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frugal n.  and  palindromic n.

First numbers that belong to both sets:

343, 1331, 10201, 14641, 31213, 94249, 1030301, 1332331, 1367631, 1478741, 2060602, 2513152, 2551552, 2570752, 2939392, 2977792, 3090903, 3498943, 3637363, 3735373, 3850583, 5221225, 5265625, 5734375, 6948496, 11288211, 11333311, 12100121, 12499421, 13577531, 14655641, 22666622, 27700772, 29399392, 31244213, 33999933, 38988983, 58344385, 71111117, 100020001, 100585001, 101000101, 104060401, 104555401, 106878601, 109040901, 112393211, 112444211, 114363411, 116969611, 121242121, 122666221, 122949221, 123454321, 124454421, 124666421, 127707721, 129505921, 131999131, 133101331, 134969431, 142161241, 142585241, 143232341, 144797441, 145777541, 146010641, 146424641, 151828151, 156010651, 157828751, 157838751, 159575951, 159676951, 159747951, 160272061, 162414261, 166141661, 169636961, 170757071, 175565571, 177535771, 177878771, 184989481, 186626681, 187323781, 190797091, 192161291, 194343491, 198060891, 200040002, 206010602, 213101312, 215040512, 215808512, 217939712, 230060032, 232767232, 237131732, 241020142, 242292242, 253636352, 263101362, 265939562, 266202662, 267666762, 270787072, 291272192, 291848192, 297313792, 297565792, 300060003, 307939703, 313454313, 313797313, 313979313, 315282513, 324151423, 328717823, 333070333, 335636533, 336212633, 338111833, 339515933, 340222043, 343686343, 353151353, 359686953, 371404173, 374121473, 387444783, 399303993, 404090404, 407808704, 420161024, 420545024, 426202624, 436434634, 466737664, 487030784, 489353984, 496282694, 515050515, 521303125, 521333125, 521343125, 521363125, 521808125, 521828125, 521838125, 521878125, 526000625, 526060625, 526090625, 526111625, 526515625, 526545625, 526555625, 526565625, 526575625, 543454345, 554979455, 569454965, 571555175, 571858175, 573434375, 573484375, 573494375, 573949375, 578121875, 578141875, 578171875, 578646875, 578696875, 594181495, 642757246, 677707776, 692535296, 707747707, 713939317, 736282637, 743222347, 746343647, 763101367, 771626177, 782222287, 823939328, 840323048, 851747158, 861161168, 921929129, 930141039, 937858739, 940525049, 942545249, 946111649, 952777259, 964171469, 971717179, 973030379, 977636779, 980545089, 985383589.