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interprime n.  and  zygodrome

First numbers that belong to both sets:

99, 111, 1100, 2277, 3300, 3366, 3399, 4422, 4444, 4488, 5544, 5566, 5577, 7755, 8844, 8855, 8877, 11166, 22000, 22211, 22444, 33555, 44433, 44499, 55544, 66699, 66777, 77799, 88800, 99555, 99777, 99966, 110055, 110066, 111222, 112244, 115566, 115599, 116688, 118800, 118899, 119922, 119988, 220011, 221199, 222111, 222333, 222555, 222999, 224455, 226666, 227766, 228844, 229900, 229944, 229955, 330044, 331144, 331177, 333311, 333444, 334422, 335533, 336622, 336677, 337755, 339999, 440000, 441111, 442233, 442277, 443344, 443366, 444000, 444111, 444455, 444466, 444555, 445522, 446600, 449900, 449955, 449988, 550055, 551188, 552277, 553366, 554400, 555522, 555666, 556611, 556633, 558866, 660000, 661188, 665566, 666622, 666677, 770033, 770044, 770055, 771100, 772288, 774433, 776688, 777333, 777444, 777666, 779933, 779955, 779988, 882244, 884499, 885500, 888999, 889944, 990000, 993399, 994455, 995522, 995544, 996600, 997733, 997788, 999444, 1100033, 1117766, 1118844, 1122266, 1144555, 1155777, 1166600, 1166999, 1177766, 1188000, 1188111, 1188555, 1199444, 2200022, 2200055, 2211144, 2211222, 2220066, 2221144, 2222211, 2222277, 2222555, 2223300, 2223377, 2223399, 2224444, 2226633, 2226666, 2227733, 2227755, 2233355, 2244111, 2244433, 2255577, 2266688, 2277000, 2288855, 2299777, 2299944, 3300066, 3311155, 3311555, 3322777, 3330033, 3331188, 3333111, 3333322, 3333399, 3333666, 3335577, 3337722, 3338855, 3339999, 3355666, 3366600, 3366633, 3366666, 3366888, 3388833, 3399900, 3399966, 4400022, 4400055, 4411666, 4422244, 4422255, 4422288, 4433000, 4441122, 4442211, 4442222, 4443300, 4444477, 4444666, 4447755, 4449900, 4455222, 4455999, 4466111, 4466333, 4499988, 5500044, 5500555, 5511144, 5522211, 5522277, 5522333, 5533444, 5544222, 5544411, 5550044, 5550066, 5557755, 5559933, 5566000, 5566666, 5588777, 5599955, 5599977, 6600444, 6611111, 6611444, 6633322, 6644422, 6677799, 6688800, 6688822, 6699900, 6699944, 6699955, 7700099, 7711133, 7711999, 7744433, 7744488, 7755566, 7770099, 7771188, 7773366, 7788333, 7788855, 7788877, 7799888, 8800099, 8811333, 8844411, 8855000, 8855566, 8866888, 8877700, 8877777, 8883355, 8884400, 8885588, 8886600, 8886633, 8888844, 8899444, 8899888, 9911199, 9944455, 9944466, 9944477, 9955444, 9966611, 9966655, 9977755, 9991155, 9996688, 9997700, 9998877, 11000055, 11000666, 11000777, 11003344.

Some larger examples :