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amenable n.  and  modest n.

First numbers that belong to both sets:

13, 29, 49, 69, 89, 109, 133, 209, 233, 309, 333, 409, 412, 433, 436, 444, 509, 533, 545, 609, 633, 709, 721, 733, 777, 809, 812, 824, 833, 836, 844, 872, 888, 933, 981, 1009, 1033, 1037, 1045, 1133, 1233, 1236, 1244, 1333, 1421, 1433, 1477, 1533, 1545, 1624, 1633, 1636, 1644, 1648, 1672, 1688, 1733, 1833, 1881, 1933, 1957, 2009, 2033, 2036, 2037, 2044, 2045, 2060, 2133, 2177, 2233, 2333, 2369, 2433, 2436, 2444, 2472, 2488, 2533, 2545, 2633, 2733, 2781, 2833, 2836, 2844, 2877, 2884, 2933, 3009, 3033, 3037, 3045, 3081, 3133, 3193, 3233, 3236, 3244, 3248, 3272, 3288, 3296, 3333, 3545, 3577, 3644, 3681, 3857, 4009, 4012, 4036, 4037, 4044, 4045, 4060, 4072, 4088, 4108, 4148, 4277, 4333, 4444, 4581, 4669, 4872, 4888, 4977, 5009, 5037, 5045, 5185, 5333, 5481, 5672, 5677, 5684, 5688, 6009, 6037, 6081, 6293, 6333, 6377, 6381, 6472, 6488, 6496, 7009, 7021, 7037, 7077, 7189, 7281, 7288, 7333, 7777, 8009, 8012, 8024, 8036, 8037, 8072, 8088, 8108, 8148, 8216, 8296, 8333, 8444, 8888, 9037, 9081, 9333, 10009, 10033, 10037, 10045, 10101, 10185, 10333, 10909, 11033, 11037, 11297, 11333, 12036, 12037, 12081, 12108, 12148, 12324, 12333, 12444, 13037, 13117, 13333, 13481, 14021, 14037, 14189, 14333, 14777, 15037, 15045, 15081, 15185, 15333, 15405, 16024, 16036, 16037, 16048, 16072, 16108, 16144, 16148, 16216, 16296, 16333, 16432, 16444, 16592, 16888, 17037, 17153, 17333, 17629, 18037, 18081, 18333, 19037, 19057, 19333, 19513, 20009, 20033, 20036, 20037, 20045, 20060, 20101, 20108, 20148, 20180, 20185, 20333, 20444, 20540, 20740, 20909, 21037, 21081, 21189, 21333, 21777, 22033, 22037, 22297, 22333, 23037, 23069, 23333, 23621, 24036, 24037, 24072, 24081, 24108, 24148, 24216, 24296, 24324, 24333, 24444, 24648, 24888, 25037, 25045, 25185.

Some larger examples :