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a-pointer prime  and  modest n.

First numbers that belong to both sets:

13, 103, 811, 1933, 2633, 5333, 7333, 50111, 56999, 100333, 130099, 133999, 170101, 200033, 240101, 550909, 600101, 1100123, 1100303, 1120303, 1300813, 1741111, 1783333, 1831111, 1891111, 2200369, 2603333, 3901111, 4223333, 5071111, 5293333, 5470909, 6241111, 6400123, 6421111, 7343333, 7500271, 8131111, 8533333, 8602439, 10141111, 14273333, 16900813, 19403333, 24000259, 25010989, 26000033, 27253333, 29000333, 32010101, 35809999, 37000231, 40000231, 41002849, 41012987, 46000231, 46000819, 46400813, 50000429, 51001001, 53202439, 54419999, 55000091, 55711111, 57400813, 57739999, 59001001, 61010101, 68004329, 70000717, 70879999, 71600813, 73001221, 75889999, 78833333, 86001001, 86533333, 89030303, 91402439, 101001443, 101002439, 102005291, 109000819, 112002439, 116202439, 120211111, 125003003, 125003861, 125311111, 129733333, 135233333, 137000407, 139010101, 139302439, 155011111, 161202439, 164000407, 170001287, 178733333, 183911111, 190333333, 197302439, 198511111, 200456621, 202004329, 204911111, 207000407, 211000819, 219511111, 222001001, 241411111, 241633333, 249000481, 262001221, 271002079, 275311111, 290000407, 293933333, 302011111, 304411111, 304633333, 306811111, 308611111, 310002079, 316025641, 325003663, 326000777, 330911111, 331633333, 337000351, 337000429, 337002331, 340006993, 340012987, 348005291, 355033333, 358001221, 359411111, 361000693, 367111111, 369511111, 380002151, 382090909, 397030303, 400025641, 400030003, 403010989, 404333333, 408133333, 410004649, 421433333, 425033333, 428009009, 432005291, 450811111, 458010101, 460004329, 463000481, 466000693, 475511111, 483433333, 485010101, 496012987, 509003003, 512008547, 532015873, 535411111, 557010101, 564611111, 574001443, 581001221, 584010101, 584090909, 585511111, 589008547, 605000999, 610142857, 630005291, 640711111, 653001001, 653037037, 656411111, 677001001, 691000693, 694411111, 701002457, 703003003, 703511111, 709111111, 710003003, 718001287, 731010989, 742211111, 744011111, 788006993, 791833333, 795002849, 808003663, 810002849, 811003663, 811025641, 842037037, 844009009, 844933333, 849002849, 850076923, 861611111, 865010101, 865411111, 866111111, 869411111, 878011111, 886399999, 887411111, 901001221, 901009009, 913006993, 915433333, 919006993, 928411111, 952001287, 952015873, 960833333, 961003663, 970511111, 982811111, 993002849, 1003133333, 1007003663, 1010111111, 1038037037, 1041911111, 1049001221, 1072111111, 1074311111, 1080811111, 1081002079, 1081004329, 1105006993, 1108111111, 1118006993, 1123010101, 1127033333, 1135025641, 1138633333, 1158005291, 1168002079, 1192010101, 1222006993, 1238009009, 1249111111, 1257003367, 1264010989, 1275499999, 1297076923, 1300000073, 1314005291, 1321010101, 1321076923, 1322027027, 1334005291, 1343076923, 1349030303, 1351015873, 1354047619, 1360002079, 1397933333, 1400022119, 1412001443, 1420010989, 1423003663, 1423333333, 1427003003, 1436003861, 1463533333, 1472009009, 1487003003, 1510010101, 1512005291, 1513025641.

Some larger examples :