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amenable n.  and  sliding n.

First numbers that belong to both sets:

20, 25, 29, 52, 65, 101, 133, 200, 205, 425, 520, 641, 700, 785, 925, 1001, 1100, 2000, 2005, 2225, 2500, 2504, 2540, 2900, 3157, 3445, 4025, 5020, 5200, 6325, 6500, 7000, 8125, 10001, 10100, 11000, 12508, 12580, 13300, 15689, 16265, 16625, 20000, 20005, 20500, 22025, 25000, 25004, 25040, 25400, 29000, 35125, 40025, 42500, 50020, 50200, 52000, 62516, 62660, 64100, 65000, 70000, 78253, 78500, 79405, 79625, 80125, 90925, 92500, 100001, 100100, 101000, 110000, 125008, 125080, 125800, 133000, 160625, 200000, 200005, 200500, 205000, 206125, 222500, 250000, 250004, 250040, 250400, 254000, 290000, 312532, 312820, 315700, 323125, 344500, 390881, 393185, 400025, 402500, 416225, 425000, 500020, 500200, 502000, 520000, 625016, 625160, 626600, 632500, 641000, 646625, 650000, 655625, 700000, 785000, 800125, 812500, 925000, 1000001, 1000100, 1001000, 1010000, 1100000, 1250008, 1250080, 1250800, 1258000, 1330000, 1358125, 1562564, 1563140, 1568900, 1600625, 1626500, 1662500, 1953637, 1958245, 2000000, 2000005, 2000500, 2004325, 2005000, 2050000, 2202500, 2225000, 2465125, 2500000, 2500004, 2500040, 2500400, 2504000, 2540000, 2900000, 2950625, 3125032, 3125320, 3128200, 3157000, 3203125, 3445000, 3512500, 4000025, 4002500, 4025000, 4250000, 5000020, 5000200, 5002000, 5020000, 5200000, 6250016, 6250160, 6251600, 6266000, 6325000, 6410000, 6415625, 6500000, 7000000, 7073125, 7812628, 7813780, 7825300, 7850000, 7940500, 7962500, 8000125, 8012500, 8125000, 9092500, 9250000, 9766649, 9775865, 9868025, 10000001, 10000100, 10001000, 10010000, 10100000, 10789625, 11000000, 12500008, 12500080, 12500800, 12508000, 12580000, 12878125, 13300000, 15625064, 15625640, 15631400, 15689000, 16000625, 16062500, 16265000, 16625000, 20000000, 20000005, 20000500, 20005000, 20005625, 20050000, 20500000, 20612500, 22025000, 22250000, 25000000, 25000004, 25000040, 25000400, 25004000, 25040000, 25400000, 25990625, 29000000, 31250032, 31250320, 31253200, 31282000, 31570000, 32003125, 32312500, 34450000, 35125000, 39062756, 39065060, 39088100, 39318500, 40000025, 40002500, 40025000, 40250000, 41622500, 42500000, 48830173, 48848605, 49032925, 50000020, 50000200, 50002000, 50020000, 50200000, 50876125, 52000000, 53153125, 62500016, 62500160, 62501600, 62516000, 62660000, 63250000, 64015625, 64100000, 64662500, 65000000, 65562500, 69308125, 70000000, 78125128, 78126280.

Some larger examples :