 326592, 326875, 334611, 350464, 352947, 355625, 357939, 360937, 363771, 378351, 378368, 380538, 386561, 390625, 397535, 403125, 405224, 405769, 408125, 417605, 418399, 424278, 436178, 436982, 437500, 441856, 455877, 461563, 464375, 470528, 474281, 478953, 482447, 493039, 493750, 499712, 500707, 513945, 516215, 535423, 540625, 557685, 560947, 605799, 614547, 620289, 622080, 625000, 634207, 643707, 649539, 654267, 663552, 671875, 682587, 684375, 685783, 702464, 704969, 709142, 711507, 722701, 737107, 743311, 758131, 759795, 761117, 765625, 777243, 779689, 785133, 796322, 806736, 809375, 828873, 837621, 852355, 859375, 863939, 876987, 906250, 915625, 917504, 920727, 928805, 937445, 942823, 963605, 964467, 982009, 985527, 996415, 1000000, 1000625, 1002861, 1003008, 1003961, 1004029, 1005967, 1006592, 1006763, 1008273, 1010394, 1010609, 1011042, 1011125, 1012879, 1013241, 1015296, 1015623, 1017839, 1017927, 1019142, 1023875, 1026250, 1026875, 1027161, 1032192, 1032256, 1032507, 1035625, 1035904, 1037651, 1039625, 1041152, 1043447, 1043750, 1044375, 1046362, 1046875, 1047808, 1048302.

Some larger examples :