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sphenic n.  and  zygodrome

First numbers that belong to both sets:

66, 222, 555, 777, 1166, 2211, 2222, 2233, 2255, 2266, 3311, 3322, 3333, 3355, 3399, 4433, 5511, 5522, 5555, 7733, 7766, 7777, 8822, 8877, 9911, 9955, 11122, 11155, 11166, 11222, 11666, 22211, 22222, 22555, 22666, 33333, 33355, 33555, 33999, 44455, 44466, 44666, 55533, 55555, 55599, 55666, 66677, 66999, 77777, 88111, 88555, 88666, 88822, 88855, 88877, 99555, 99777, 99922, 99966, 110011, 110033, 110066, 111122, 111999, 112222, 112277, 113366, 114411, 114433, 114455, 114477, 114499, 116633, 116666, 117722, 117755, 118811, 118855, 118877, 119977, 220033, 220055, 221133, 221155, 221199, 222233, 222266, 222299, 222333, 223322, 223333, 223399, 224411, 224499, 225566, 226622, 226666, 226677, 226699, 227711, 228833, 229911, 229966, 330011, 330077, 331111, 331166, 332211, 332222, 332277, 332299, 333111, 333311, 333399, 334477, 334499, 335555, 335577, 336611, 336655, 336677, 338811, 338822, 339911, 339922, 339933, 339977, 339999, 440033, 441111, 441122, 441199, 442211, 442222, 442277, 443311, 443333, 443377, 443399, 444111, 444333, 444422, 444455, 444477, 444499, 444777, 445511, 445555, 446633, 446677, 447711, 447766, 448855, 449911, 449977, 550033, 550099, 551177, 551199, 552211, 552233, 553355, 553366, 553399, 554411, 555333, 555566, 555577, 555599, 555999, 556622, 556633, 556666, 557711, 557733, 557755, 557799, 558811, 558833, 559933, 559955, 559966, 660011, 660077, 662255, 662266, 663311, 663333, 663377, 664433, 664466, 664477, 664499, 665533, 665555, 665566, 666633, 666777, 667711, 667777, 668833, 668855, 668866, 668877, 771122, 771166, 771177, 771199, 773333, 773366, 773377, 774422, 774433, 774455, 774499, 775522, 776611, 776633, 777111, 777711, 777733, 777766, 778811, 778822, 778899, 779999, 880055, 880077, 880099, 881111, 881133, 882233, 883322, 883333, 883355, 883366, 884433, 885511, 885566, 886699, 887722, 887755, 887799, 888877, 888999, 889933, 991166, 991199, 992255, 993311, 993355, 993399, 995577, 995599, 996655, 996699, 997711, 997777, 998866, 998877, 998899, 999111, 999777, 999955, 1100077, 1100333, 1100555, 1110022, 1111133, 1111155, 1111177, 1111666, 1111999, 1112222, 1112255, 1113333, 1113355, 1114422, 1114455, 1114466.

Some larger examples :