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Cunningham n.  and  evil n.

First numbers that belong to both sets:

3, 5, 9, 10, 15, 17, 24, 33, 48, 63, 65, 80, 99, 101, 120, 126, 129, 170, 195, 197, 215, 226, 255, 257, 288, 323, 325, 344, 360, 399, 401, 442, 483, 485, 513, 528, 624, 730, 783, 785, 840, 960, 999, 1023, 1025, 1088, 1155, 1157, 1224, 1295, 1297, 1370, 1443, 1445, 1520, 1599, 1601, 1680, 1848, 1935, 1937, 2026, 2049, 2115, 2117, 2186, 2188, 2196, 2210, 2400, 2499, 2501, 2600, 2743, 2810, 3024, 3126, 3135, 3137, 3250, 3363, 3365, 3480, 3722, 3843, 3845, 3970, 4095, 4097, 4224, 4355, 4357, 4488, 4623, 4625, 4762, 4899, 4901, 4914, 5040, 5183, 5185, 5330, 5624, 5775, 5777, 5831, 5928, 6083, 6085, 6240, 6399, 6401, 6562, 6723, 6725, 6890, 7224, 7395, 7397, 7568, 7743, 7745, 7775, 7920, 8193, 8280, 8463, 8465, 8650, 9024, 9262, 9408, 9603, 9605, 9802, 9999, 10001, 10200, 10403, 10405, 10608, 10647, 11026, 11450, 11882, 12099, 12101, 12166, 12322, 12543, 12545, 12768, 13226, 13455, 13457, 13688, 13823, 13923, 13925, 14162, 14640, 15130, 15375, 15377, 15624, 16128, 16383, 16385, 16640, 16806, 16899, 16901, 17160, 17423, 17425, 17577, 17690, 17955, 17957, 18224, 18495, 18497, 18770, 19320, 19599, 19601, 19882, 20163, 20165, 20448, 20735, 20737, 21024, 21608, 22200, 22499, 22501, 22802, 23103, 23105, 23408, 23715, 23717, 24026, 24335, 24337, 24388, 24648, 24963, 24965, 25282, 25599, 25601, 25922, 26568, 26895, 26897, 26999, 27226, 27888, 28560, 28899, 28901, 29242, 29583, 29585, 29792, 29928, 30275, 30277, 30624, 30975, 30977, 31330, 31683, 31685, 32040, 32760, 32769, 33123, 33125, 33490, 33855, 33857, 34224, 34970, 35720, 35938, 36099, 36101, 36482, 37248, 37635, 37637, 38026, 38415, 38417, 38808, 39303, 39602, 39999, 40001, 40400, 40803, 40805, 41210, 41615, 41617, 42026, 42435, 42437, 42850, 42874, 42876, 43680, 44522, 45370, 46224, 47088.

Some larger examples :