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nialpdrome  and  sphenic n.

First numbers that belong to both sets:

30, 42, 66, 70, 110, 222, 310, 322, 410, 430, 442, 530, 555, 610, 642, 651, 654, 663, 665, 710, 730, 741, 742, 754, 762, 777, 822, 830, 854, 861, 874, 885, 942, 962, 970, 986, 987, 994, 2110, 2211, 2222, 3110, 3111, 3310, 3311, 3322, 3333, 4210, 4310, 4330, 4430, 4431, 4433, 5210, 5222, 5322, 5410, 5421, 5442, 5511, 5522, 5542, 5551, 5555, 6310, 6322, 6410, 6430, 6441, 6522, 6530, 6531, 6554, 6610, 6643, 6654, 6665, 7221, 7222, 7322, 7330, 7422, 7430, 7510, 7511, 7521, 7553, 7554, 7610, 7611, 7622, 7654, 7662, 7730, 7733, 7743, 7761, 7766, 7777, 8110, 8210, 8421, 8530, 8533, 8555, 8630, 8642, 8643, 8655, 8662, 8666, 8733, 8754, 8755, 8762, 8763, 8770, 8774, 8810, 8822, 8830, 8841, 8853, 8854, 8870, 8877, 8886, 9110, 9321, 9322, 9331, 9410, 9422, 9443, 9530, 9541, 9542, 9554, 9622, 9642, 9654, 9710, 9741, 9762, 9766, 9770, 9821, 9822, 9830, 9831, 9843, 9854, 9861, 9877, 9885, 9910, 9911, 9942, 9951, 9955, 9962, 9970, 9994, 21110, 21111, 22210, 22211, 22222, 32210, 33310, 33321, 33333, 41110, 42110, 42211, 44210, 44321, 44331, 44410, 53322, 53330, 53331, 53333, 54111, 54310, 54321, 54322, 54410, 54411, 54430, 54431, 54442, 55210, 55211, 55221, 55310, 55311, 55322, 55442, 55533, 55542, 55555, 62110, 62111, 62210, 62211, 62222, 63110, 63111, 63322, 64210, 64222, 64322, 64442, 65210, 65221, 65422, 65433, 65510, 65530, 65541, 65554, 65555, 66442, 66443, 66522, 66530, 66531, 66543, 66554, 66610, 66621, 66651, 66661, 66665, 71111, 72110, 72222, 73210, 73222, 73310, 73311, 73321, 73322, 73330, 74110, 74211, 74221, 74330, 74422, 74433, 74443, 75221, 75322, 75410, 75422, 75442, 75531, 75542, 75551, 75554, 76111, 76210, 76222, 76322, 76430, 76431, 76433, 76442, 76443, 76521, 76533, 76542, 76555, 76641, 77221, 77311, 77331, 77410, 77421.

Some larger examples :