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frugal n.  and  untouchable n.

First numbers that belong to both sets:

2048, 10240, 10368, 10496, 10752, 11008, 11664, 12032, 12288, 13778, 13824, 14336, 15872, 16000, 17152, 17496, 17920, 18176, 18688, 18818, 18944, 20992, 21952, 24576, 24832, 25000, 32000, 34992, 38416, 39366, 40448, 40960, 42496, 43750, 43904, 48778, 49152, 65536, 69984, 93312, 100352, 100602, 101250, 101632, 103518, 103750, 103808, 105856, 106250, 106496, 107264, 109312, 109760, 109952, 110336, 110592, 111250, 111392, 112768, 113536, 113920, 114176, 114242, 115248, 116096, 117248, 117632, 118016, 118784, 118912, 120000, 120448, 121670, 121984, 122880, 123392, 124160, 124288, 124416, 125440, 127616, 127744, 129654, 129762, 131220, 131726, 133888, 134656, 137216, 137728, 137842, 140032, 141568, 141824, 143648, 144128, 145152, 145408, 147456, 148736, 150000, 155648, 157464, 157922, 159232, 159488, 160178, 161536, 161792, 161838, 163296, 163840, 164608, 166698, 167936, 170338, 170368, 174848, 175000, 175616, 176128, 177674, 178688, 179334, 181250, 182250, 182272, 184064, 187648, 187904, 188082, 190976, 192080, 192512, 193750, 194048, 195112, 195938, 196096, 196864, 199168, 199712, 200704, 203264, 205312, 207104, 207360, 209408, 210688, 212224, 214326, 215168, 215296, 217088, 219904, 220928, 221184, 221696, 223074, 224512, 224768, 227072, 227138, 227840, 228488, 234256, 235264, 236032, 236196, 236672, 238328, 240128, 240818, 243968, 245248, 248576, 248832, 250000, 251648, 253696, 254506, 258066, 260608, 266814, 267776, 270848, 274432, 275562, 278528, 279936, 280000, 281216, 282752, 283318, 285184, 287296, 288256, 290304, 291328, 300000, 302526, 307328, 312500, 314432, 315218, 316928, 319302, 320000, 321602, 322102, 323072, 326592, 327680, 328192, 334084, 335872, 336140, 337408, 339968, 340736, 344064, 346624, 352256, 354294, 360448, 363042, 367416, 368750, 373248, 375296, 378368, 379358, 387584, 393216, 393660, 395776, 398566, 403202, 406782, 408064, 410758, 414208, 415292, 419904, 421376, 424448, 429568, 434176, 435456, 436736, 448000, 449024, 452096, 456976, 466432, 466560, 470528, 473344, 475136, 475648, 476288, 476656, 477042, 479744, 480000, 481792, 482162, 483328, 491520, 497152, 503296, 506250, 506530, 507392, 537824, 546750, 547058, 562432, 564246, 571438.

Some larger examples :