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Duffinian n.  and  zygodrome

First numbers that belong to both sets:

55, 77, 111, 333, 777, 999, 1111, 1133, 1177, 2233, 2255, 3355, 4411, 4433, 4477, 4499, 5533, 5555, 5599, 6611, 6655, 6677, 7711, 7744, 7777, 7799, 8833, 8855, 8899, 9911, 9955, 9977, 11111, 11133, 11155, 11199, 11333, 11555, 11999, 22233, 22255, 22333, 22555, 22999, 33355, 33399, 33777, 44411, 44455, 44477, 44999, 55111, 55555, 55577, 55777, 55999, 66333, 66611, 66655, 66677, 66699, 77111, 77333, 77555, 77755, 77799, 88111, 88333, 88777, 88833, 88855, 88999, 99111, 99333, 99777, 99911, 99955, 110011, 110077, 111133, 111199, 111999, 112211, 112255, 112277, 113311, 113333, 113377, 114433, 114455, 114499, 115511, 115555, 115577, 116611, 116677, 116699, 117755, 117799, 118811, 118855, 118877, 119911, 119933, 119977, 119999, 220055, 220099, 221111, 221155, 222211, 222233, 222277, 222299, 222777, 223333, 223399, 224411, 224477, 225511, 225533, 225577, 225599, 226633, 226655, 226699, 227711, 227755, 227777, 228833, 228877, 228899, 229933, 229955, 229999, 330011, 330055, 330077, 331111, 331133, 331199, 332233, 332255, 332299, 333111, 333311, 333377, 333777, 334499, 335533, 335555, 335599, 336611, 336655, 337711, 337733, 337777, 338833, 338855, 338899, 339911, 339955, 339977, 440077, 440099, 441133, 441155, 442211, 443311, 443377, 443399, 444333, 444455, 444499, 445511, 445555, 445577, 446611, 446633, 446677, 446699, 447733, 447755, 447799, 448811, 449911, 449933, 449977, 449999, 550033, 550055, 551111, 551155, 551177, 552211, 552233, 552277, 552299, 553333, 553355, 553399, 554411, 555511, 555533, 555577, 555777, 556633, 556699, 557711, 557777, 558811, 558833, 558877, 558899, 559955, 559999, 660011, 660055, 660077, 661111, 661177, 661199, 662233, 662255, 662299, 663311, 663355, 663377, 664433, 664477, 664499, 665533, 665555, 665599, 666611, 666655, 666677, 666777, 667711, 667733, 667777, 667799, 668833, 668855, 668899, 669911, 669955, 770011, 770077, 770099, 771133, 771155, 771199, 772277, 773377, 773399, 774400, 774433, 774455, 774499, 775511, 775577, 776611, 776633, 776677, 777733, 777799, 777999, 778811, 778855, 778877, 779911, 779933, 779999, 880055, 880099, 881111, 881155, 881177, 882211.

Some larger examples :