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d-powerful n.  and  plaindrome

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 89, 135, 224, 226, 267, 333, 334, 357, 377, 378, 379, 445, 1234, 1255, 1349, 2223, 2224, 2225, 2227, 2244, 2245, 2246, 2247, 2248, 2249, 2333, 2334, 2335, 2336, 2355, 2356, 2379, 2445, 2449, 2577, 3345, 3457, 3477, 3566, 3569, 3678, 4447, 4449, 4469, 4599, 5567, 6669, 12345, 12347, 12367, 13337, 22247, 22249, 22267, 22269, 22333, 22334, 22335, 22337, 22338, 22355, 22358, 22378, 22447, 22467, 22489, 22557, 22558, 23345, 23347, 23348, 23477, 23568, 23679, 24467, 24489, 24599, 24667, 24669, 24688, 24689, 25677, 33338, 33447, 33467, 33578, 33778, 33779, 34568, 34677, 35688, 36789, 44449, 45899, 46777, 46778, 46779, 46799, 112226, 117789, 122278, 122346, 122347, 122479, 123378, 123557, 123578, 123579, 124479, 124499, 124679, 124789, 125579, 126899, 133344, 133459, 133566, 134445, 134557, 134578, 134777, 134778, 134779, 134799, 144459, 146699, 147888, 147889, 166699, 167779, 222223, 222224, 222247, 222334, 222335, 222359, 222377, 222555, 222558, 222559, 222579, 222889, 223345, 223347, 223349, 223367, 223455, 223456, 223479, 223569, 223678, 223699, 224466, 224489, 224599, 224666, 226779, 233335, 233337, 233357, 233377, 233468, 233469, 233577, 233578, 233579, 233666, 233668, 233669, 234456, 234567, 235577, 235668, 235777, 235779, 236679, 236789, 237777, 237778, 237779, 237999, 244667, 244777, 244778, 244779, 245567, 245677, 245678, 245679, 256677, 256699, 256789, 266888, 333346, 333368, 333455, 333477, 333499, 334447, 334466, 334467, 334468, 334469, 334488, 334555, 334559, 334579, 334668, 344455, 344456, 344457, 344458, 344459, 344566, 344569, 344677, 345556, 345599, 345666, 345667, 345668, 345669, 345688, 345689, 346788, 346789, 445677, 445678, 445679, 446667, 455578, 455779, 456679, 456788, 456789, 457889, 458899, 555588, 566789, 567889, 1114456, 1122578, 1123366, 1123459, 1123678, 1124779, 1134566, 1134567, 1134568, 1134569, 1136788, 1146888, 1222258, 1222457, 1222567, 1225579, 1225779, 1233344, 1233348, 1233369, 1233389, 1233457, 1233458, 1233477, 1233478, 1233479, 1233679, 1234444, 1234448, 1234467.

Some larger examples :