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a-pointer prime  and  happy n.

First numbers that belong to both sets:

13, 103, 293, 1933, 2039, 3391, 3643, 5281, 6053, 10151, 14087, 14207, 15121, 15473, 19141, 20369, 22921, 24181, 30713, 31547, 33013, 33091, 33301, 33413, 36607, 41117, 41131, 41911, 44071, 50111, 60703, 63443, 64303, 74531, 80963, 82051, 89533, 90203, 100333, 102481, 105541, 106993, 110051, 110251, 113041, 114031, 114143, 115201, 115223, 117223, 123127, 128629, 133403, 133999, 140207, 140281, 141107, 156749, 160603, 162229, 165479, 171007, 181639, 184133, 185189, 185491, 197713, 200257, 205081, 210283, 210407, 211051, 216289, 218401, 227131, 230663, 230779, 232171, 240743, 246251, 262981, 265021, 270379, 274403, 279451, 280561, 302609, 307451, 308003, 311137, 316271, 316819, 326063, 330413, 354587, 360007, 360197, 360869, 363989, 368911, 379931, 382021, 384113, 394291, 401311, 401551, 403063, 405829, 409397, 409441, 410461, 411031, 411143, 414061, 426611, 434267, 447331, 459181, 464561, 465041, 472643, 474263, 477637, 480071, 482101, 491923, 501121, 502261, 502861, 505033, 511201, 511223, 512011, 513137, 515153, 522113, 547301, 582601, 593083, 593539, 600433, 604411, 621317, 622051, 634421, 636023, 638269, 644411, 650359, 660013, 660103, 666901, 693701, 701033, 701453, 703499, 705787, 707011, 709561, 709703, 712631, 715579, 717719, 718813, 735311, 752149, 772921, 780401, 784249, 786553, 792073, 793399, 806521, 806581, 808651, 809603, 810223, 815291, 817183, 818249, 820051, 820411, 822233, 830003, 833509, 838483, 846529, 849427, 856021, 884617, 886819, 887113, 891251, 892481, 907073, 913771, 914293, 916073, 918613, 922261, 929431, 934079, 939061, 949213, 955063, 957773, 961703, 964049, 973919, 985181, 993137, 1000151, 1004461, 1006007, 1009303, 1009963, 1010501, 1012637, 1026229, 1033517, 1036271, 1039111, 1042399, 1049101, 1067509, 1067851, 1073881, 1081859, 1084313, 1087561, 1090493, 1102523, 1104833, 1108369, 1111741, 1114733, 1129861, 1131307, 1140143, 1143371, 1144417, 1153367, 1157033, 1158089, 1160839, 1164899, 1180549, 1195387, 1198261, 1213607, 1217269, 1220803, 1224133, 1231733, 1235669, 1241893, 1257409, 1266197, 1277267, 1282241, 1286119, 1303517, 1304929, 1307261, 1311383, 1311901, 1322341, 1327201, 1330157, 1333811, 1334371, 1340011, 1341713, 1359529, 1371031, 1373321, 1373501, 1386901, 1390003, 1391941.

Some larger examples :