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balanced n.  and  palprime

First numbers that belong to both sets:

2, 11, 787, 929, 10301, 10601, 11411, 12721, 13831, 15451, 16061, 35053, 35753, 38183, 3016103, 3065603, 3181813, 3193913, 3198913, 3218123, 3228223, 3233323, 3236323, 3256523, 3260623, 3286823, 3291923, 3305033, 3307033, 3321233, 3329233, 3380833, 3447443, 3460643, 3487843, 3541453, 3558553, 3607063, 3689863, 3716173, 3717173, 3728273, 3746473, 3792973, 3871783, 3916193, 3942493, 3983893, 7069607, 7256527, 7324237, 7381837, 7415147, 7434347, 7472747, 7489847, 7540457, 7690967, 7693967, 7821287, 7832387, 7873787, 7913197, 9078709, 9091909, 9095909, 9136319, 9255529, 9332339, 9357539, 9433349, 9451549, 9477749, 9492949, 9514159, 9547459, 9556559, 9604069, 9610169, 9620269, 9626269, 9657569, 9724279, 9732379, 9733379, 9770779, 9776779, 9781879, 9807089, 9817189, 9836389, 9837389, 9845489, 9852589, 9871789, 9908099, 9921299, 9931399, 9978799, 9980899, 9989899, 134858431, 134909431, 135101531, 135121531, 135161531, 135626531, 135707531, 135929531, 135959531, 136171631, 136252631, 136303631, 136363631, 137060731, 137606731, 137636731, 137696731, 138959831, 139131931, 139222931, 139282931, 139474931, 139969931, 139999931, 140868041, 141070141, 141131141, 141151141, 141343141, 141484141, 141767141, 141848141, 142030241, 142545241, 143474341, 143585341, 144020441, 144505441, 144808441, 145353541, 146222641, 146252641, 146555641, 146676641, 147313741, 148020841, 148060841, 149000941, 149696941, 150070051, 150434051, 150505051, 150818051, 151222151, 152565251, 153292351, 153323351, 153424351, 153626351, 153838351, 154030451, 154555451, 154575451, 155313551, 155333551, 155424551, 155474551, 155535551, 155666551, 155808551, 155868551, 156343651, 156545651, 156707651, 157161751, 157393751, 157444751, 158111851, 158696851, 158898851, 159565951, 159919951, 159929951, 159959951, 160101061, 160696061, 160707061, 161313161, 162686261, 162898261, 162949261, 162989261, 163333361, 163464361, 163555361, 163606361, 163878361, 164070461, 164454461, 164717461, 165212561, 165515561, 166000661, 166171661, 166404661, 166555661, 166888661, 167262761, 167454761, 168191861, 169333961, 169777961, 169797961, 170333071, 170838071, 171292171, 171565171, 172585271, 172747271, 172959271, 173030371, 174595471, 174646471, 174989471, 175444571, 175777571, 175909571, 176393671, 176646671, 176696671, 176757671, 176898671, 177161771, 177616771, 177757771, 178525871, 178656871, 178717871, 179868971, 180161081, 180545081, 181111181, 181545181, 184212481, 185393581, 187111781, 187272781, 187444781, 187909781, 188060881, 188535881, 188979881, 190080091, 190252091, 190777091, 194000491, 194232491, 194292491, 194595491, 194787491, 195707591, 196878691, 197202791, 198383891, 198707891, 199393991.