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alternating n.  and  palprime

First numbers that belong to both sets:

2, 3, 5, 7, 101, 181, 383, 727, 787, 929, 10301, 10501, 12721, 14341, 14741, 16361, 16561, 18181, 30103, 30703, 32323, 34543, 36563, 38183, 38783, 70507, 72727, 74747, 76367, 78787, 90709, 94349, 94949, 96769, 98389, 1074701, 1092901, 1212121, 1218121, 1250521, 1276721, 1278721, 1412141, 1452541, 1456541, 1490941, 1496941, 1616161, 1630361, 1654561, 1658561, 1670761, 1832381, 1856581, 1876781, 1878781, 3016103, 3072703, 3212123, 3218123, 3236323, 3252523, 3256523, 3258523, 3272723, 3452543, 3470743, 3618163, 3670763, 3698963, 3812183, 3814183, 3836383, 3858583, 3878783, 7014107, 7036307, 7096907, 7250527, 7256527, 7276727, 7278727, 7434347, 7436347, 7452547, 7472747, 7630367, 7632367, 7654567, 7674767, 7690967, 7696967, 7832387, 7838387, 7850587, 7856587, 9076709, 9078709, 9212129, 9230329, 9414149, 9470749, 9492949, 9610169, 9632369, 9634369, 9650569, 9670769, 9818189, 9836389, 9852589, 9896989, 101030101, 101292101, 101414101, 101474101, 101616101, 101838101, 101898101, 103212301, 103696301, 103818301, 105272501, 105616501, 105656501, 105818501, 107070701, 107232701, 107414701, 107636701, 107858701, 109434901, 109474901, 109656901, 109818901, 121272121, 121414121, 121818121, 121878121, 123292321, 123494321, 123838321, 125010521, 125232521, 125252521, 125292521, 125474521, 125616521, 125838521, 127090721, 127212721, 127494721, 127636721, 127656721, 129292921, 129494921, 141070141, 141494141, 141616141, 143090341, 143454341, 143474341, 143636341, 145030541, 145090541, 145494541, 147232741, 147434741, 147616741, 147838741, 149616941, 149696941, 149858941, 161474161, 161636161, 161838161, 163434361, 163474361, 163494361, 163696361, 163878361, 165212561, 165878561, 165898561, 167454761, 167474761, 167636761, 167898761, 169656961, 169858961, 183232381, 183656381, 183898381, 185232581, 185676581, 185838581, 185858581, 187090781, 187272781, 187434781, 189292981, 189838981, 189898981, 301050103, 301434103, 301494103, 301818103, 303050303, 303272303, 303292303, 303616303, 303878303, 305090503, 305454503, 305474503, 307050703, 307696703, 309010903, 309070903, 309272903, 309434903, 309656903, 309818903, 309878903, 321898123, 323070323, 323090323, 323232323, 323414323, 323676323, 323696323, 325090523, 325212523, 325272523, 325636523, 327050723, 327272723, 327292723, 327656723, 327898723, 329414923, 329474923, 329858923, 341010143, 341292143, 341898143, 343050343, 343090343, 343272343, 343696343, 343858343, 343878343, 345232543, 345292543, 345494543, 345656543, 345676543, 345898543, 347010743, 347090743, 347252743, 347454743, 347616743, 347676743, 347898743, 349050943, 349818943, 349878943, 363010363, 363272363, 363434363, 363676363, 363818363, 363878363, 365292563, 365898563, 369070963, 369454963, 381232183, 381818183.

Some larger examples :