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alternating n.  and  tau n.

First numbers that belong to both sets:

1, 2, 8, 9, 12, 18, 36, 56, 72, 96, 232, 252, 276, 296, 450, 472, 492, 612, 632, 636, 672, 852, 856, 872, 876, 896, 1016, 1056, 1096, 1212, 1236, 1250, 1256, 1432, 1476, 1632, 1656, 1692, 1812, 1816, 1832, 3012, 3032, 3096, 3252, 3272, 3276, 3456, 3492, 3636, 3656, 3816, 3832, 3852, 3896, 4761, 5052, 5256, 5272, 5292, 5416, 5436, 5472, 5652, 5672, 5816, 5856, 5892, 6561, 7016, 7092, 7096, 7212, 7256, 7272, 7296, 7416, 7432, 7496, 7616, 7692, 7812, 7816, 7836, 9012, 9032, 9036, 9252, 9276, 9432, 9496, 9696, 9832, 9852, 9856, 9876, 9896, 12321, 21036, 21056, 21096, 21216, 21256, 21272, 21416, 21496, 21612, 21636, 21656, 21832, 21852, 21876, 23032, 23076, 23096, 23272, 23292, 23412, 23416, 23656, 23676, 23832, 25056, 25092, 25096, 25216, 25236, 25416, 25452, 25472, 25496, 25632, 25672, 25692, 25832, 25836, 27012, 27036, 27252, 27256, 27276, 27612, 27656, 29056, 29076, 29096, 29272, 29292, 29412, 29416, 29472, 29672, 29676, 29816, 29856, 41076, 41292, 41432, 41436, 41652, 41672, 41816, 41856, 41892, 41896, 43096, 43236, 43256, 43272, 43296, 43452, 43456, 43476, 43496, 43812, 43816, 43832, 43872, 45216, 45256, 45272, 45432, 45612, 45636, 45696, 45852, 45876, 45896, 47016, 47032, 47052, 47076, 47232, 47416, 47896, 49056, 49092, 49212, 49632, 49832, 49836, 56169, 61056, 61092, 61212, 61416, 61496, 61812, 61816, 61836, 63016, 63032, 63036, 63072, 63252, 63256, 63276, 63416, 63432, 63456, 63496, 63616, 63636, 63872, 63876, 65052, 65292, 65412, 65432, 65652, 65672, 65856, 65896, 67016, 67032, 67092, 67096, 67212, 67296, 67416, 67432, 67456, 67476, 67692, 67812, 67836, 67872, 69012, 69016, 69032, 69216, 69416, 69492, 69612, 69656, 69852, 69896, 81036, 81252, 81272, 81416, 81492, 81612, 81636, 81696, 81876, 83016, 83072, 83412, 83416, 83432, 83616, 83652, 83656, 83672, 83816, 83892, 83896, 85016, 85032.

Some larger examples :