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modest n.  and  plaindrome

First numbers that belong to both sets:

13, 19, 23, 26, 29, 39, 46, 49, 59, 69, 79, 89, 111, 133, 199, 222, 233, 266, 299, 333, 399, 444, 466, 499, 555, 599, 666, 699, 777, 799, 888, 899, 999, 1111, 1133, 1199, 1222, 1227, 1233, 1236, 1244, 1266, 1299, 1333, 1339, 1399, 1466, 1477, 1499, 1555, 1599, 1666, 1688, 1699, 1799, 1899, 1999, 2222, 2233, 2266, 2299, 2333, 2369, 2399, 2444, 2466, 2488, 2499, 2555, 2599, 2666, 2678, 2699, 2799, 2899, 2999, 3333, 3399, 3466, 3499, 3555, 3577, 3599, 3666, 3699, 3799, 3899, 3999, 4444, 4466, 4499, 4555, 4599, 4666, 4669, 4699, 4799, 4888, 4899, 4999, 5555, 5599, 5666, 5677, 5688, 5699, 5799, 5899, 5999, 6666, 6699, 6799, 6899, 6999, 7777, 7799, 7899, 7999, 8888, 8899, 8999, 9999, 11111, 11333, 11999, 12222, 12333, 12444, 12666, 12999, 13333, 13999, 14666, 14777, 14999, 15555, 15999, 16666, 16888, 16999, 17999, 18999, 19999, 22222, 22333, 22666, 22999, 23333, 23999, 24444, 24666, 24888, 24999, 25555, 25999, 26666, 26999, 27999, 28999, 29999, 33333, 33999, 34459, 34666, 34999, 35555, 35777, 35999, 36666, 36999, 37999, 38999, 39999, 44444, 44666, 44999, 45555, 45999, 46666, 46999, 47999, 48888, 48999, 49999, 55555, 55999, 56666, 56777, 56888, 56999, 57999, 58999, 59999, 66666, 66999, 67999, 68999, 69999, 77777, 77999, 78999, 79999, 88888, 88999, 89999, 99999, 111111, 111333, 111999, 112222, 112259, 112333, 112336, 112378, 112444, 112666, 112777, 112888, 112999, 113333, 113339, 113999, 114666, 114999, 115555, 115999, 116666, 116999, 117999, 118999, 119999, 122222, 122333, 122366, 122666, 122999, 123333, 123369, 123999, 124444, 124558, 124666, 124999, 125555, 125999, 126666, 126777, 126999, 127999, 128888, 128999, 129999, 133333, 133399, 133777, 133999, 134666, 134999, 135555, 135999, 136666, 136888, 136999, 137999, 138999, 139999, 144444, 144666, 144888, 144999, 145555, 145999, 146666, 146999, 147777, 147999, 148999, 149999, 155555, 155999.

Some larger examples :