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evil n.  and  sliding n.

First numbers that belong to both sets:

20, 29, 65, 101, 250, 520, 650, 700, 785, 1100, 1258, 2000, 2005, 2050, 2900, 3157, 3445, 5002, 5200, 6500, 7850, 9250, 10001, 10100, 11000, 15689, 16625, 20500, 22025, 25000, 25040, 29000, 31282, 34450, 40025, 52000, 62516, 62660, 70000, 79625, 92500, 100010, 100100, 101000, 125080, 125800, 133000, 156314, 160625, 166250, 200000, 200005, 205000, 220250, 222500, 250004, 290000, 312532, 312820, 315700, 344500, 351250, 390881, 393185, 402500, 416225, 500002, 500200, 502000, 625160, 626600, 632500, 646625, 781378, 782530, 785000, 800125, 801250, 812500, 1000001, 1010000, 1250800, 1330000, 1563140, 1568900, 1600625, 1606250, 1626500, 1662500, 1953637, 1958245, 2000050, 2004325, 2005000, 2050000, 2465125, 2500000, 2504000, 2950625, 3125320, 3157000, 3906506, 3908810, 3931850, 4000025, 4002500, 4025000, 4162250, 4250000, 5000020, 5002000, 6250016, 6250160, 6266000, 6325000, 6410000, 6415625, 6500000, 7000000, 7812628, 7825300, 7850000, 7962500, 8001250, 8125000, 9092500, 9766649, 10000010, 10001000, 10789625, 12500080, 12500800, 12508000, 12580000, 13300000, 13581250, 15625064, 15625640, 15631400, 16000625, 16062500, 16265000, 19531762, 19536370, 19582450, 20000000, 20000005, 20005625, 20043250, 20050000, 20500000, 22025000, 22250000, 25000000, 25000040, 25004000, 25040000, 25990625, 29506250, 31250032, 31250320, 32003125, 32031250, 34450000, 39062756, 39088100, 39318500, 40000250, 40250000, 42500000, 49032925, 50000020, 50000200, 50002000, 52000000, 62500016, 62501600, 62516000, 63250000, 64015625, 64662500, 65000000, 70731250, 78125128, 78126280, 78137800, 79405000, 79625000, 80000125, 80001250, 80012500, 81250000, 97666490, 100000010, 100001000, 100010000, 100100000, 101000000, 112165625, 125000008, 125000080, 125000800, 125080000, 128781250, 135812500, 156250064, 156250640, 156256400, 156314000, 156890000, 160006250, 162650000, 195824500, 200000000, 200000005, 200000500, 200005000, 200056250, 200500000, 222500000, 244144721, 250000004, 250004000, 254000000, 256390625, 285100625, 290000000, 295062500, 312500320, 312532000, 320003125, 320312500, 344500000, 390625256, 390881000, 400000250, 400025000, 488283298, 488301730, 500000002, 500000200, 500002000, 500200000, 502000000, 520000000, 531531250, 625000016, 625001600, 625016000, 625160000, 626600000, 632500000, 640015625, 640156250, 641562500, 650000000, 653740625, 693081250, 700000000, 781250128, 781251280, 781378000, 785000000, 794050000, 796250000, 800000125, 800012500, 800125000, 801250000, 976563524, 977586500, 986802500, 1000000001.