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frugal n.  and  gapful n.

First numbers that belong to both sets:

1215, 1250, 1280, 1331, 1458, 1536, 1875, 2187, 2560, 10000, 10125, 10240, 10368, 10496, 10752, 10935, 10976, 11776, 12416, 12500, 12544, 12800, 13125, 14336, 14641, 15552, 15616, 16000, 16875, 17920, 18176, 18225, 18750, 20000, 20480, 21627, 21875, 23125, 24057, 24389, 25000, 25088, 25625, 26875, 28125, 29282, 29375, 30625, 31232, 36015, 36352, 40000, 40960, 45619, 50000, 80000, 81920, 100000, 100736, 100845, 101120, 101250, 102016, 102400, 102656, 102885, 102912, 102973, 103125, 103335, 103518, 103680, 103750, 103936, 104960, 104976, 105705, 105856, 106097, 106240, 106250, 106496, 107653, 107776, 107811, 108045, 108135, 108864, 109056, 109350, 109696, 109760, 110080, 110336, 110592, 110625, 110894, 111104, 111250, 111537, 112000, 112256, 112995, 113536, 113920, 114176, 114375, 116096, 116640, 117855, 118016, 118098, 118125, 118336, 118579, 118750, 118815, 119296, 119936, 120000, 120050, 120064, 120285, 120320, 121216, 121250, 121670, 121875, 122472, 122880, 123776, 124160, 124416, 124659, 125000, 125056, 125440, 125625, 125696, 126736, 126976, 127575, 127616, 128000, 128625, 129623, 129654, 130816, 131220, 131250, 131712, 133125, 133376, 134656, 134657, 134865, 135680, 136875, 137216, 138496, 138915, 139968, 140000, 140625, 141135, 141376, 142155, 142477, 143360, 143750, 144039, 144896, 145152, 146176, 146410, 146944, 147456, 148125, 148736, 148992, 149445, 150000, 150016, 150499, 151040, 151875, 153090, 153664, 153856, 155520, 155625, 156160, 156250, 156735, 157216, 159375, 160000, 160256, 161051, 161536, 161838, 163296, 163840, 164025, 164096, 165888, 166698, 166875, 167936, 168070, 168750, 169216, 171315, 171520, 172032, 173563, 173824, 174960, 175000, 175616, 176896, 177674, 178125, 178605, 179456, 179776, 180075, 180736, 181250, 181760, 181875, 182250, 182505, 183708, 185895, 186880, 187500, 188416, 190333, 190976, 192000, 192080, 192256, 193185, 193750, 194816, 195533, 196096, 196830, 196875, 198656, 200000, 201447, 202240, 203125, 203877, 204800, 205625, 206307, 206875, 207360, 208737, 209375, 210125, 210625, 212480, 212625, 213597, 213867, 214375, 215625, 216875, 217728, 218125, 219520, 220625, 220887, 221184, 221875, 223317.

Some larger examples :