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happy n.  and  zygodrome

First numbers that belong to both sets:

44, 888, 1122, 1177, 1188, 2211, 3355, 4400, 4455, 4477, 5533, 5544, 5555, 7711, 7744, 7788, 8811, 8877, 22244, 44000, 44222, 44488, 55588, 55999, 66688, 66777, 77766, 88444, 88555, 88666, 88800, 88888, 99955, 110022, 110077, 110088, 112200, 112233, 112266, 113322, 113355, 115533, 116622, 116699, 117700, 117799, 118800, 119966, 119977, 119999, 220011, 221100, 221133, 221166, 223311, 223333, 223399, 225566, 226611, 226655, 226688, 228866, 229933, 330055, 331122, 331155, 332211, 332233, 332299, 333322, 333344, 333355, 333888, 334433, 334444, 334455, 335500, 335511, 335533, 335544, 335599, 336677, 337766, 339922, 339955, 440000, 440055, 440077, 443333, 443344, 443355, 444433, 444488, 444499, 444999, 445500, 445533, 446666, 447700, 448844, 449944, 449999, 550033, 550044, 550055, 551133, 552266, 553300, 553311, 553333, 553344, 553399, 554400, 554433, 555500, 555599, 556622, 557799, 559933, 559955, 559977, 661122, 661199, 662211, 662255, 662288, 663377, 664466, 665522, 666644, 667733, 668822, 668899, 669911, 669988, 770011, 770044, 770088, 771100, 771199, 773366, 774400, 775599, 776633, 778800, 779911, 779955, 880011, 880077, 881100, 882266, 884444, 886622, 886699, 887700, 888000, 888333, 889966, 991166, 991177, 991199, 992233, 993322, 993355, 994444, 994499, 995533, 995555, 995577, 996611, 996688, 997711, 997755, 998866, 999444, 999911, 999944, 1100022, 1100077, 1100088, 1111111, 1111122, 1111133, 1111177, 1111188, 1111199, 1111333, 1111555, 1112211, 1112222, 1112277, 1112288, 1113311, 1114477, 1115555, 1116688, 1117711, 1117722, 1117744, 1117799, 1118811, 1118822, 1118866, 1118899, 1119911, 1119977, 1119988, 1122000, 1122111, 1122233, 1122266, 1122299, 1133111, 1133222, 1133311, 1133355, 1133444, 1133777, 1133999, 1144433, 1144444, 1144455, 1144555, 1144888, 1155333, 1155444, 1155511, 1155544, 1155599, 1166222, 1166677, 1177000, 1177111, 1177666, 1177733, 1188000, 1188111, 1188844, 1188899, 1199111, 1199222, 1199555, 1199888, 1199933, 2200011, 2211000, 2211111, 2211122, 2211177, 2211188, 2220044, 2221133, 2221166, 2221199, 2222111, 2222222, 2222255, 2222555, 2222888, 2223311, 2223399, 2224400, 2224455, 2225522, 2225544, 2225588, 2226611, 2227777, 2228855, 2228899, 2229911, 2229933, 2229988, 2233377, 2255222, 2255522, 2255555, 2255999, 2266666, 2277111.

Some larger examples :